Realizability interpretation of generalized inductive definitions
Theoretical Computer Science
A semantics of evidence for classical arithmetic
Journal of Symbolic Logic
Towards Limit Computable Mathematics
TYPES '00 Selected papers from the International Workshop on Types for Proofs and Programs
An Arithmetical Hierarchy of the Law of Excluded Middle and Related Principles
LICS '04 Proceedings of the 19th Annual IEEE Symposium on Logic in Computer Science
Mathematics based on incremental learning: excluded middle and inductive inference
Theoretical Computer Science - Algorithmic learning theory(ALT 2002)
Can Proofs be Animated by Games?
Fundamenta Informaticae - Typed Lambda Calculi and Applications 2005, Selected Papers
Semantics for intuitionistic arithmetic based on Tarski games with retractable moves
TLCA'07 Proceedings of the 8th international conference on Typed lambda calculi and applications
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Most research of algorithm extraction from classical proofs is based on double negation translation or its variants. From the viewpoint of Curry-Howard isomorphism, double negation translation corresponds to CPS translation. Unfortunately, CPS translation makes resulting programs very complex. In this paper, we study a new translation for a semi-classical logic which is not based on double negation translation. Though it does not validate full classical logic, it translates Limit Computable Mathematics (LCM) into constructive mathematics. Our translation is inspired by game semantics with backtracking rules. Using the translation, we can extract an algorithm from a proof of a proposition A in LCM. The extracted algorithm gives a recursive winning strategy for the first mover of the game defined from A, at least when A is implication-free.