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In computer science, functional programming is a programming paradigm, a style of building the structure and elements of computer programs, that treats computation as the evaluation of mathematical functions and avoids state and mutable data. Functional programming emphasizes functions that produce results that depend only on their inputs and not on the program state—i.e. pure mathematical functions. It is a declarative programming paradigm, which means programming is done with expressions. In functional code, the output value of a function depends only on the arguments that are input to the function, so calling a function f twice with the same value for an argument x will produce the same result f(x) both times. Eliminating side effects, i.e. changes in state that do not depend on the function inputs, can make it much easier to understand and predict the behavior of a program, which is one of the key motivations for the development of functional programming.

Functional programming has its roots in lambda calculus, a formal system developed in the 1930s to investigate computability, the Entscheidungsproblem, function definition, function application, and recursion. Many functional programming languages can be viewed as elaborations on the lambda calculus, where computation is treated as the evaluation of mathematical functions and avoids state and mutable data. In the other well known declarative programming paradigm, logic programming, relations are at the base of respective languages.^[1]

In contrast, imperative programming changes state with commands in the source language, the most simple example is the assignment. Functions do exist, not in the mathematical sense, but the sense of subroutine. They can have side effects that may change the value of program state. Functions without return value therefore make sense. Because of this, they lack referential transparency, i.e. the same language expression can result in different values at different times depending on the state of the executing program.^[1]

Functional programming languages, especially purely functional ones such as Hope and Rex, have largely been emphasized in academia rather than in commercial software development. However, prominent functional programming languages such as Common Lisp, Scheme,^[2]^[3]^[4]^[5] Clojure, Racket,^[6] Erlang,^[7]^[8]^[9] OCaml,^[10]^[11] Haskell,^[12]^[13] Scala^[14] and F#^[15]^[16] have been used in industrial and commercial applications by a wide variety of organizations. Functional programming is also supported in some domain-specific programming languages like R (statistics),^[17]^[18] Mathematica (symbolic and numeric math),^[19] J, K and Q from Kx Systems (financial analysis), XQuery/XSLT (XML),^[20]^[21] and Opal.^[22] Widespread domain-specific declarative languages like SQL and Lex/Yacc use some elements of functional programming, especially in eschewing mutable values.^[23]

Programming in a functional style can also be accomplished in languages that aren't specifically designed for functional programming. For example, the imperative Perl programming language has been the subject of a book describing how to apply functional programming concepts.^[24] C# 3.0 and Java 8 added constructs to facilitate the functional style.

History

Lambda calculus provides a theoretical framework for describing functions and their evaluation. Although it is a mathematical abstraction rather than a programming language, it forms the basis of almost all functional programming languages today. An equivalent theoretical formulation, combinatory logic, is commonly perceived as more abstract than lambda calculus and preceded it in invention. Combinatory logic and lambda calculus were both originally developed to achieve a clearer approach to the foundations of mathematics.^[25]

An early functional-flavored language was Lisp, developed by John McCarthy while at Massachusetts Institute of Technology (MIT) for the IBM 700/7000 series scientific computers in the late 1950s.^[26] Lisp introduced many features now found in functional languages, though Lisp is technically a multi-paradigm language. Scheme and Dylan were later attempts to simplify and improve Lisp.

Information Processing Language (IPL) is sometimes cited as the first computer-based functional programming language.^[27] It is an assembly-style language for manipulating lists of symbols. It does have a notion of "generator", which amounts to a function accepting a function as an argument, and, since it is an assembly-level language, code can be used as data, so IPL can be regarded as having higher-order functions. However, it relies heavily on mutating list structure and similar imperative features.

Kenneth E. Iverson developed APL in the early 1960s, described in his 1962 book A Programming Language (ISBN 9780471430148). APL was the primary influence on John Backus's FP. In the early 1990s, Iverson and Roger Hui created J. In the mid-1990s, Arthur Whitney, who had previously worked with Iverson, created K, which is used commercially in financial industries along with its descendant Q.

John Backus presented FP in his 1977 Turing Award lecture "Can Programming Be Liberated From the von Neumann Style? A Functional Style and its Algebra of Programs".^[28] He defines functional programs as being built up in a hierarchical way by means of "combining forms" that allow an "algebra of programs"; in modern language, this means that functional programs follow the principle of compositionality. Backus's paper popularized research into functional programming, though it emphasized function-level programming rather than the lambda-calculus style which has come to be associated with functional programming.

In the 1970s, ML was created by Robin Milner at the University of Edinburgh, and David Turner developed initially the language SASL at the University of St. Andrews and later the language Miranda at the University of Kent. ML eventually developed into several dialects, the most common of which are now OCaml and Standard ML. Also in the 1970s, the development of Scheme (a partly functional dialect of Lisp), as described in the influential Lambda Papers and the 1985 textbook Structure and Interpretation of Computer Programs, brought awareness of the power of functional programming to the wider programming-languages community.

In the 1980s, Per Martin-Löf developed intuitionistic type theory (also called constructive type theory), which associated functional programs with constructive proofs of arbitrarily complex mathematical propositions expressed as dependent types. This led to powerful new approaches to interactive theorem proving and has influenced the development of many subsequent functional programming languages.

The Haskell language began with a consensus in 1987 to form an open standard for functional programming research; implementation releases have been ongoing since 1990.

Concepts

A number of concepts and paradigms are specific to functional programming, and generally foreign to imperative programming (including object-oriented programming). However, programming languages are often hybrids of several programming paradigms, so programmers using "mostly imperative" languages may have utilized some of these concepts.^[29]

First-class and higher-order functions

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Higher-order functions are functions that can either take other functions as arguments or return them as results. In calculus, an example of a higher-order function is the differential operator $d/dx$ , which returns the derivative of a function $f$ .

Higher-order functions are closely related to first-class functions in that higher-order functions and first-class functions both allow functions as arguments and results of other functions. The distinction between the two is subtle: "higher-order" describes a mathematical concept of functions that operate on other functions, while "first-class" is a computer science term that describes programming language entities that have no restriction on their use (thus first-class functions can appear anywhere in the program that other first-class entities like numbers can, including as arguments to other functions and as their return values).

Higher-order functions enable partial application or currying, a technique in which a function is applied to its arguments one at a time, with each application returning a new function that accepts the next argument. This allows one to succinctly express, for example, the successor function as the addition operator partially applied to the natural number one.

Pure functions

Purely functional functions (or expressions) have no side effects (memory or I/O). This means that pure functions have several useful properties, many of which can be used to optimize the code:

If the result of a pure expression is not used, it can be removed without affecting other expressions.
If a pure function is called with parameters that cause no side-effects, the result is constant with respect to that parameter list (sometimes called referential transparency), i.e. if the pure function is again called with the same parameters, the same result will be returned (this can enable caching optimizations such as memoization).
If there is no data dependency between two pure expressions, then their order can be reversed, or they can be performed in parallel and they cannot interfere with one another (in other terms, the evaluation of any pure expression is thread-safe).
If the entire language does not allow side-effects, then any evaluation strategy can be used; this gives the compiler freedom to reorder or combine the evaluation of expressions in a program (for example, using deforestation).

While most compilers for imperative programming languages detect pure functions and perform common-subexpression elimination for pure function calls, they cannot always do this for pre-compiled libraries, which generally do not expose this information, thus preventing optimizations that involve those external functions. Some compilers, such as gcc, add extra keywords for a programmer to explicitly mark external functions as pure, to enable such optimizations. Fortran 95 also allows functions to be designated "pure".

Recursion

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Iteration (looping) in functional languages is usually accomplished via recursion. Recursive functions invoke themselves, allowing an operation to be performed over and over until the base case is reached. Though some recursion requires maintaining a stack, tail recursion can be recognized and optimized by a compiler into the same code used to implement iteration in imperative languages. The Scheme language standard requires implementations to recognize and optimize tail recursion. Tail recursion optimization can be implemented by transforming the program into continuation passing style during compiling, among other approaches.

Common patterns of recursion can be factored out using higher order functions, with catamorphisms and anamorphisms (or "folds" and "unfolds") being the most obvious examples. Such higher order functions play a role analogous to built-in control structures such as loops in imperative languages.

Most general purpose functional programming languages allow unrestricted recursion and are Turing complete, which makes the halting problem undecidable, can cause unsoundness of equational reasoning, and generally requires the introduction of inconsistency into the logic expressed by the language's type system. Some special purpose languages such as Coq allow only well-founded recursion and are strongly normalizing (nonterminating computations can be expressed only with infinite streams of values called codata). As a consequence, these languages fail to be Turing complete and expressing certain functions in them is impossible, but they can still express a wide class of interesting computations while avoiding the problems introduced by unrestricted recursion. Functional programming limited to well-founded recursion with a few other constraints is called total functional programming. See Turner 2004 for more discussion.^[30]

Strict versus non-strict evaluation

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Functional languages can be categorized by whether they use strict (eager) or non-strict (lazy) evaluation, concepts that refer to how function arguments are processed when an expression is being evaluated. The technical difference is in the denotational semantics of expressions containing failing or divergent computations. Under strict evaluation, the evaluation of any term containing a failing subterm will itself fail. For example, the expression:

print length([2+1, 3*2, 1/0, 5-4])

will fail under strict evaluation because of the division by zero in the third element of the list. Under lazy evaluation, the length function will return the value 4 (i.e., the number of items in the list), since evaluating it will not attempt to evaluate the terms making up the list. In brief, strict evaluation always fully evaluates function arguments before invoking the function. Lazy evaluation does not evaluate function arguments unless their values are required to evaluate the function call itself.

The usual implementation strategy for lazy evaluation in functional languages is graph reduction.^[31] Lazy evaluation is used by default in several pure functional languages, including Miranda, Clean, and Haskell.

Template:Harvnb argues for lazy evaluation as a mechanism for improving program modularity through separation of concerns, by easing independent implementation of producers and consumers of data streams.^[32] Launchbury 1993 describes some difficulties that lazy evaluation introduces, particularly in analyzing a program's storage requirements, and proposes an operational semantics to aid in such analysis.^[33] Harper 2009 proposes including both strict and lazy evaluation in the same language, using the language's type system to distinguish them.^[34]

Type systems

Especially since the development of Hindley–Milner type inference in the 1970s, functional programming languages have tended to use typed lambda calculus, as opposed to the untyped lambda calculus used in Lisp and its variants (such as Scheme). The use of algebraic datatypes and pattern matching makes manipulation of complex data structures convenient and expressive; the presence of strong compile-time type checking makes programs more reliable, while type inference frees the programmer from the need to manually declare types to the compiler.

