Teichmüller space: Difference between revisions

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In [[compiler theory]], a '''reaching definition''' for a given instruction is another instruction, the target variable of which may reach the given instruction without an intervening assignment. For example, in the following code:
Of course plants include a variety of leafy greens, nuts, seeds, fruits, roots, and other wild vegetables. This diet program consists largely of meat, fruit, greens, nuts and seeds. Doctors and scientists used to think that it was a simple matter of people eating too many calories and fat and so gaining weight. However there's also numerous food items that may be consumed and loved. Mother Natures Diet Recipes macro-nutrition for Breakfast, Lunch and Dinner. <br><br>Enjoy Paleo baking recipes  wheat flour has to be substituted with gluten free and soy free friendly alternative flours. There are many unique salads but the main thing meals are prepared fresh containing no preservatives. Fitness expert Ben Greenfield trained for the 2013 Ironman Triathlon World Championships in Kona, Hawaii by following a high-fat, low-carb ketogenic diet and completed the epic endurance race in a blistering 9:59:26. These benefits could expand the health claims now permitted to be identified by the FDA. Somersizing taught me a lot about the digestive system, as well as how to adjust my diet in a way that 'worked with my body. <br><br>The idea behind the Paleo Diet is that ancient people ate natural foods, and were leaner and healthier than we are today, with our myriad of modern diseases such as obesity, diabetes, heart disease and cancer. Meals such as grilled or roasted pork, beef and chicken along with broccoli, carrots and sweet potatoes are part of the Paleo diet. Both fruit and veggies contain a number of vitamins. You might know, I arrived so close to giving up now this healthy diet. The process of preparing this type of apparently complicated checking seafood dinner is not that mind dazzling. <br><br>Still, he said that's better than his previously sedentary lifestyle of couch-surfing and boozing. The Paleo diet has additional food restrictions that encourages optimal long term health. And, of course, a complicit media regurgitates these nonsensical studies, reports and findings without any alternative viewpoints or meaningful investigation. Also the time frame in which you lose weight is typically much longer than that of the 24 Day Challenge. Results from most diets take a great deal of time, but not with this plan. <br><br>Or at least the leftover carcass of a wolf-pack kill. Another good thing is that few people really eat a good variety of fresh fruit. Try drying them out if you can't use all of them or buy some of the potted plants that you can keep for a long time. The occurrence of diabetes, for example, is almost unknown to aboriginal people even now who naturally follow this sort of diet. No wonder that anti obesity solutions form a billion dollar business worldwide. <br><br>Allen, 39, came back from the summer break in significantly better shape than he was the previous year after adopting a low-carb, sugar-free Paleo diet. Here are some items that you will surely love about this. However, there are some exceptions, along with some specific foods that this diet is centered around; furthermore, it is crucial to stick to these foods. After all, if the animals have been consuming processed foods, then you won't get the levels of protein that you are looking for. Some of the most devoted Paleolithic adherents also adopt a workout regimen that is thought to be based more closely on the workouts of our ancestors.<br><br>If you have any kind of questions relating to where and how to utilize [http://gritsandgroceries.info/ easy paleo crock pot recipes], you could contact us at our own internet site.
 
d1 : y := 3
d2 : x := y
 
<code>d1</code> is a reaching definition at <code>d2</code>. In the following, example, however:
 
d1 : y := 3
d2 : y := 4
d3 : x := y
 
<code>d1</code> is no longer a reaching definition at <code>d3</code>, because <code>d2</code> kills its reach.
 
== As analysis ==
 
The similarly named '''reaching definitions''' is a [[data-flow analysis]] which statically determines which definitions may reach a given point in the code. Because of its simplicity, it is often used as the canonical example of a data-flow analysis in textbooks. The [[data-flow confluence operator]] used is set union, and the analysis is forward flow. Reaching definitions are used to compute [[use-def chain]]s and [[def-use chain]]s.
 
The data-flow equations used for a given basic block <math>S</math> in reaching definitions are:
 
* <math>{\rm REACH}_{\rm in}[S] = \bigcup_{p \in pred[S]} {\rm REACH}_{\rm out}[p]</math>
* <math>{\rm REACH}_{\rm out}[S] = {\rm GEN}[S] \cup ({\rm REACH}_{\rm in}[S] - {\rm KILL}[S])</math>
 
In other words, the set of reaching definitions going into <math>S</math> are all of the reaching definitions from <math>S</math>'s predecessors, <math>pred[S]</math>. <math>pred[S]</math> consists of all of the basic blocks that come before <math>S</math> in the [[control flow graph]]. The reaching definitions coming out of <math>S</math> are all reaching definitions of its predecessors minus those reaching definitions whose variable is killed by <math>S</math> plus any new definitions generated within <math>S</math>.
 
