Journal of Automated Reasoning
Program Extraction from Normalization Proofs
TLCA '93 Proceedings of the International Conference on Typed Lambda Calculi and Applications
A Formalization of the Strong Normalization Proof for System F in LEGO
TLCA '93 Proceedings of the International Conference on Typed Lambda Calculi and Applications
From Semantics to Rules: A Machine Assisted Analysis
CSL '93 Selected Papers from the 7th Workshop on Computer Science Logic
Program extraction in simply-typed higher order logic
TYPES'02 Proceedings of the 2002 international conference on Types for proofs and programs
TYPES'02 Proceedings of the 2002 international conference on Types for proofs and programs
Isabelle/HOL: a proof assistant for higher-order logic
Isabelle/HOL: a proof assistant for higher-order logic
Mechanized metatheory for the masses: the PoplMark challenge
TPHOLs'05 Proceedings of the 18th international conference on Theorem Proving in Higher Order Logics
Implementing a normalizer using sized heterogeneous types
Journal of Functional Programming
Implementing a normalizer using sized heterogeneous types
MSFP'06 Proceedings of the 2006 international conference on Mathematically Structured Functional Programming
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We present a formalization of a constructive proof of weak normalization for the simply-typed λ-calculus in the theorem prover Isabelle/HOL, and show how a program can be extracted from it. Unlike many other proofs of weak normalization based on Tait's strong computability predicates, which require a logic supporting strong eliminations and can give rise to dependent types in the extracted program, our formalization requires only relatively simple proof principles. Thus, the program obtained from this proof is typable in simply-typed higher-order logic as implemented in Isabelle/HOL, and a proof of its correctness can automatically be derived within the system.