Some research-oriented functional languages such as Coq, Agda, Cayenne, and Epigram are based on intuitionistic type theory, which allows types to depend on terms. Such types are called dependent types. These type systems do not have decidable type inference and are difficult to understand and program withPotter or Ceramic Artist Truman Bedell from Rexton, has interests which include ceramics, best property developers in singapore developers in singapore and scrabble. Was especially enthused after visiting Alejandro de Humboldt National Park.. But dependent types can express arbitrary propositions in predicate logic. Through the Curry–Howard isomorphism, then, well-typed programs in these languages become a means of writing formal mathematical proofs from which a compiler can generate certified code. While these languages are mainly of interest in academic research (including in formalized mathematics), they have begun to be used in engineering as well. Compcert is a compiler for a subset of the C programming language that is written in Coq and formally verified.^[35]

A limited form of dependent types called generalized algebraic data types (GADT's) can be implemented in a way that provides some of the benefits of dependently typed programming while avoiding most of its inconvenience.^[36] GADT's are available in the Glasgow Haskell Compiler, in OCaml (since version 4.00) and in Scala (as "case classes"), and have been proposed as additions to other languages including Java and C#.^[37]

Functional programming in non-functional languages

It is possible to use a functional style of programming in languages that are not traditionally considered functional languages.^[38] For example, both D and Fortran 95 explicitly support pure functions.^[39]

First-class functions have slowly been added to mainstream languages. For example, in early 1994, support for lambda, filter, map, and reduce was added to Python. Then during the development of Python 3000, Guido van Rossum called for the removal of these features.^[40] However, he later changed his mind, and only reduce was removed,^[41] though it remains accessible via the functools standard library module.^[42] First-class functions were also introduced in PHP 5.3, Visual Basic 9, C# 3.0, and C++11.

In Java, anonymous classes can sometimes be used to simulate closures;^[43] however, anonymous classes are not always proper replacements to closures because they have more limited capabilities.^[44] Java 8, scheduled for release in 2014,^[45] will support lambda expressions as a replacement for some anonymous classes.^[46] However, the presence of checked exceptions in Java can make functional programming inconvenient, because it can be necessary to catch checked exceptions and then rethrow them—a problem that does not occur in other JVM languages that do not have checked exceptions, such as Scala.

Many object-oriented design patterns are expressible in functional programming terms: for example, the strategy pattern simply dictates use of a higher-order function, and the visitor pattern roughly corresponds to a catamorphism, or fold.

Similarly, the idea of immutable data from functional programming is often included in imperative programming languages,^[47] for example the tuple in Python, which is an immutable array.

Comparison to imperative programming

Functional programming is very different from imperative programming. The most significant differences stem from the fact that functional programming avoids side effects, which are used in imperative programming to implement state and I/O. Pure functional programming completely prevents side-effects and provides referential transparency, which makes it easier to verify, optimize, and parallelize programs, and easier to write automated tools to perform those tasks.

Higher-order functions are rarely used in older imperative programming. Where a traditional imperative program might use a loop to traverse a list, a functional program would use a different technique. It would use a higher-order function that takes as arguments a function and a list. The higher-order function would then apply the given function to each element of the given list and then return a new list with the results.

Simulating state

There are tasks (for example, maintaining a bank account balance) that often seem most naturally implemented with state. Pure functional programming performs these tasks, and I/O tasks such as accepting user input and printing to the screen, in a different way.

The pure functional programming language Haskell implements them using monads, derived from category theory. Monads offer a way to abstract certain types of computational patterns, including (but not limited to) modeling of computations with mutable state (and other side effects such as I/O) in an imperative manner without losing purity. While existing monads may be easy to apply in a program, given appropriate templates and examples, many students find them difficult to understand conceptually, e.g., when asked to define new monads (which is sometimes needed for certain types of libraries).^[48]

Another way in which functional languages can simulate state is by passing around a data structure that represents the current state as a parameter to function calls. On each function call, a copy of this data structure is created with whatever differences are the result of the function. This is referred to as 'state-passing style'.

Impure functional languages usually include a more direct method of managing mutable state. Clojure, for example, uses managed references that can be updated by applying pure functions to the current state. This kind of approach enables mutability while still promoting the use of pure functions as the preferred way to express computations.

Alternative methods such as Hoare logic and uniqueness have been developed to track side effects in programs. Some modern research languages use effect systems to make explicit the presence of side effects.

Efficiency issues

Functional programming languages are typically less efficient in their use of CPU and memory than imperative languages such as C and Pascal.^[49] This is related to the fact that some mutable data structures like arrays have a very straightforward implementation using present hardware (which is a highly evolved Turing machine). Flat arrays may be accessed very efficiently with deeply pipelined CPUs, prefetched efficiently through caches (with no complex pointer-chasing), or handled with SIMD instructions. And it is not easy to create their equally efficient general-purpose immutable counterparts. For purely functional languages, the worst-case slowdown is logarithmic in the number of memory cells used, because mutable memory can be represented by a purely functional data structure with logarithmic access time (such as a balanced tree).^[50] However, such slowdowns are not universal. For programs that perform intensive numerical computations, functional languages such as OCaml and Clean are only slightly slower than C.^[51] For programs that handle large matrices and multidimensional databases, array functional languages (such as J and K) were designed with speed optimization.

Immutability of data can in many cases lead to execution efficiency by allowing the compiler to make assumptions that are unsafe in an imperative language, thus increasing opportunities for inline expansion.^[52]

Lazy evaluation may also speed up the program, even asymptotically, whereas it may slow it down at most by a constant factor (however, it may introduce memory leaks if used improperly). Launchbury 1993^[33] discusses theoretical issues related to memory leaks from lazy evaluation, and O'Sullivan et al. 2008^[53] give some practical advice for analyzing and fixing them. However, the most general implementations of lazy evaluation making extensive use of dereferenced code and data perform poorly on modern processors with deep pipelines and multi-level caches (where a cache miss may cost hundreds of cycles)

Coding styles

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# Fibonacci numbers, imperative style
# http://docs.python.org/2.7/tutorial/modules.html
def fibonacci():
  first, second = 0, 1  # initial seed values
  while True:  # Perform infinite iterations
    first, second = second, first + second # Assign all the new values.
    yield first  # Return current iterate

for n, x in enumerate(fibonacci()):
  if n == 10: break  # print first 10 fibonacci elements
  print x

Haskell

A functional version (in Haskell) has a different feel to it:

-- Fibonacci numbers, functional style

-- describe an infinite list based on the recurrence relation for Fibonacci numbers
fibRecurrence first second = first : fibRecurrence second (first + second)

-- describe fibonacci list as fibRecurrence with initial values 0 and 1
fibonacci = fibRecurrence 0 1

-- describe action to print the 10th element of the fibonacci list
main = print (fibonacci !! 10)

Or, more concisely:

fibonacci2 = 0:1:zipwith (+) fibonacci2 (tail fibonacci2)

The imperative style describes the intermediate steps involved in calculating fibonacci(N), and places those steps inside a loop statement. In contrast, the functional implementation shown here states the mathematical recurrence relation that defines the entire Fibonacci sequence, then selects an element from the sequence (see also recursion). This example relies on Haskell's lazy evaluation to create an "infinite" list of which only as much as needed (the first 10 elements in this case) will actually be computed. That computation happens when the runtime system carries out the action described by "main".

Erlang

The same program in Erlang provides a simple example of how functional languages in general do not require their syntax to contain an "if" statement.

-module(fibonacci).
-export([start/1]).

%% Fibonacci numbers in Erlang
start(N) -> do_fib(0,1,N).

do_fib(_,B,1) -> B;
do_fib(A,B,N) -> do_fib(B,A+B,N-1).

This program is contained within a module called "fibonacci" and declares that the start/1 function will be visible from outside the scope of this module.

The function start/1 accepts a single parameter (as denoted by the "/1" syntax) and then calls an internal function called do_fib/3.

In direct contrast to the imperative coding style, Erlang does not need an "if" statement because the Erlang runtime will examine the parameters being passed to a function, and call the first function having a signature that matches the current pattern of parameters. (Erlang syntax does provide an "if" statement, but it is considered syntactic sugar and, compared to its usage in imperative languages, plays only a minor role in application logic design).

In this case, it is unnecessary to test for a parameter value within the body of the function because such a test is implicitly performed by providing a set of function signatures that describe the different patterns of values that could be received by a function.

In the case above, the first version of do_fib/3 will only be called when the third parameter has the precise value of 1. In all other cases, the second version of do_fib/3 will be called.

This example demonstrates that functional programming languages often implement conditional logic implicitly by matching parameter patterns rather than explicitly by means of an "if" statement.

