Introduction to higher order categorical logic
Introduction to higher order categorical logic
Introduction to combinators and &lgr;-calculus
Introduction to combinators and &lgr;-calculus
The definition of Standard ML
Programming in Martin-Lo¨f's type theory: an introduction
Programming in Martin-Lo¨f's type theory: an introduction
Telescopic mappings in typed lambda calculus
Information and Computation
Metacircularity in the polymorphic &lgr;-calculus
TAPSOFT '89 2nd international joint conference on Theory and practice of software development
Denotational Semantics: The Scott-Strachey Approach to Programming Language Theory
Denotational Semantics: The Scott-Strachey Approach to Programming Language Theory
Program Extraction from Normalization Proofs
TLCA '93 Proceedings of the International Conference on Typed Lambda Calculi and Applications
CSL '92 Selected Papers from the Workshop on Computer Science Logic
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
Semantic analysis of normalisation by evaluation for typed lambda calculus
Proceedings of the 4th ACM SIGPLAN international conference on Principles and practice of declarative programming
Higher-Order and Symbolic Computation
Memoization in Type-Directed Partial Evaluation
GPCE '02 Proceedings of the 1st ACM SIGPLAN/SIGSOFT conference on Generative Programming and Component Engineering
Type-Directed Partial Evaluation
Partial Evaluation - Practice and Theory, DIKU 1998 International Summer School
Proceedings of the ESPRIT Working Group 8533 on Prospects for Hardware Foundations: NADA - New Hardware Design Methods, Survey Chapters
Formalising Formulas-as-Types-as-Objects
TYPES '99 Selected papers from the International Workshop on Types for Proofs and Programs
Normalization and Partial Evaluation
Applied Semantics, International Summer School, APPSEM 2000, Caminha, Portugal, September 9-15, 2000, Advanced Lectures
Reduction-free normalisation for a polymorphic system
LICS '96 Proceedings of the 11th Annual IEEE Symposium on Logic in Computer Science
Term rewriting for normalization by evaluation
Information and Computation - Special issue: ICC '99
A symmetric approach to compilation and decompilation
The essence of computation
Normalization and the Yoneda embedding
Mathematical Structures in Computer Science
Normalization by evaluation with typed abstract syntax
Journal of Functional Programming
Operational aspects of untyped Normalisation by Evaluation
Mathematical Structures in Computer Science
Journal of Functional Programming
A Context-based Approach to Proving Termination of Evaluation
Electronic Notes in Theoretical Computer Science (ENTCS)
Context-based proofs of termination for typed delimited-control operators
PPDP '09 Proceedings of the 11th ACM SIGPLAN conference on Principles and practice of declarative programming
Program Extraction From Proofs of Weak Head Normalization
Electronic Notes in Theoretical Computer Science (ENTCS)
Normalization by evaluation for the computational lambda-calculus
TLCA'01 Proceedings of the 5th international conference on Typed lambda calculi and applications
A new one-pass transformation into monadic normal form
CC'03 Proceedings of the 12th international conference on Compiler construction
On normalization by evaluation for object calculi
TYPES'07 Proceedings of the 2007 international conference on Types for proofs and programs
A formalisation of a dependently typed language as an inductive-recursive family
TYPES'06 Proceedings of the 2006 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
Representing model theory in a type-theoretical logical framework
Theoretical Computer Science
Towards a formal semantics for a structurally dynamic noncausal modelling language
TLDI '12 Proceedings of the 8th ACM SIGPLAN workshop on Types in language design and implementation
PADL'10 Proceedings of the 12th international conference on Practical Aspects of Declarative Languages
MSFP'06 Proceedings of the 2006 international conference on Mathematically Structured Functional Programming
New equations for neutral terms: a sound and complete decision procedure, formalized
Proceedings of the 2013 ACM SIGPLAN workshop on Dependently-typed programming
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The traditional notions of strong and weak normalization refer to properties of a binary reduction relation. In this paper we explore an alternative approach to normalization, in which we bypass the reduction relation and instead focus on the normalization function, that is, the function that maps a term to its normal form. We work in an intuitionistic metalanguage, and characterize a normalization function as an algorithm that picks a canonical representative from the equivalence class of convertible terms. This means that we also get a decision algorithm for convertibility. Such a normalization function can be constructed by building an appropriate model and a function quote, which inverts the interpretation function. The normalization function is then obtained by composing the quote function with the interpretation function. We also discuss how to get a simple proof of the property that constructors are one-to-one, which is usually obtained as a corollary of Church–Rosser and normalization in the traditional sense. We illustrate this approach by showing how a glueing model (closely related to the glueing construction used in category theory) gives rise to a normalization algorithm for a combinatory formulation of Gödel System T. We then show how the method extends in a straightforward way when we add cartesian products and disjoint unions (full intuitionistic propositional logic under a Curry–Howard interpretation) and transfinite inductive types such as the Brouwer ordinals.