For a generic instruction, we define the <math>{\rm GEN}</math> and <math>{\rm KILL}</math> sets as follows:
 
* <math>{\rm GEN}[d : y \leftarrow f(x_1,\cdots,x_n)] = \{d\}</math>
* <math>{\rm KILL}[d : y \leftarrow f(x_1,\cdots,x_n)] = {\rm DEFS}[y] - \{d\}</math>
 
where <math>{\rm DEFS}[y]</math> is the set of all definitions that assign to the variable <math>y</math>. Here <math>d</math> is a unique label attached to the assigning instruction; thus, the domain of values in reaching definitions are these instruction labels.
 
== Further reading ==
*{{cite book
|author=Aho, Alfred V.; Sethi, Ravi; & Ullman, Jeffrey D.
|title=[[Compilers: Principles, Techniques, and Tools]]
|publisher=Addison Wesley
|year=1986
|isbn=0-201-10088-6}}
*{{cite book
|author=Appel, Andrew W.
|title=Modern Compiler Implementation in ML
|publisher=Cambridge University Press
|year=1999
|isbn=0-521-58274-1}}
*{{cite book
|author=Cooper, Keith D.; & Torczon, Linda.
|title=Engineering a Compiler
|publisher=Morgan Kaufmann
|year=2005
|isbn=1-55860-698-X}}
*{{cite book
|author=Muchnick, Steven S.
|title=Advanced Compiler Design and Implementation
|publisher=Morgan Kaufmann
|year=1997
|isbn=1-55860-320-4}}
 
== See also ==
 
*[[Static single assignment form]]
 
[[Category:Program analysis]]
[[Category:Data-flow analysis]]

Latest revision as of 14:32, 10 January 2015

Of course plants include a variety of leafy greens, nuts, seeds, fruits, roots, and other wild vegetables. This diet program consists largely of meat, fruit, greens, nuts and seeds. Doctors and scientists used to think that it was a simple matter of people eating too many calories and fat and so gaining weight. However there's also numerous food items that may be consumed and loved. Mother Natures Diet Recipes macro-nutrition for Breakfast, Lunch and Dinner.

Enjoy Paleo baking recipes wheat flour has to be substituted with gluten free and soy free friendly alternative flours. There are many unique salads but the main thing meals are prepared fresh containing no preservatives. Fitness expert Ben Greenfield trained for the 2013 Ironman Triathlon World Championships in Kona, Hawaii by following a high-fat, low-carb ketogenic diet and completed the epic endurance race in a blistering 9:59:26. These benefits could expand the health claims now permitted to be identified by the FDA. Somersizing taught me a lot about the digestive system, as well as how to adjust my diet in a way that 'worked with my body.

The idea behind the Paleo Diet is that ancient people ate natural foods, and were leaner and healthier than we are today, with our myriad of modern diseases such as obesity, diabetes, heart disease and cancer. Meals such as grilled or roasted pork, beef and chicken along with broccoli, carrots and sweet potatoes are part of the Paleo diet. Both fruit and veggies contain a number of vitamins. You might know, I arrived so close to giving up now this healthy diet. The process of preparing this type of apparently complicated checking seafood dinner is not that mind dazzling.

Still, he said that's better than his previously sedentary lifestyle of couch-surfing and boozing. The Paleo diet has additional food restrictions that encourages optimal long term health. And, of course, a complicit media regurgitates these nonsensical studies, reports and findings without any alternative viewpoints or meaningful investigation. Also the time frame in which you lose weight is typically much longer than that of the 24 Day Challenge. Results from most diets take a great deal of time, but not with this plan.

Or at least the leftover carcass of a wolf-pack kill. Another good thing is that few people really eat a good variety of fresh fruit. Try drying them out if you can't use all of them or buy some of the potted plants that you can keep for a long time. The occurrence of diabetes, for example, is almost unknown to aboriginal people even now who naturally follow this sort of diet. No wonder that anti obesity solutions form a billion dollar business worldwide.

Allen, 39, came back from the summer break in significantly better shape than he was the previous year after adopting a low-carb, sugar-free Paleo diet. Here are some items that you will surely love about this. However, there are some exceptions, along with some specific foods that this diet is centered around; furthermore, it is crucial to stick to these foods. After all, if the animals have been consuming processed foods, then you won't get the levels of protein that you are looking for. Some of the most devoted Paleolithic adherents also adopt a workout regimen that is thought to be based more closely on the workouts of our ancestors.

If you have any kind of questions relating to where and how to utilize easy paleo crock pot recipes, you could contact us at our own internet site.

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