Information and Computation - Semantics of Data Types
Computational foundations of basic recursive function theory
Theoretical Computer Science - A collection of contributions in honour of Corrado Bo¨hm on the occasion of his 70th birthday
Structural Recursive Definitions in Type Theory
ICALP '98 Proceedings of the 25th International Colloquium on Automata, Languages and Programming
Codifying Guarded Definitions with Recursive Schemes
TYPES '94 Selected papers from the International Workshop on Types for Proofs and Programs
TYPES '00 Selected papers from the International Workshop on Types for Proofs and Programs
Simple general recursion in type theory
Nordic Journal of Computing
Partial Objects in Type Theory
Partial Objects in Type Theory
Verifying haskell programs using constructive type theory
Proceedings of the 2005 ACM SIGPLAN workshop on Haskell
Proceedings of the 2005 ACM SIGPLAN workshop on Haskell
Defining and reasoning about recursive functions: a practical tool for the coq proof assistant
FLOPS'06 Proceedings of the 8th international conference on Functional and Logic Programming
Fixed point semantics and partial recursion in Coq
Proceedings of the 10th international ACM SIGPLAN conference on Principles and practice of declarative programming
A Type of Partial Recursive Functions
TPHOLs '08 Proceedings of the 21st International Conference on Theorem Proving in Higher Order Logics
Algebra of programming in agda: Dependent types for relational program derivation
Journal of Functional Programming
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This paper develops machinery necessary to mechanically import arbitrary functional programs into Coq's type theory, manually strengthen their specifications with additional proofs, and then mechanicaly re-extracting the newly-certified program in a form which is as efficient as the original program. In order to facilitate this goal, the coinductive technique of[Capretta2005] is modified to form a monad whose operators are the constructors of a coinductive type rather than functions defined over the type. The inductive invariant technique of [Krstic2003] is extended to allow optional "after the fact" termination proofs. These proofs inhabit members of Prop, and therefore do not affect extracted code. Compared to [Capretta2005], the new monad makes it possible to directly represent unrestricted recursion without violating productivity requirements [Gimenez1995], and it produces efficient code via Coq's extraction mechanism. The disadvantages of this technique include reliance on the JMeq axiom [McBride2000] and a significantly more complex notion of equality. The resulting technique is packaged as a Coq library, and is suitable for formalizing programs written in any side-effect-free functional language with call-by-value semantics. It can be downloaded from: http://www.cs.berkeley.edu/~megacz/computation.