Lisp

The Fibonacci function can be written in Common Lisp as follows:

(defun fib (n &optional (a 0) (b 1))
  (if (= n 0)
      a
      (fib (- n 1) b (+ a b))))

The program can then be called as

(fib 10)

Use in industry

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To give you some perspective, the entire number of personal properties in Singapore (together with govt condominiums) is 297,689 in 2013Q3. Primarily based on the projection that there will be 19,302 units accomplished in 2014, the rise in residential models works out to be more than 6%. With a lot New Ec Launch Singapore provide, buyers might be spoilt for alternative and this in flip will lead to their reluctance to pay a premium for potential models. The complete textual content of the Copyright Act (Cap sixty three) and different statutes regarding IPR might be found on the Singapore Statutes Online Website online The Group's income jumped forty.1 p.c to $324.5 million from $231.6 million in FY 2013, lifted by increased development income and sales of growth properties in Singapore and China. Actual Estate Shopping for

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Within the event the Bank's valuation is decrease than the acquisition price, the purchaser has to pay the distinction between the purchase value and the Bank's valuation utilizing money. As such, the money required up-front might be increased so it's at all times essential to know the valuation of the property before making any offer. Appoint Lawyer The Bank will prepare for a proper valuation of the property by way of physical inspection The completion statement will present you the balance of the acquisition price that you must pay after deducting any deposit, pro-rated property tax and utility costs, upkeep prices, and different relevant expenses in addition to any fees payable to the agent and the lawyer. Stamp Responsibility Primarily based on the Purchase Price or Market Value, whichever is larger However, recently several prominent functional programming languages have been used in commercial or industrial systems. For example, the Erlang programming language, which was developed by the Swedish company Ericsson in the late 1980s, was originally used to implement fault-tolerant telecommunications systems.^[8] It has since become popular for building a range of applications at companies such as T-Mobile, Nortel, Facebook, Électricité de France and WhatsApp.^[7]^[9]^[55]^[56]^[57] The Scheme dialect of Lisp was used as the basis for several applications on early Apple Macintosh computers,^[2]^[3] and has more recently been applied to problems such as training simulation software^[4] and telescope control.^[5] OCaml, which was introduced in the mid-1990s, has seen commercial use in areas such as financial analysis,^[10] driver verification, industrial robot programming, and static analysis of embedded software.^[11] Haskell, although initially intended as a research language,^[13] has also been applied by a range of companies, in areas such as aerospace systems, hardware design, and web programming.^[12]^[13]

Other functional programming languages that have seen use in industry include Scala (which is a hybrid functional-OO language and has support for both purely functional and imperative programming),^[58] F#,^[15]^[16] Lisp,^[59] Standard ML,^[60]^[61] and Clojure.^[62]

References

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External links

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This rule, which applies to all new Singapore property sales, is to ensure that monies for a challenge, whether loans or sale proceeds, only be used for the project and not diverted to other makes use of, or worse, absconded with. By Property Soul, a profitable property investor and fanatic who shares her experiences and data on her blog Posted courtesy of www.Propwise.sg , a Singapore property weblog dedicated to serving to you perceive the real estate market and make higher choices. Click right here to get your free Property Newbie's and Purchaser's Information Developers may conduct property launches in Singapore by way of an in-home advertising crew, or more doubtless (to minimise staffing), by appointing external actual estate businesses to do the advertising. The Panorama

The Bridge @ Cambodia is situated alongside Nationwide Meeting Street is a Phnom Penh new launch property that is being developed by a famend Singapore listed developer Oxley Holdings. Oxley Holdings is a way of life property developer and their development carters to the rising wants of young and classy homebuyers who worth high quality living and finer lifestyle. They have now introduced this high quality residing proposition overseas to Phnom Penh, Cambodia. This Oxley Cambodia property launch is priced to start out at USD$153K solely. The very best thing about this Phnom Penh new launch is that the first three years rental is guaranteed at 6% per year and the subsequent 3 years at 7% per 12 months on the option of the developer. That could be a potential 6 years rental income assure.

For those who are fervently wishing property costs will fall, the unhealthy information is they don't seem to be prone to. Based on Knight Frank chairman Tan Tiong Cheng, "So what in the event that they delay launches for a couple of months. In spite of everything, most of them have strong stability sheets and the Singapore financial system seems to be persevering with to carry out nicely." One Surin is a freehold strata terrace development located alongside 1 Surin Avenue in Singapore District 19. This cluster house terraces consists of 27 e Learn More City Villas @ Paya Lebar Crescent is an upcoming Cluster Housing Landed improvement situated at Paya Lebar Crescent, Singapore District 19. This Free Read Extra Good Investment Property with Excessive Rental Returns Is it safe to buy uncompleted property in Singapore?

Template:Cite web
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Functional programming in Python (by David Mertz): part 1, part 2, part 3

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↑ ^1.0 ^1.1 One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang
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↑ ^15.0 ^15.1 55 years old Systems Administrator Antony from Clarence Creek, really loves learning, PC Software and aerobics. Likes to travel and was inspired after making a journey to Historic Ensemble of the Potala Palace.

You can view that web-site... ccleaner free download
↑ ^16.0 ^16.1 55 years old Systems Administrator Antony from Clarence Creek, really loves learning, PC Software and aerobics. Likes to travel and was inspired after making a journey to Historic Ensemble of the Potala Palace.

You can view that web-site... ccleaner free download
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↑ 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.

My blog: http://www.primaboinca.com/view_profile.php?userid=5889534
↑ 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.

My blog: http://www.primaboinca.com/view_profile.php?userid=5889534
↑ One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang
↑ The memoir of Herbert A. Simon (1991), Models of My Life pp.189-190 ISBN 0-465-04640-1 claims that he, Al Newell, and Cliff Shaw are "commonly adjudged to be the parents of [the] artificial intelligence [field]", for writing Logic Theorist, a program which proved theorems from Principia Mathematica automatically. In order to accomplish this, they had to invent a language and a paradigm which, which viewed retrospectively, embeds functional programming.
↑ http://www.stanford.edu/class/cs242/readings/backus.pdf
↑ Template:Cite web
↑ One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang
↑ The Implementation of Functional Programming Languages. Simon Peyton Jones, published by Prentice Hall, 1987
↑ Template:Cite web
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↑ 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.

My blog: http://www.primaboinca.com/view_profile.php?userid=5889534
↑ Template:Cite web
↑ Template:Cite web
↑ Template:Cite web source of citation
↑ One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang; Template:Cite web(Part 1, Part 2)
↑ Template:Cite web
↑ Template:Cite web
↑ Template:Cite web
↑ Template:Cite web
↑ 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.

My blog: http://www.primaboinca.com/view_profile.php?userid=5889534
↑ Template:Cite web
↑ Template:Cite web
↑ Template:Cite web
↑ 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.

My blog: http://www.primaboinca.com/view_profile.php?userid=5889534
↑ Template:Cite web
↑ 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.

My blog: http://www.primaboinca.com/view_profile.php?userid=5889534
↑ Cite error: Invalid <ref> tag; no text was provided for refs named Spiewak
↑ Template:Cite web
↑ One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang
↑ Template:Cite web
↑ 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.

My blog: http://www.primaboinca.com/view_profile.php?userid=5889534
↑ 55 years old Systems Administrator Antony from Clarence Creek, really loves learning, PC Software and aerobics. Likes to travel and was inspired after making a journey to Historic Ensemble of the Potala Palace.

You can view that web-site... ccleaner free download
↑ Cite error: Invalid <ref> tag; no text was provided for refs named Sim-Diasca
↑ 1 million is so 2011 // WhatsApp blog, 2012-01-06: "the last important piece of our infrastracture is Erlang"
↑ 55 years old Systems Administrator Antony from Clarence Creek, really loves learning, PC Software and aerobics. Likes to travel and was inspired after making a journey to Historic Ensemble of the Potala Palace.

You can view that web-site... ccleaner free download
↑ Template:Cite web
↑ 55 years old Systems Administrator Antony from Clarence Creek, really loves learning, PC Software and aerobics. Likes to travel and was inspired after making a journey to Historic Ensemble of the Potala Palace.

You can view that web-site... ccleaner free download
↑ 55 years old Systems Administrator Antony from Clarence Creek, really loves learning, PC Software and aerobics. Likes to travel and was inspired after making a journey to Historic Ensemble of the Potala Palace.

You can view that web-site... ccleaner free download
↑ Template:Cite web

[hudak1989-1] 1.0 ^1.1 One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang

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[quantFSharp-15] 15.0 ^15.1 55 years old Systems Administrator Antony from Clarence Creek, really loves learning, PC Software and aerobics. Likes to travel and was inspired after making a journey to Historic Ensemble of the Potala Palace.

You can view that web-site... ccleaner free download

[businessAppsFSharp-16] 16.0 ^16.1 55 years old Systems Administrator Antony from Clarence Creek, really loves learning, PC Software and aerobics. Likes to travel and was inspired after making a journey to Historic Ensemble of the Potala Palace.

You can view that web-site... ccleaner free download

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[24] 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.

My blog: http://www.primaboinca.com/view_profile.php?userid=5889534

[25] 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.

My blog: http://www.primaboinca.com/view_profile.php?userid=5889534

[26] One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang

[27] The memoir of Herbert A. Simon (1991), Models of My Life pp.189-190 ISBN 0-465-04640-1 claims that he, Al Newell, and Cliff Shaw are "commonly adjudged to be the parents of [the] artificial intelligence [field]", for writing Logic Theorist, a program which proved theorems from Principia Mathematica automatically. In order to accomplish this, they had to invent a language and a paradigm which, which viewed retrospectively, embeds functional programming.

[28] ttp://www.stanford.edu/class/cs242/readings/backus.pdf

[29] Template:Cite web

[totalfp-30] One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang

[31] The Implementation of Functional Programming Languages. Simon Peyton Jones, published by Prentice Hall, 1987

[32] Template:Cite web

[launchbury1993-33] 33.0 ^33.1 Template:Cite web

[34] 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.

My blog: http://www.primaboinca.com/view_profile.php?userid=5889534

[35] Template:Cite web

[36] Template:Cite web

[37] Template:Cite web source of citation

[38] One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang; Template:Cite web(Part 1, Part 2)

[39] Template:Cite web

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[43] 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.

My blog: http://www.primaboinca.com/view_profile.php?userid=5889534

[44] Template:Cite web

[45] Template:Cite web

[46] Template:Cite web

[47] 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.

My blog: http://www.primaboinca.com/view_profile.php?userid=5889534

[48] Template:Cite web

[49] 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.

My blog: http://www.primaboinca.com/view_profile.php?userid=5889534

[Spiewak-50] Cite error: Invalid <ref> tag; no text was provided for refs named Spiewak

[51] Template:Cite web

[52] One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang

[53] Template:Cite web

[programmingScala-54] 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.

My blog: http://www.primaboinca.com/view_profile.php?userid=5889534

[55] 55 years old Systems Administrator Antony from Clarence Creek, really loves learning, PC Software and aerobics. Likes to travel and was inspired after making a journey to Historic Ensemble of the Potala Palace.

You can view that web-site... ccleaner free download

[Sim-Diasca-56] Cite error: Invalid <ref> tag; no text was provided for refs named Sim-Diasca

[whatsapp.blog.2012-57] 1 million is so 2011 // WhatsApp blog, 2012-01-06: "the last important piece of our infrastracture is Erlang"

[58] 55 years old Systems Administrator Antony from Clarence Creek, really loves learning, PC Software and aerobics. Likes to travel and was inspired after making a journey to Historic Ensemble of the Potala Palace.

