A framework for defining logics
Journal of the ACM (JACM)
Computation and reasoning: a type theory for computer science
Computation and reasoning: a type theory for computer science
Higher-Order Abstract Syntax in Coq
TLCA '95 Proceedings of the Second 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
Categorical Reconstruction of a Reduction Free Normalization Proof
CTCS '95 Proceedings of the 6th International Conference on Category Theory and Computer Science
Intuitionistic model constructions and normalization proofs
Mathematical Structures in Computer Science
Memoization in Type-Directed Partial Evaluation
GPCE '02 Proceedings of the 1st ACM SIGPLAN/SIGSOFT conference on Generative Programming and Component Engineering
Normalization and Partial Evaluation
Applied Semantics, International Summer School, APPSEM 2000, Caminha, Portugal, September 9-15, 2000, Advanced Lectures
Normalization by evaluation with typed abstract syntax
Journal of Functional Programming
Operational aspects of untyped Normalisation by Evaluation
Mathematical Structures in Computer Science
Weak βη -Normalization and Normalization by Evaluation for System F
LPAR '08 Proceedings of the 15th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning
On normalization by evaluation for object calculi
TYPES'07 Proceedings of the 2007 international conference on Types for proofs and programs
Typed applicative structures and normalization by evaluation for system Fω
CSL'09/EACSL'09 Proceedings of the 23rd CSL international conference and 18th EACSL Annual conference on Computer science logic
Polymorphic abstract syntax via Grothendieck construction
FOSSACS'11/ETAPS'11 Proceedings of the 14th international conference on Foundations of software science and computational structures: part of the joint European conferences on theory and practice of software
MSFP'06 Proceedings of the 2006 international conference on Mathematically Structured Functional Programming
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We give a semantical proof that every term of a combinator version of system F has a normal form. As the argument is entirely formalisable in an impredicative constructive type theory a reduction-free normalisation algorithm can be extracted from this. The proof is presented as the construction of a model of the calculus inside a category of presheaves. Its definition is given entirely in terms of the internal language.