Logic for computer science: foundations of automatic theorem proving
Logic for computer science: foundations of automatic theorem proving
Implementing mathematics with the Nuprl proof development system
Implementing mathematics with the Nuprl proof development system
Constructing recursion operators in intuitionistic type theory
Journal of Symbolic Computation
Automating reasoning in an implementation of constructive type theory
Automating reasoning in an implementation of constructive type theory
The logical basis for computer programming: vol. 2, deductive systems
The logical basis for computer programming: vol. 2, deductive systems
Program development in constructive type theory
Theoretical Computer Science - Special issue on discrete mathematics and applications to computer science
Recursive programming with proofs
Theoretical Computer Science - Special issue on discrete mathematics and applications to computer science
Enhancing the NUPRL proof development system and applying it to computational abstract algebra
Enhancing the NUPRL proof development system and applying it to computational abstract algebra
Formal Methods Technology Transfer: A View from NASA
Formal Methods in System Design - Special issue: industrial critical systems
Fix-Point Equations for Well-Founded Recursion in Type Theory
TPHOLs '00 Proceedings of the 13th International Conference on Theorem Proving in Higher Order Logics
Nested General Recursion and Partiality in Type Theory
TPHOLs '01 Proceedings of the 14th International Conference on Theorem Proving in Higher Order Logics
Intuitionistic Tableau Extracted
TABLEAUX '99 Proceedings of the International Conference on Automated Reasoning with Analytic Tableaux and Related Methods
Reasoning About Functional Programs in Nuprl
Functional Programming, Concurrency, Simulation and Automated Reasoning: International Lecture Series 1991-1992, McMaster University, Hamilton, Ontario, Canada
Safe Proof Checking in Type Theory with Y
CSL '99 Proceedings of the 13th International Workshop and 8th Annual Conference of the EACSL on Computer Science Logic
A Certified Version of Buchberger's Algorithm
CADE-15 Proceedings of the 15th International Conference on Automated Deduction: Automated Deduction
Simple general recursion in type theory
Nordic Journal of Computing
Moving proofs-as-programs into practice
ASE '97 Proceedings of the 12th international conference on Automated software engineering (formerly: KBSE)
A non-type-theoretic semantics for type-theoretic language
A non-type-theoretic semantics for type-theoretic language
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Nuprl supports program synthesis by extracting programs from proofs. In this paper we describe the extraction of "efficient" recursion schemes from proofs of well-founded induction principles. This is part of a larger methodology; when these well-founded induction principles are used in proofs, the structure of the program extracted from the proof is determined by the recursion scheme inhabiting the induction principle. Our development is based on Paulson's paper Constructing recursion operators in intuitionistic type theory, but we specifically address two possibilities raised in the conclusion of his paper: the elimination of non-computational content from the recursion schemes themselves and, the use of the Y combinator to allow the recursion schemes to be extracted directly from the proofs of well-founded relations.