You can view that web-site... ccleaner free download

[59] Template:Cite web

[60] 55 years old Systems Administrator Antony from Clarence Creek, really loves learning, PC Software and aerobics. Likes to travel and was inspired after making a journey to Historic Ensemble of the Potala Palace.

You can view that web-site... ccleaner free download

[61] 55 years old Systems Administrator Antony from Clarence Creek, really loves learning, PC Software and aerobics. Likes to travel and was inspired after making a journey to Historic Ensemble of the Potala Palace.

You can view that web-site... ccleaner free download

[62] Template:Cite web

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Finite-state machine: Difference between revisions

Revision as of 17:09, 18 January 2014

Contents

History

Concepts

First-class and higher-order functions

Pure functions

Recursion

Strict versus non-strict evaluation

Type systems

Functional programming in non-functional languages

Comparison to imperative programming

Simulating state

Efficiency issues

Coding styles

Haskell

Erlang

Lisp

Use in industry

See also

References

Further reading

External links

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+{{for|subroutine-oriented programming|Procedural programming}}
+{{Programming paradigms}}
+In [[computer science]], '''functional programming''' is a [[programming paradigm]], a style of building the structure and elements of computer programs, that treats [[computation]] as the evaluation of [[function (mathematics)|mathematical function]]s and avoids [[program state|state]] and [[immutable object|mutable]] data. Functional programming emphasizes [[Function (computer science)|function]]s that produce results that depend only on their inputs and not on the program state—i.e. [[Pure function|pure]] [[Function (mathematics)|mathematical functions]]. It is a [[declarative programming]] paradigm, which means programming is done with [[Expression (computer science)|expressions]]. In functional code, the output value of a function depends only on the arguments that are input to the function, so calling a function ''f'' twice with the same value for an argument ''x'' will produce the same result ''f(x)'' both times. Eliminating [[side effect (computer science)|side effects]], i.e. changes in state that do not depend on the function inputs, can make it much easier to understand and predict the behavior of a program, which is one of the key motivations for the development of functional programming.
+Functional programming has its roots in [[lambda calculus]], a [[formal system]] developed in the 1930s to investigate [[computability]], the [[Entscheidungsproblem]], function definition, function application, and [[recursion]]. Many functional [[programming language]]s can be viewed as elaborations on the lambda calculus, where [[computation]] is treated as the evaluation of mathematical functions and avoids state and [[Immutable object|mutable]] data. In the other well known declarative [[programming paradigm]], [[logic programming]], [[Relation (logic)|relations]] are at the base of respective languages.<ref name="hudak1989"/>
+In contrast, [[imperative programming]] changes state with commands in the source language, the most simple example is the assignment. Functions do exist, not in the mathematical sense, but the sense of [[subroutine]]. They can have [[side effect (computer science)|side effects]] that may change the value of program state. Functions without return value therefore make sense. Because of this, they lack [[referential transparency (computer science)|referential transparency]], i.e. the same language expression can result in different values at different times depending on the state of the executing program.<ref name="hudak1989">{{cite journal | last = Hudak | first = Paul | authorlink = Paul Hudak | title = Conception, evolution, and application of functional programming languages | journal = [[Association for Computing Machinery|ACM]] Computing Surveys|volume=21|issue=3 | pages = 359–411 |date=September 1989 | url = http://www.dbnet.ece.ntua.gr/~adamo/languages/books/p359-hudak.pdf|format=PDF|doi=10.1145/72551.72554 }}</ref>
+Functional programming languages, especially [[purely functional]] ones such as [[Hope (programming language)|Hope]] and [[Rex_(programming_language)|Rex]], have largely been emphasized in [[academic|academia]] rather than in commercial software development. However, prominent functional programming languages such as [[Common Lisp|Common]] [[Lisp (programming language)|Lisp]], [[Scheme (programming language)|Scheme]],<ref name="clinger1987"/><ref name="hartheimer1987"/><ref name="kidd2007"/><ref name="cleis2006"/> [[Clojure]], [[Racket (programming language)|Racket]],<ref name="racket-video-games"/> [[Erlang (programming language)|Erlang]],<ref name="erlang-faq"/><ref name="armstrong2007"/><ref name="larson2009"/> [[OCaml]],<ref name="minksy2008"/><ref name="leroy2007"/> [[Haskell (programming language)|Haskell]],<ref name="haskell-industry"/><ref name="hudak2007"/> [[Scala (programming language)|Scala]]<ref name="effective-scala"/> and [[F Sharp (programming language)|F#]]<ref name='quantFSharp'>{{cite conference | last = Mansell | first = Howard | title = Quantitative Finance in F# | url = http://cufp.galois.com/2008/abstracts.html#MansellHoward | year = 2008 | conference = CUFP 2008 | accessdate = 2009-08-29 }}</ref><ref name='businessAppsFSharp'>{{cite conference | last = Peake | first = Alex | title = The First Substantial Line of Business Application in F# | url = http://cufp.galois.com/2009/abstracts.html#AlexPeakeAdamGranicz | year = 2009 | conference = CUFP 2009 | accessdate = 2009-08-29 }}</ref> have been used in industrial and commercial applications by a wide variety of organizations. Functional programming is also supported in some [[domain-specific programming language]]s like [[R (programming language)|R]] (statistics),<ref name="useR"/><ref name="Chambers"/> [[Mathematica]] (symbolic and numeric math),<ref name="Amath-CO"/> [[J (programming language)|J]], [[K (programming language)|K]] and [[Q (programming language from Kx Systems)|Q from Kx Systems]] (financial analysis), [[XQuery]]/[[XSLT]] ([[XML]]),<ref name="Novatchev"/><ref name="Mertz"/> and Opal.<ref name="Opal (programming language)"/> Widespread domain-specific declarative languages like [[SQL]] and [[Lex (software)|Lex]]/[[Yacc]] use some elements of functional programming, especially in eschewing [[mutable object|mutable value]]s.<ref name="Chamberlin_Boyce"/>
+Programming in a functional style can also be accomplished in languages that aren't specifically designed for functional programming. For example, the imperative [[Perl]] programming language has been the subject of a book describing how to apply functional programming concepts.<ref>{{cite book | last = Dominus | first = Mark J. | authorlink = Mark Jason Dominus | title = [[Higher-Order Perl]] |publisher=[[Morgan Kaufmann]] | year = 2005 |isbn = 1-55860-701-3 }}</ref> [[C Sharp (programming language)|C#]] 3.0 and [[Java_programming|Java]] 8 added constructs to facilitate the functional style.
+== History ==
+[[Lambda calculus]] provides a theoretical framework for describing functions and their evaluation. Although it is a mathematical abstraction rather than a programming language, it forms the basis of almost all functional programming languages today. An equivalent theoretical formulation, [[combinatory logic]], is commonly perceived as more abstract than lambda calculus and preceded it in invention. Combinatory logic and lambda calculus were both originally developed to achieve a clearer approach to the [[foundations of mathematics]].<ref>{{cite book|author1=Haskell Brooks Curry|author2=Robert Feys|title=Combinatory Logic|url=http://books.google.com/books?id=fEnuAAAAMAAJ|accessdate=10 February 2013|year=1958|publisher=North-Holland Publishing Company}}</ref>
+An early functional-flavored language was [[Lisp (programming language)|Lisp]], developed by [[John McCarthy (computer scientist)|John McCarthy]] while at [[Massachusetts Institute of Technology]] (MIT) for the [[IBM 700/7000 series#Scientific Architecture|IBM 700/7000 series]] scientific computers in the late 1950s.<ref>{{cite journal | first = John | last = McCarthy | authorlink = John McCarthy (computer scientist) | title = History of Lisp | journal = In [[Association for Computing Machinery|ACM]] SIGPLAN History of Programming Languages Conference | pages = 217–223 |date=June 1978 | url = http://citeseer.ist.psu.edu/mccarthy78history.html|doi=10.1145/800025.808387 }}</ref> Lisp introduced many features now found in functional languages, though Lisp is technically a multi-paradigm language. [[Scheme (programming language)|Scheme]] and [[Dylan (programming language)|Dylan]] were later attempts to simplify and improve Lisp.
+[[Information Processing Language]] (IPL) is sometimes cited as the first computer-based functional programming language.<ref>The memoir of [[Herbert A. Simon]] (1991), ''Models of My Life'' pp.189-190 ISBN 0-465-04640-1 claims that he, Al Newell, and Cliff Shaw are "commonly adjudged to be the parents of [the] artificial intelligence [field]", for writing [[Logic Theorist]], a program which proved theorems from ''[[Principia Mathematica]]'' automatically. In order to accomplish this, they had to invent a language and a paradigm which, which viewed retrospectively, embeds functional programming.</ref> It is an assembly-style language for manipulating lists of symbols. It does have a notion of "generator", which amounts to a function accepting a function as an argument, and, since it is an assembly-level language, code can be used as data, so IPL can be regarded as having higher-order functions. However, it relies heavily on mutating list structure and similar imperative features.
+[[Kenneth E. Iverson]] developed [[APL (programming language)|APL]] in the early 1960s, described in his 1962 book ''A Programming Language'' (ISBN 9780471430148). APL was the primary influence on [[John Backus]]'s [[FP (programming language)|FP]]. In the early 1990s, Iverson and [[Roger Hui]] created [[J (programming language)|J]]. In the mid-1990s, [[Arthur Whitney (computer scientist)|Arthur Whitney]], who had previously worked with Iverson, created [[K (programming language)|K]], which is used commercially in financial industries along with its descendant [[Q (programming language from Kx Systems)|Q]].
+[[John Backus]] presented [[FP (programming language)|FP]] in his 1977 [[Turing Award]] lecture "Can Programming Be Liberated From the [[Von Neumann architecture|von Neumann]] Style? A Functional Style and its Algebra of Programs".<ref>http://www.stanford.edu/class/cs242/readings/backus.pdf</ref> He defines functional programs as being built up in a hierarchical way by means of "combining forms" that allow an "algebra of programs"; in modern language, this means that functional programs follow the [[principle of compositionality]]. Backus's paper popularized research into functional programming, though it emphasized [[function-level programming]] rather than the lambda-calculus style which has come to be associated with functional programming.
