Catalan's conjecture: Difference between revisions

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{{distinguish|Partial application}}
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{{more footnotes|date=May 2013}}
{{Programming evaluation}}
In [[computing]], '''partial evaluation''' is a technique for several different types of [[optimization (computer science)|program optimization]] by [[Specialization (logic)|specialization]]. The most straightforward application is to produce new programs which run faster than the originals while being guaranteed to behave in the same way.
 
A [[computer program]], ''prog'', is seen as a [[map (mathematics)|map]]ping of input data into output data:
:<math>prog : I_{static} \times I_{dynamic} \to O</math>
 
<math>I_{static}</math>, the ''static data'', is the part of the input data known at compile time.
 
The partial evaluator transforms <math>\langle prog, I_{static}\rangle</math>
into <math>prog^* : I_{dynamic} \to O</math> by precomputing all static input at compile time. <math>prog^*</math> is called the "residual program" and should run more efficiently than the original program. The act of partial evaluation is said to "residualize" <math>prog</math> to <math>prog^*</math>.
 
== Futamura projections ==
A particularly interesting example of this, first described in the 1970s by [[Yoshihiko Futamura]],<ref>[http://fi.ftmr.info/ Yoshihiko Futamura's Website]</ref> is when ''prog'' is an interpreter for a programming language.
 
If I<sub>static</sub> is source code designed to run inside said interpreter, then partial evaluation of the interpreter with respect to this data/program produces ''prog*'', a version of the interpreter that only runs that source code, is written in the implementation language of the interpreter, does not require the source code to be resupplied, and runs faster than the original combination of the interpreter and the source. In this case prog* is effectively a compiled version of I<sub>static</sub>.
 
This technique is known as the first Futamura projection, of which there are three:
 
#Specializing an interpreter for given source code, yielding an executable
#Specializing the specializer for the interpreter (as applied in #1), yielding a compiler
#Specializing the specializer for itself (as applied in #2), yielding a tool that can convert any interpreter to an equivalent compiler
 
==See also==
* [[Run-time algorithm specialisation]]
* [[Partial application]]
* [[Memoization]]
* [[Strength reduction]]
* [[Smn theorem]]
* [[Template metaprogramming]]
* [[PyPy]]
 
== References ==
* Yoshihiko Futamura, http://www.brics.dk/~hosc/local/HOSC-12-4-pp381-391.pdf Partial Evaluation of Computation Process &ndash; An Approach to a Compiler-Compiler
<!-- |journal=Systems, Computers, Controls|volume=2|issue=5|pages=45&ndash;50|year=1971}}  Reprinted in ''Higher-Order and Symbolic Computation'' '''12''' (4): 381&ndash;391, 1999, with a foreword. -->
{{reflist}}
* {{cite journal|author=Charles Consel and [[Olivier Danvy]]|title=Tutorial Notes on Partial Evaluation|journal=Proceedings of the Twentieth Annual ACM Symposium on Principles of Programming Languages|pages=493&ndash;501|year=1993}}
 
== External links ==
* [http://www.itu.dk/people/sestoft/pebook/ Neil D. Jones, Carsten K. Gomard, and Peter Sestoft: ''Partial Evaluation and Automatic Program Generation'' (1993)] Book, full text available online.
* [http://partial-eval.org partial-eval.org] - a large "Online Bibliography of Partial Evaluation Research".
* [http://www.brics.dk/~pepm99/ 1999 ACM SIGPLAN Workshop on Partial Evaluation and Semantics-Based Program Manipulation (PEPM'99)]
* [http://osl.iu.edu/~tveldhui/papers/pepm99/ C++ Templates as Partial Evaluation, 1999 ACM SIGPLAN Workshop on Partial Evaluation and Semantics-Based Program Manipulation (PEPM'99)]
* [http://arxiv.org/pdf/cs.PL/9810010 C++ Templates as Partial Evaluation] a different version including Catat (pdf)
* [http://people.csail.mit.edu/gregs/dynamic-pe.html Applying Dynamic Partial Evaluation to  dynamic, reflective programming languages]
 
{{DEFAULTSORT:Partial Evaluation}}
[[Category:Compiler optimizations]]
[[Category:Incremental computing]]
[[Category:Evaluation strategy]]

Latest revision as of 23:03, 19 March 2014

Hello. Let me introduce the writer. Her title is Refugia Shryock. Minnesota has always been his house but his spouse desires them to move. Managing people is what I do and the wage has been really fulfilling. To play baseball is the pastime he will by no means quit performing.

Feel free to surf to my weblog ... topbuddies.com