A Formal Proof of Square Root and Division Elimination in Embedded Programs
| Autor: | Pierre Neron |
|---|---|
| Rok vydání: | 2012 |
| Předmět: |
Theoretical computer science
Computer science Proof assistant Program transformation 0102 computer and information sciences 02 engineering and technology Division (mathematics) 01 natural sciences Formal proof Transformation (function) Square root 010201 computation theory & mathematics 0202 electrical engineering electronic engineering information engineering Computer Science::Programming Languages 020201 artificial intelligence & image processing Multiplication Real number |
| Zdroj: | Certified Programs and Proofs ISBN: 9783642353079 CPP |
| Popis: | The use of real numbers in a program can introduce differences between the expected and the actual behavior of the program, due to the finite representation of these numbers. Therefore, one may want to define programs using real numbers such that this difference vanishes. This paper defines a program transformation for a certain class of programs that improves the accuracy of the computations on real number representations by removing the square root and division operations from the original program in order to enable exact computation with addition, multiplication and subtraction. This transformation is meant to be used on embedded systems, therefore the produced programs have to respect constraints relative to this kind of code. In order to ensure that the transformation is correct, i.e., preserves the semantics, we also aim at specifying and proving this transformation using the PVS proof assistant. |
| Databáze: | OpenAIRE |
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