+In the 1970s, [[ML (programming language)|ML]] was created by [[Robin Milner]] at the [[University of Edinburgh]], and [[David Turner (computer scientist)|David Turner]] developed initially the language [[SASL (programming language)|SASL]] at the [[University of St. Andrews]] and later the language [[Miranda (programming language)|Miranda]] at the [[University of Kent]]. ML eventually developed into several dialects, the most common of which are now [[OCaml]] and [[Standard ML]]. Also in the 1970s, the development of [[Scheme (programming language)|Scheme]] (a partly functional dialect of Lisp), as described in the influential [[Lambda Papers]] and the 1985 textbook ''[[Structure and Interpretation of Computer Programs]]'', brought awareness of the power of functional programming to the wider programming-languages community.
+In the 1980s, [[Per Martin-Löf]] developed [[intuitionistic type theory]] (also called ''constructive'' type theory), which associated functional programs with [[constructive proof]]s of arbitrarily complex mathematical propositions expressed as [[dependent type]]s. This led to powerful new approaches to [[interactive theorem proving]] and has influenced the development of many subsequent functional programming languages.
+The [[Haskell (programming language)|Haskell language]] began with a consensus in 1987 to form an [[open standard]] for functional programming research; implementation releases have been ongoing since 1990.
+== Concepts ==
+A number of concepts and paradigms are specific to functional programming, and generally foreign to [[imperative programming]] (including [[object-oriented programming]]). However, programming languages are often hybrids of several programming paradigms, so programmers using "mostly imperative" languages may have utilized some of these concepts.<ref>{{cite web | url = http://www.byte.com/art/9408/sec11/art1.htm | title = Functional Programming Comes of Age | author = Dick Pountain | work=BYTE.com (August 1994) | accessdate = August 31, 2006 }}</ref>
+=== First-class and higher-order functions ===
+{{main|First-class function|Higher-order function}}
+[[Higher-order function]]s are functions that can either take other functions as arguments or return them as results. In calculus, an example of a higher-order function is the [[differential operator]] <math>d/dx</math>, which returns the [[derivative]] of a function <math>f</math>.
+Higher-order functions are closely related to [[first-class function]]s in that higher-order functions and first-class functions both allow functions as arguments and results of other functions. The distinction between the two is subtle: "higher-order" describes a mathematical concept of functions that operate on other functions, while "first-class" is a computer science term that describes programming language entities that have no restriction on their use (thus first-class functions can appear anywhere in the program that other first-class entities like numbers can, including as arguments to other functions and as their return values).
+Higher-order functions enable [[partial application]] or [[currying]], a technique in which a function is applied to its arguments one at a time, with each application returning a new function that accepts the next argument. This allows one to succinctly express, for example, the successor function as the addition operator partially applied to the natural number one.
+=== Pure functions ===
+[[Purely functional]] functions (or expressions) have no [[side effect (computer science)|side effects]] (memory or I/O). This means that pure functions have several useful properties, many of which can be used to optimize the code:
+* If the result of a pure expression is not used, it can be removed without affecting other expressions.
+* If a pure function is called with parameters that cause no side-effects, the result is constant with respect to that parameter list (sometimes called [[referential transparency (computer science)|referential transparency]]), i.e. if the pure function is again called with the same parameters, the same result will be returned (this can enable caching optimizations such as [[memoization]]).
+* If there is no data dependency between two pure expressions, then their order can be reversed, or they can be performed in [[parallelization|parallel]] and they cannot interfere with one another (in other terms, the evaluation of any pure expression is [[thread-safe]]).
+* If the entire language does not allow side-effects, then any evaluation strategy can be used; this gives the compiler freedom to reorder or combine the evaluation of expressions in a program (for example, using [[deforestation (computer science)|deforestation]]).
+While most compilers for imperative programming languages detect pure functions and perform common-subexpression elimination for pure function calls, they cannot always do this for pre-compiled libraries, which generally do not expose this information, thus preventing optimizations that involve those external functions. Some compilers, such as [[GNU Compiler Collection|gcc]], add extra keywords for a programmer to explicitly mark external functions as pure, to enable such optimizations. [[Fortran 95]] also allows functions to be designated "pure".
+=== Recursion ===
+{{Main|Recursion (computer science)}}
+[[Iteration]] (looping) in functional languages is usually accomplished via [[recursion]]. [[recursion (computer science)|Recursive function]]s invoke themselves, allowing an operation to be performed over and over until the [[Recursion (computer science)|base case]] is reached. Though some recursion requires maintaining a stack, [[tail recursion]] can be recognized and optimized by a compiler into the same code used to implement iteration in imperative languages. The [[Scheme (programming language)|Scheme]] language standard requires implementations to recognize and optimize tail recursion. Tail recursion optimization can be implemented by transforming the program into [[continuation passing style]] during compiling, among other approaches.
+Common patterns of recursion can be factored out using higher order functions, with [[catamorphism]]s and [[anamorphism]]s (or "folds" and "unfolds") being the most obvious examples. Such higher order functions play a role analogous to built-in control structures such as [[Program loops|loops]] in [[imperative languages]].
+Most general purpose functional programming languages allow unrestricted recursion and are [[Turing complete]], which makes the [[halting problem]] [[undecidable problem|undecidable]], can cause unsoundness of [[equational reasoning]], and generally requires the introduction of [[inconsistency]] into the logic expressed by the language's [[type system]]. Some special purpose languages such as [[Coq]] allow only [[well-founded]] recursion and are [[strongly normalizing]] (nonterminating computations can be expressed only with infinite streams of values called [[codata]]). As a consequence, these languages fail to be Turing complete and expressing certain functions in them is impossible, but they can still express a wide class of interesting computations while avoiding the problems introduced by unrestricted recursion. Functional programming limited to well-founded recursion with a few other constraints is called [[total functional programming]]. See Turner 2004 for more discussion.<ref name=totalfp>{{cite journal | last = Turner | first = D.A.|author-link=David Turner (computer scientist) | title = Total Functional Programming | journal = Journal of Universal Computer Science|volume=10| date = 2004-07-28 | pages = 751–768 | url = http://www.jucs.org/jucs_10_7/total_functional_programming|doi=10.3217/jucs-010-07-0751|issue=7}}</ref>
+=== Strict versus non-strict evaluation ===
+{{Main|Evaluation strategy}}
+Functional languages can be categorized by whether they use ''strict (eager)'' or ''non-strict (lazy)'' evaluation, concepts that refer to how function arguments are processed when an expression is being evaluated. The technical difference is in the [[denotational semantics]] of expressions containing failing or divergent computations. Under strict evaluation, the evaluation of any term containing a failing subterm will itself fail. For example, the expression:
+<!-- language? -->
+ print length([2+1, 3*2, 1/0, 5-4])
+will fail under strict evaluation because of the division by zero in the third element of the list. Under lazy evaluation, the length function will return the value 4 (i.e., the number of items in the list), since evaluating it will not attempt to evaluate the terms making up the list. In brief, strict evaluation always fully evaluates function arguments before invoking the function. Lazy evaluation does not evaluate function arguments unless their values are required to evaluate the function call itself.
+The usual implementation strategy for lazy evaluation in functional languages is [[graph reduction]].<ref>[http://research.microsoft.com/~simonpj/papers/slpj-book-1987/index.htm The Implementation of Functional Programming Languages]. Simon Peyton Jones, published by Prentice Hall, 1987</ref> Lazy evaluation is used by default in several pure functional languages, including [[Miranda (programming language)|Miranda]], [[Clean (programming language)|Clean]], and [[Haskell (programming language)|Haskell]].
+{{Harvnb|Hughes|1984}} argues for lazy evaluation as a mechanism for improving program modularity through [[separation of concerns]], by easing independent implementation of producers and consumers of data streams.<ref>{{cite web |url=http://www.cse.chalmers.se/~rjmh/Papers/whyfp.html |title=Why Functional Programming Matters |authorlink=John Hughes (computer scientist) |first=John |last=Hughes |year=1984 |ref=harv}}</ref> Launchbury 1993 <!-- a cite arguing more strongly against lazy evaluation would be preferable here, if someone knows of one. --> describes some difficulties that lazy evaluation introduces, particularly in analyzing a program's storage requirements, and proposes an [[operational semantics]] to aid in such analysis.<ref name=launchbury1993>{{cite web | url = http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.35.2016 | author = John Launchbury | title = A Natural Semantics for Lazy Evaluation | year = 1993 }}</ref> Harper 2009 proposes including both strict and lazy evaluation in the same language, using the language's type system to distinguish them.<ref>{{cite book | url = http://www.cs.cmu.edu/~rwh/plbook/book.pdf | title = Practical Foundations for Programming Languages | author = Robert W. Harper | authorlink=Robert_Harper_(computer_scientist) | year = 2009 }}</ref>
+=== Type systems ===
