Efficient Exhaustive Generation of Functional Programs Using Monte-Carlo Search with Iterative Deepening
Genetic programming and inductive synthesis of functional programs are two major approaches to inductive functional programming. Recently, in addition to them, some researchers pursue efficient exhaustive program generation algorithms, partly for the purpose of providing a comparator and knowing how essential the ideas such as heuristics adopted by those major approaches are, partly expecting that approaches that exhaustively generate programs with the given type and pick up those which satisfy the given specification may do the task well. In exhaustive program generation, since the number of programs exponentially increases as the program size increases, the key to success is how to restrain the exponential bloat by suppressing semantically equivalent but syntactically different programs. In this paper we propose an algorithm applying random testing of program equivalences (or Monte-Carlo search for functional differences) to the search results of iterative deepening, by which we can totally remove redundancies caused by semantically equivalent programs. Our experimental results show that applying our algorithm to subexpressions during program generation remarkably reduces the computational costs when applied to rich primitive sets.
KeywordsGenetic Programming Random Testing Program Generation Hypothesis Space Intuitionistic Propositional Logic
Unable to display preview. Download preview PDF.
- 3.Schmid, U.: Inductive Synthesis of Functional Programs – Learning Domain-Specific Control Rules and Abstract Schemes. Springer, Heidelberg (2001); Habilitation thesisGoogle Scholar
- 4.Kitzelmann, E.: Data-driven induction of recursive functions from input/output-examples. In: AAIP 2007: Proceedings of the Workshop on Approaches and Applications of Inductive Programming, pp. 15–26 (2007)Google Scholar
- 6.Katayama, S.: Library for systematic search for expressions and its efficiency evaluation. WSEAS Transactions on Computers 12(5), 3146–3153 (2006)Google Scholar
- 7.Katayama, S.: Systematic search for lambda expressions. In: Trends in Functional Programming, Intellect, vol. 6, pp. 111–126 (2007)Google Scholar
- 8.Claessen, K., Hughes, J.: QuickCheck: a lightweight tool for random testing of Haskell programs. In: ICFP 2000: Proceedings of the 5th ACM SIGPLAN International Conference on Functional Programming, pp. 268–279. ACM, New York (2000)Google Scholar
- 10.Spivey, M.: Algebras for combinatorial search. In: Workshop on Mathematically Structured Functional Programming (2006)Google Scholar
- 12.Dyckhoff, R.: Contraction-free sequent calculi for intuitionistic logic. Journal of Symbolic Logic, 795–807 (1992)Google Scholar
- 13.Katayama, S.: MagicHaskeller (2005), http://nautilus.cs.miyazaki-u.ac.jp/~skata/MagicHaskeller.html