+<!-- expand this section!!! also split it into several sections -->
+Especially since the development of [[Hindley–Milner type inference]] in the 1970s, functional programming languages have tended to use [[typed lambda calculus]], as opposed to the [[untyped lambda calculus]] used in Lisp and its variants (such as [[Scheme (programming language)|Scheme]]). The use of [[algebraic datatypes]] and [[pattern matching]] makes manipulation of complex data structures convenient and expressive; the presence of strong compile-time type checking makes programs more reliable, while [[type inference]] frees the programmer from the need to manually declare types to the compiler.
+Some research-oriented functional languages such as [[Coq]], [[Agda (theorem prover)|Agda]], [[Cayenne (programming language)|Cayenne]], and [[Epigram (programming language)|Epigram]] are based on [[intuitionistic type theory]], which allows types to depend on terms. Such types are called [[dependent type]]s. These type systems do not have decidable type inference and are difficult to understand and program with{{Citation needed| date = December 2011}}. But dependent types can express arbitrary propositions in [[predicate logic]]. Through the [[Curry–Howard isomorphism]], then, well-typed programs in these languages become a means of writing formal [[mathematical proof]]s from which a compiler can generate [[formal verification|certified code]]. While these languages are mainly of interest in academic research (including in [[formalized mathematics]]), they have begun to be used in engineering as well. [[Compcert]] is a [[compiler]] for a subset of the [[C (programming language)|C programming language]] that is written in Coq and formally verified.<ref>{{cite web | url = http://compcert.inria.fr/doc/index.html | title = The Compcert verified compiler }}</ref>
+A limited form of dependent types called [[generalized algebraic data type]]s (GADT's) can be implemented in a way that provides some of the benefits of dependently typed programming while avoiding most of its inconvenience.<ref>{{cite web | url = http://research.microsoft.com/en-us/um/people/simonpj/papers/gadt/ | title = Simple unification-based type inference for GADTs | author = Simon Peyton Jones, Dimitrios Vytiniotis, Stephanie Weirich, and Geoffrey Washburn | work=ICFP 2006 | pages = 50–61 }}</ref> GADT's are available in the [[Glasgow Haskell Compiler]], in [[OCaml]] (since version 4.00)  and in [[Scala (programming language)|Scala]] (as "case classes"), and have been proposed as additions to other languages including Java and C#.<ref>{{cite web | title = Generalized Algebraic Data Types and Object-Oriented Programming | author = Andrew Kennedy and Claudio Russo | work=OOPSLA | date = October 2005 | location = San Diego, California | url = http://research.microsoft.com/~akenn/generics/gadtoop.pdf }} [http://lambda-the-ultimate.org/node/1134 source of citation]</ref>
+=== Functional programming in non-functional languages ===
+It is possible to use a functional style of programming in languages that are not traditionally considered functional languages.<ref>{{cite journal | last = Hartel | first = Pieter | coauthors = Henk Muller and Hugh Glaser | title = The Functional C experience | journal = The Journal of Functional Programming | volume=14 |issue=2 | pages = 129–135 |date=March 2004 | url = http://www.ub.utwente.nl/webdocs/ctit/1/00000084.pdf |format=PDF| doi=10.1017/S0956796803004817}}; {{cite web | title = Functional programming in Python, Part 3 | url = http://www-128.ibm.com/developerworks/linux/library/l-prog3.html | author = David Mertz | accessdate = 2006-09-17 | work=IBM developerWorks}}([http://www-128.ibm.com/developerworks/library/l-prog.html Part 1], [http://www-128.ibm.com/developerworks/library/l-prog2.html Part 2])</ref> For example, both [[D (programming language)|D]] and [[Fortran 95]] explicitly support pure functions.<ref>{{cite web | url = http://www.digitalmars.com/d/2.0/function.html#pure-functions | title = Functions&nbsp;— D Programming Language 2.0 |publisher=Digital Mars | date = | accessdate = 2011-06-20 }}</ref>
+First-class functions have slowly been added to mainstream languages. For example, in early 1994, support for lambda, filter, map, and reduce was added to [[Python (programming language)|Python]]. Then during the development of Python 3000, [[Guido van Rossum]] called for the removal of these features.<ref>{{cite web | url = http://www.artima.com/weblogs/viewpost.jsp?thread=98196 | title = The fate of reduce() in Python 3000 |last=van Rossum |first=Guido |authorlink=Guido van Rossum |publisher=Artima.com | date = 2005-03-10  | accessdate = 2012-09-27 }}</ref> However, he later changed his mind, and only reduce was removed,<ref>{{cite web |url=http://python-history.blogspot.de/2009/04/origins-of-pythons-functional-features.html |title=Origins of Python's "Functional" Features |last=van Rossum |first=Guido |authorlink=Guido van Rossum |publisher=[http://python-history.blogspot.de/ The History of Python] |date=2009-04-21 |accessdate=2012-09-27 }}</ref> though it remains accessible via the <code>functools</code> standard library module.<ref>{{cite web | url = http://docs.python.org/dev/library/functools.html#functools.reduce | title = functools — Higher order functions and operations on callable objects | publisher=Python Software Foundation | date = 2011-07-31 | accessdate = 2011-07-31}}</ref>  First-class functions were also introduced in [[PHP]] 5.3, [[Visual Basic]] 9, [[C Sharp (programming language)|C#]] 3.0, and [[C++11]].
+In [[Java (programming language)|Java]], [[anonymous class]]es can sometimes be used to simulate [[Closure (computer science)|closure]]s;<ref>{{cite book | last = Skarsaune | first = Martin | title = The SICS Java Port Project Automatic Translation of a Large Object Oriented System from Smalltalk to Java | year = 2008 }}</ref> however, anonymous classes are not always proper replacements to [[Closure (computer science)|closure]]s because they have more limited capabilities.<ref>{{cite web|last=Gosling|first=James|title=Closures|url=http://blogs.oracle.com/jag/entry/closures|work=James Gosling: on the Java Road|publisher=Oracle|accessdate=11 May 2013}}</ref> Java 8, scheduled for release in 2014,<ref>{{cite web|url=https://blogs.oracle.com/java/entry/java_se_8_schedule|title=Java SE 8 Schedule: March 2014}}</ref> will support lambda expressions as a replacement for some anonymous classes.<ref>{{cite web|url=https://blogs.oracle.com/javatraining/entry/java_se_8_lambda_quick|title=Java SE 8 Lambda Quick Start}}</ref> However, the presence of checked exceptions in Java can make functional programming inconvenient, because it can be necessary to catch checked exceptions and then rethrow them—a problem that does not occur in other JVM languages that do not have checked exceptions, such as Scala.
+Many [[object-oriented]] [[Design pattern (computer science)|design pattern]]s are expressible in functional programming terms: for example, the [[strategy pattern]] simply dictates use of a higher-order function, and the [[visitor (design pattern)|visitor]] pattern roughly corresponds to a [[catamorphism]], or [[fold (higher-order function)|fold]].
+Similarly, the idea of immutable data from functional programming is often included in imperative programming languages,<ref>{{cite book | title = Effective Java | edition = Second | first = Joshua | last = Bloch | pages = Item 15 }}</ref> for example the tuple in Python, which is an immutable array.
+== Comparison to imperative programming ==
+Functional programming is very different from [[imperative programming]]. The most significant differences stem from the fact that functional programming avoids [[side effect (computer science)|side effects]], which are used in imperative programming to implement state and I/O. Pure functional programming completely prevents side-effects and provides [[referential transparency (computer science)|referential transparency]], which makes it easier to verify, optimize, and parallelize programs, and easier to write automated tools to perform those tasks.
+Higher-order functions are rarely used in older imperative programming. Where a traditional imperative program might use a loop to traverse a list, a functional program would use a different technique. It would use a higher-order function that takes as arguments a function and a list. The higher-order function would then apply the given function to each element of the given list and then return a new list with the results.
+=== Simulating state ===
+There are tasks (for example, maintaining a bank account balance) that often seem most naturally implemented with state. Pure functional programming performs these tasks, and I/O tasks such as accepting user input and printing to the screen, in a different way.
+The pure functional programming language [[Haskell (programming language)|Haskell]] implements them using [[monad (functional programming)|monads]], derived from [[category theory]]. Monads offer a way to abstract certain types of computational patterns, including (but not limited to) modeling of computations with mutable state (and other side effects such as I/O) in an imperative manner without losing purity. While existing monads may be easy to apply in a program, given appropriate templates and examples, many students find them difficult to understand conceptually, e.g., when asked to define new monads (which is sometimes needed for certain types of libraries).<ref>{{cite web | last = Newbern | first = J. | title = All About Monads: A comprehensive guide to the theory and practice of monadic programming in Haskell | url = http://monads.haskell.cz/html/index.html/html/ | accessdate = 2008-02-14 }}</ref>
+Another way in which functional languages can simulate state is by passing around a [[data structure]] that represents the current state as a parameter to function calls. On each function call, a copy of this data structure is created with whatever differences are the result of the function. This is referred to as '[[state-passing style]]'.
+<!-- TO DO: Expand -->
+Impure functional languages usually include a more direct method of managing mutable state. [[Clojure]], for example, uses managed references that can be updated by applying pure functions to the current state. This kind of approach enables mutability while still promoting the use of pure functions as the preferred way to express computations.
+<!-- TO DO: Expand / example code?? -->
+Alternative methods such as [[Hoare logic]] and [[uniqueness type|uniqueness]] have been developed to track side effects in programs. Some modern research languages use [[effect system]]s to make explicit the presence of side effects.
+<!-- TO DO: Expand -->
+=== Efficiency issues ===
+Functional programming languages are typically less efficient in their use of [[central processing unit|CPU]] and memory than imperative languages such as [[C (programming language)|C]] and [[Pascal (programming language)|Pascal]].<ref>{{cite book|author=Larry C. Paulson|title=ML for the Working Programmer|url=http://books.google.com/books?id=XppZdaDs7e0C|accessdate=10 February 2013|date=28 June 1996|publisher=Cambridge University Press|isbn=978-0-521-56543-1}}</ref> <!-- Paulson mentions the reputation for inefficiency in Sec. 1.5; perhaps a more in-depth discussion could be found. --> This is related to the fact that some mutable data structures like arrays have a very straightforward implementation using present hardware (which is a highly evolved Turing machine). Flat arrays may be accessed very efficiently with deeply pipelined CPUs, prefetched efficiently through caches (with no complex pointer-chasing), or handled with SIMD instructions. <!-- perhaps this could be formulated by someone who knows the subject, I was simply curious about unexplained statement "logarythmic slowdown" --> And it is not easy to create their equally efficient general-purpose immutable counterparts. For purely functional languages, the worst-case slowdown is logarithmic in the number of memory cells used, because mutable memory can be represented by a purely functional data structure with logarithmic access time (such as a balanced tree).<ref name="Spiewak"/> However, such slowdowns are not universal. For programs that perform intensive numerical computations, functional languages such as [[OCaml]] and [[Clean (programming language)|Clean]] are only slightly slower than C.<ref>{{cite web | url = http://benchmarksgame.alioth.debian.org/u32/which-programs-are-fastest.php?gcc=on&ghc=on&clean=on&ocaml=on&sbcl=on&fsharp=on&racket=on&clojure=on&hipe=on&calc=chart | title =  Which programs are fastest? &#124; Computer Language Benchmarks Game | publisher=benchmarksgame.alioth.debian.org | date =  | accessdate = 2011-06-20 }}</ref> For programs that handle large [[matrix (mathematics)|matrices]] and multidimensional [[database]]s, [[array programming|array]] functional languages (such as [[J (programming language)|J]] and [[K (programming language)|K]]) were designed with speed optimization.
+Immutability of data can in many cases lead to execution efficiency by allowing the compiler to make assumptions that are unsafe in an imperative language, thus increasing opportunities for [[inline expansion]].<ref>{{cite journal | title = Immutability specification and its applications | author = Igor Pechtchanski and Vivek Sarkar | journal = Concurrency and Computation: Practice and Experience | volume = 17 | issue = 5–6 | pages = 639–662 | year = 2005 | doi = 10.1002/cpe.853 }}</ref>
+[[Lazy evaluation]] may also speed up the program, even asymptotically, whereas it may slow it down at most by a constant factor (however, it may introduce [[memory leak]]s if used improperly). Launchbury 1993<ref name=launchbury1993/> discusses theoretical issues related to memory leaks from lazy evaluation, and O'Sullivan ''et al.'' 2008<ref>{{cite web | url = http://book.realworldhaskell.org/read/profiling-and-optimization.html#x_eK1 | title = Chapter 25. Profiling and optimization |publisher=Book.realworldhaskell.org | date =  | accessdate = 2011-06-20 }}</ref> give some practical advice for analyzing and fixing them.
+However, the most general implementations of lazy evaluation making extensive use of dereferenced code and data perform poorly on modern processors with deep pipelines and multi-level caches (where a cache miss may cost hundreds of cycles)
+=== Coding styles ===
+{{unreferenced section|date=July 2013}}
+Imperative programs tend to emphasize the series of steps taken by a program in carrying out an action, while functional programs tend to emphasize the composition and arrangement of functions, often without specifying explicit ''steps''. A simple example illustrates this with two solutions to the same programming goal (calculating [[Fibonacci number]]s). The imperative example is in [[Python (programming language)|Python]].
+<source lang="python">
+# Fibonacci numbers, imperative style
+# http://docs.python.org/2.7/tutorial/modules.html
+def fibonacci():
+  first, second = 0, 1  # initial seed values
+  while True:  # Perform infinite iterations
+    first, second = second, first + second # Assign all the new values.
+    yield first  # Return current iterate
+for n, x in enumerate(fibonacci()):
+  if n == 10: break  # print first 10 fibonacci elements
+  print x
+</source>
+====Haskell====
+A functional version (in [[Haskell (programming language)|Haskell]]) has a different feel to it:
+<source lang="haskell">
+-- Fibonacci numbers, functional style
+-- describe an infinite list based on the recurrence relation for Fibonacci numbers
+fibRecurrence first second = first : fibRecurrence second (first + second)
+-- describe fibonacci list as fibRecurrence with initial values 0 and 1
+fibonacci = fibRecurrence 0 1
+-- describe action to print the 10th element of the fibonacci list
+main = print (fibonacci !! 10)
+</source>
+Or, more concisely:
+<source lang="haskell">
+fibonacci2 = 0:1:zipwith (+) fibonacci2 (tail fibonacci2)
+</source>
+The imperative style describes the intermediate steps involved in calculating <code>fibonacci(N)</code>, and places those steps inside a [[Program loops|loop statement]]. In contrast, the functional implementation shown here states the mathematical [[recurrence relation]] that defines the entire Fibonacci sequence, then selects an element from the sequence (see also [[recursion (computer science)|recursion]]). This example relies on Haskell's [[lazy evaluation]] to create an "infinite" list of which only as much as needed (the first 10 elements in this case) will actually be computed. That computation happens when the runtime system carries out the action described by "main".
+====Erlang====
+[[File:LYME_software_bundle.svg|thumb|300px|The '''[[LYME (software bundle)]]''' is based on [[Erlang (programming language)|Erlang]]]]
+The same program in [[Erlang (programming language)|Erlang]] provides a simple example of how functional languages in general do not require their syntax to contain an "[[If statement|if]]" statement.
+<source lang="erlang">
+-module(fibonacci).
+-export([start/1]).
+%% Fibonacci numbers in Erlang
+start(N) -> do_fib(0,1,N).
+do_fib(_,B,1) -> B;
+do_fib(A,B,N) -> do_fib(B,A+B,N-1).
+</source>
+This program is contained within a module called "fibonacci" and declares that the start/1 function will be visible from outside the scope of this module.
+The function start/1 accepts a single parameter (as denoted by the "/1" syntax) and then calls an internal function called do_fib/3.
+In direct contrast to the imperative coding style, Erlang does not need an "if" statement because the Erlang runtime will examine the parameters being passed to a function, and call the first function having a signature that matches the current pattern of parameters.  (Erlang syntax does provide an "if" statement, but it is considered syntactic sugar and, compared to its usage in imperative languages, plays only a minor role in application logic design).
+In this case, it is unnecessary to test for a parameter value within the body of the function because such a test is implicitly performed by providing a set of function signatures that describe the different patterns of values that could be received by a function.
+In the case above, the first version of do_fib/3 will only be called when the third parameter has the precise value of 1.  In all other cases, the second version of do_fib/3 will be called.
+This example demonstrates that functional programming languages often implement conditional logic ''implicitly'' by matching parameter patterns rather than ''explicitly'' by means of an "if" statement.
+====Lisp====
+The Fibonacci function can be written in [[Common Lisp]] as follows:
+<source lang="lisp">
+(defun fib (n &optional (a 0) (b 1))
+  (if (= n 0)
+      a
+      (fib (- n 1) b (+ a b))))
+</source>
+The program can then be called as
+<source lang="lisp">
+(fib 10)
+</source>
+== Use in industry ==
+Functional programming has long been popular in academia, but with few industrial applications.<ref name='programmingScala'>{{cite book | first1 = Martin | last1 = Odersky | first2 = Lex | last2 = Spoon | first3 = Bill | last3 = Venners | date = December 13, 2010 | title = Programming in Scala: A Comprehensive Step-by-step Guide | publisher = [[Artima Inc]] | edition = 2nd | pages = 883/852 | isbn = 978-0-9815316-4-9 | url = http://www.artima.com/shop/programming_in_scala_2ed }}</ref>{{rp|page 11}} However, recently several prominent functional programming languages have been used in commercial or industrial systems. For example, the [[Erlang (programming language)|Erlang]] programming language, which was developed by the [[Sweden|Swedish]] company [[Ericsson]] in the late 1980s, was originally used to implement fault-tolerant telecommunications systems.<ref name="armstrong2007"/> It has since become popular for building a range of applications at companies such as [[T-Mobile]], [[Nortel]], [[Facebook]], [[Électricité de France]] and [[WhatsApp]].<ref name="erlang-faq"/><ref name="larson2009"/><ref>{{cite conference | last = Piro | first = Christopher | title = Functional Programming at Facebook | url = http://cufp.galois.com/2009/abstracts.html#ChristopherPiroEugeneLetuchy | year = 2009 | conference = CUFP 2009 | accessdate = 2009-08-29 }}</ref><ref name="Sim-Diasca"/><ref name="whatsapp.blog.2012">[http://blog.whatsapp.com/index.php/2012/01/1-million-is-so-2011/ 1 million is so 2011] // WhatsApp blog, 2012-01-06: "the last important piece of our infrastracture is Erlang"</ref> The [[Scheme (programming language)|Scheme]] dialect of [[Lisp (programming language)|Lisp]] was used as the basis for several applications on early [[Apple Macintosh]] computers,<ref name="clinger1987"/><ref name="hartheimer1987"/> and has more recently been applied to problems such as training [[software simulation|simulation software]]<ref name="kidd2007"/> and [[telescope]] control.<ref name="cleis2006"/> [[OCaml]], which was introduced in the mid-1990s, has seen commercial use in areas such as financial analysis,<ref name="minksy2008"/> [[software driver|driver]] verification, industrial [[robot]] programming, and static analysis of [[embedded software]].<ref name="leroy2007"/> [[Haskell (programming language)|Haskell]], although initially intended as a research language,<ref name="hudak2007"/> has also been applied by a range of companies, in areas such as aerospace systems, hardware design, and web programming.<ref name="haskell-industry"/><ref name="hudak2007"/>
+Other functional programming languages that have seen use in industry include [[Scala (programming language)|Scala]] (which is a hybrid functional-OO language and has support for both [[purely functional]] and imperative programming),<ref>{{cite conference | last = Momtahan | first = Lee | title = Scala at EDF Trading: Implementing a Domain-Specific Language for Derivative Pricing with Scala | url = http://cufp.galois.com/2009/abstracts.html#LeeMomtahan | year = 2009 | conference = CUFP 2009 | accessdate = 2009-08-29 }}</ref> [[F Sharp (programming language)|F#]],<ref name='quantFSharp'/><ref name='businessAppsFSharp'/> [[Lisp (programming language)|Lisp]],<ref>{{cite web | last = Graham | first = Paul | title = Beating the Averages | url = http://www.paulgraham.com/avg.html | year = 2003 | accessdate = 2009-08-29 }}</ref> [[Standard ML]],<ref>{{cite conference | last = Sims | first = Steve | title = Building a Startup with Standard ML | url = http://cufp.galois.com/2006/slides/SteveSims.pdf | year = 2006 | conference = CUFP 2006 | accessdate = 2009-08-29 }}</ref><ref>{{cite conference | last = Laurikari | first = Ville | title = Functional Programming in Communications Security. | url = http://cufp.galois.com/2007/abstracts.html#VilleLaurikari | year = 2007 | conference = CUFP 2007 | accessdate = 2009-08-29 }}</ref> and [[Clojure]].<ref>{{cite web | url = http://www.infoq.com/news/2009/01/clojure_production | last = Lorimer | first = R. J. | title = Live Production Clojure Application Announced }}</ref>
+== See also ==
+* [[Comparison of programming paradigms]]
+* [[Eager evaluation]]
+* [[List of functional programming topics]]
+* [[Nested function]]
+* [[Inductive functional programming]]
+== References ==
+{{reflist|colwidth=30em|refs=
+<ref name="clinger1987">{{cite journal | last = Clinger | first = Will | title = MultiTasking and MacScheme | magazine = MacTech | volume = 3 | issue = 12 | year = 1987 | url = http://www.mactech.com/articles/mactech/Vol.03/03.12/Multitasking/index.html | accessdate = 2008-08-28 }}</ref>
+<ref name="hartheimer1987">{{cite journal | last = Hartheimer | first = Anne | title = Programming a Text Editor in MacScheme+Toolsmith | magazine = MacTech | volume = 3 | issue = 1 | year = 1987 | url = http://www.mactech.com/articles/mactech/Vol.03/03.1/SchemeWindows/index.html | accessdate = 2008-08-28 }}</ref>
+<ref name="kidd2007">{{cite conference | last = Kidd | first = Eric | url = http://cufp.galois.com/2007/abstracts.html#EricKidd | title = Terrorism Response Training in Scheme | conference = CUFP 2007 | accessdate = 2009-08-26 }}</ref>
+<ref name="cleis2006">{{cite conference | last = Cleis | first = Richard | url = http://cufp.galois.com/2006/abstracts.html#RichardCleis | title = Scheme in Space | conference = CUFP 2006 | accessdate = 2009-08-26 }}</ref>
+<ref name="erlang-faq">{{cite web | title = Who uses Erlang for product development? | work=Frequently asked questions about Erlang | url = http://www.erlang.org/faq/faq.html#AEN50 | accessdate = 2007-08-05 }}</ref>
+<ref name="armstrong2007">{{cite conference | last = Armstrong | first = Joe | title = A history of Erlang | conference = Third ACM SIGPLAN Conference on History of Programming Languages | location = San Diego, California | date = June 2007 | url = http://doi.acm.org/10.1145/1238844.1238850 | accessdate = 2009-08-29 }}</ref>
+<ref name="larson2009">{{cite journal | last = Larson | first = Jim | title = Erlang for concurrent programming | journal = Communications of the ACM | volume= 52 | issue= 3 | date = March 2009 | doi=10.1145/1467247.1467263 | page=48 }}</ref>
+<ref name="minksy2008">{{cite journal | last = Minsky | first = Yaron | last2 = Weeks | first2 = Stephen | title = Caml Trading&nbsp;— experiences with functional programming on Wall Street | journal = Journal of Functional Programming | volume = 18 | issue = 4 | pages = 553–564 | publisher = Cambridge University Press | location = |date=July 2008 | url = http://journals.cambridge.org/action/displayAbstract?aid=1899164 | doi = 10.1017/S095679680800676X | accessdate = 2008-08-27 }}</ref>
+<ref name="leroy2007">{{cite conference | last = Leroy | first = Xavier | title = Some uses of Caml in Industry | url = http://cufp.galois.com/2007/slides/XavierLeroy.pdf | conference = CUFP 2007 | accessdate = 2009-08-26 }}</ref><ref name="haskell-industry">{{cite web | title = Haskell in industry | work = Haskell Wiki | url = http://www.haskell.org/haskellwiki/Haskell_in_industry | accessdate = 2009-08-26 | quote=Haskell has a diverse range of use commercially, from aerospace and defense, to finance, to web startups, hardware design firms and lawnmower manufacturers. }}</ref>
+<ref name="effective-scala">{{cite web | title = Effective Scala | work = Scala Wiki | url = http://twitter.github.com/effectivescala/?sd | accessdate = 2012-02-21 | quote=Effective Scala. }}</ref><ref name="racket-video-games">{{cite web | title = State-Based Scripting in Uncharted 2 | url = http://www.gameenginebook.com/gdc09-statescripting-uncharted2.pdf | accessdate = 2011-08-08 }}</ref>
+<ref name="hudak2007">{{cite conference | last = Hudak | first = Paul | coauthors = Hughes, J., Jones, S. P., and Wadler, P. | authorlink=Paul Hudak | title = A history of Haskell: being lazy with class | url=http://dl.acm.org/citation.cfm?doid=1238844.1238856 | conference = Third ACM SIGPLAN Conference on History of Programming Languages | location = San Diego, California| date = June 2007 | doi = 10.1145/1238844.1238856 | accessdate = 2013-09-26 }}</ref>
+<ref name="useR">{{cite web | url = http://www.r-project.org/useR-2006/program.html | title = The useR! 2006 conference schedule includes papers on the commercial use of R |publisher=R-project.org | date = 2006-06-08  | accessdate = 2011-06-20 }}</ref><ref name="Chambers">{{cite book | last = Chambers | first = John M. | authorlink=John Chambers (programmer) | title = Programming with Data: A Guide to the S Language | publisher=Springer Verlag | year = 1998 | pages = 67–70 | isbn = 978-0-387-98503-9 }}</ref><ref name="Amath-CO">{{cite web | author = Department of Applied Math, University of Colorado | title = Functional vs. Procedural Programming Language | url = http://amath.colorado.edu/computing/mmm/funcproc.html | accessdate = 2006-08-28 }}</ref>
+<ref name="Novatchev">{{cite web | url = http://www.topxml.com/xsl/articles/fp/ | author = Dimitre Novatchev | title = The Functional Programming Language XSLT&nbsp;— A proof through examples | accessdate = May 27, 2006 | work=TopXML }}</ref><ref name="Mertz">{{cite web | url = http://gnosis.cx/publish/programming/xml_models_fp.html | author = David Mertz | title = XML Programming Paradigms (part four): Functional Programming approached to XML processing | accessdate = May 27, 2006 | work=IBM developerWorks }}</ref>
+<ref name="Chamberlin_Boyce">{{cite journal | title = SEQUEL: A structured English query language | author = [[Donald D. Chamberlin]] and [[Raymond F. Boyce]] | journal = Proceedings of the 1974 ACM SIGFIDET | pages = 249–264 | year = 1974 }}</ref><ref name="Sim-Diasca">{{cite web | title = Sim-Diasca: a large-scale discrete event concurrent simulation engine in Erlang | url = http://research.edf.com/research-and-the-scientific-community/software/sim-diasca-80704.html |date=November 2011 }}</ref>
+<ref name="Spiewak">{{cite web | url = http://www.codecommit.com/blog/scala/implementing-persistent-vectors-in-scala | author = Pawel Spiewak | title = Implementing Persistent Vectors in Scala | accessdate = Apr 17, 2012}}</ref><ref name="Opal (programming language)">[[Opal (programming language)|OPtimized Applicative Language]]</ref>
+}}
+== Further reading ==
+* {{cite book|last1=Abelson|first1=Hal|authorlink1=Hal Abelson|last2=Sussman|first2=Gerald Jay|authorlink2=Gerald Jay Sussman | title = Structure and Interpretation of Computer Programs | url = http://mitpress.mit.edu/sicp/ | year = 1985|publisher=MIT Press}}
+* Cousineau, Guy and Michel Mauny. ''The Functional Approach to Programming''. Cambridge, UK: [[Cambridge University Press]], 1998.
+* Curry, Haskell Brooks and Feys, Robert and Craig, William. ''Combinatory Logic''. Volume I. North-Holland Publishing Company, Amsterdam, 1958.
+* {{cite book | last1 = Curry | first1 = Haskell B. | first2 = J. Roger | last2 = Hindley | first3 = Jonathan P. | last3 = Seldin | authorlink1 = Haskell Curry | authorlink2 = J. Roger Hindley | authorlink3 = Jonathan P. Seldin | title = Combinatory Logic | volume = Vol. II | year = 1972 | publisher = North Holland | location = Amsterdam | isbn = 0-7204-2208-6 }}
+* [[Mark Jason Dominus|Dominus, Mark Jason]]. ''[http://hop.perl.plover.com/book/pdf/HigherOrderPerl.pdf Higher-Order Perl]''. [[Morgan Kaufmann]]. 2005.
+* {{cite book|last1=Felleisen|first1=Matthias|last2=Findler|first2=Robert|last3=Flatt|first3=Matthew|first4=Shriram |last4=Krishnamurthi | title = How to Design Programs | url = http://www.htdp.org | year = 2001|publisher=MIT Press}}
+* Graham, Paul. ''ANSI Common LISP''. Englewood Cliffs, New Jersey: [[Prentice Hall]], 1996.
+* MacLennan, Bruce J. ''Functional Programming: Practice and Theory''. Addison-Wesley, 1990.
+* {{cite book|last1=O'Sullivan|first1=Brian|last2=Stewart|first2=Don|last3=Goerzen|first3=John | title = Real World Haskell | url = http://book.realworldhaskell.org/read/ | year = 2008|publisher=O'Reilly}}
+* Pratt, Terrence, W. and Marvin V. Zelkowitz. ''Programming Languages: Design and Implementation''. 3rd ed. Englewood Cliffs, New Jersey: [[Prentice Hall]], 1996.
+* Salus, Peter H. ''Functional and Logic Programming Languages''. Vol. 4 of Handbook of Programming Languages. Indianapolis, Indiana: [[Macmillan Technical Publishing]], 1998.
+* Thompson, Simon. ''Haskell: The Craft of Functional Programming''. Harlow, England: [[Addison-Wesley Longman Limited]], 1996.
+== External links ==
+{{Spoken Wikipedia|En-Functional_programming.ogg|2011-08-25}}
+*{{Cite web
+| last = Ford
+| first = Neal
+| title = Functional thinking: Why functional programming is on the rise
+| accessdate = 2013-02-24
+| date = 2012-01-29
+| url = http://www.ibm.com/developerworks/java/library/j-ft20/index.html
+}}
+* {{Cite web
+| last = Akhmechet
+| first = Slava
+| title = defmacro – Functional Programming For The Rest of Us
+| accessdate = 2013-02-24
+| date = 2006-06-19
+| url = http://www.defmacro.org/ramblings/fp.html
+}} An introduction
+* ''Functional programming in Python'' (by David Mertz): [http://gnosis.cx/publish/programming/charming_python_13.html part 1], [http://gnosis.cx/publish/programming/charming_python_16.html part 2], [http://gnosis.cx/publish/programming/charming_python_19.html part 3]
+{{Programming language}}
+{{DEFAULTSORT:Functional programming}}
+[[Category:Programming paradigms]]
+[[Category:Functional programming| ]]

Finite-state machine: Difference between revisions

Revision as of 17:09, 18 January 2014

History

Concepts

First-class and higher-order functions

Pure functions

Recursion

Strict versus non-strict evaluation

Type systems

Functional programming in non-functional languages

Comparison to imperative programming

Simulating state

Efficiency issues

Coding styles

Haskell

Erlang

Lisp

Use in industry

See also

References

Further reading

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