Information and Computation - Semantics of Data Types
Mechanical procedure for proof construction via closed terms in typed &lgr; calculus
Journal of Automated Reasoning
Higher-order unification with dependent function types
RTA-89 Proceedings of the 3rd international conference on Rewriting Techniques and Applications
A framework for defining logics
Journal of the ACM (JACM)
Unification under a mixed prefix
Journal of Symbolic Computation
From λσ to λν: a journey through calculi of explicit substitutions
POPL '94 Proceedings of the 21st ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Confluence properties of weak and strong calculi of explicit substitutions
Journal of the ACM (JACM)
A Machine-Oriented Logic Based on the Resolution Principle
Journal of the ACM (JACM)
A Lambda-Calculus `a la de Bruijn with Explicit Substitutions
PLILPS '95 Proceedings of the 7th International Symposium on Programming Languages: Implementations, Logics and Programs
Explicit Substitutions with de Bruijn's Levels
RTA '95 Proceedings of the 6th International Conference on Rewriting Techniques and Applications
RTA '96 Proceedings of the 7th International Conference on Rewriting Techniques and Applications
Lambda-Calculi with Explicit Substitutions and Composition Which Preserve Beta-Strong Normalization
ALP '96 Proceedings of the 5th International Conference on Algebraic and Logic Programming
Higher-Order Equational Unification via Explicit Substitutions
ALP '97-HOA '97 Proceedings of the 6th International Joint Conference on Algebraic and Logic Programming
A Left-Linear Variant of Lambda-Sigma
ALP '97-HOA '97 Proceedings of the 6th International Joint Conference on Algebraic and Logic Programming
Dependent Types with Explicit Substitutiuons: A Meta-theoretical development
TYPES '96 Selected papers from the International Workshop on Types for Proofs and Programs
Higher-order Unification via Explicit Substitutions
LICS '95 Proceedings of the 10th Annual IEEE Symposium on Logic in Computer Science
Confluence and Preservation of Strong Normalisation in an Explicit Substitutions Calculus
LICS '96 Proceedings of the 11th Annual IEEE Symposium on Logic in Computer Science
Constrained resolution: a complete method for higher-order logic.
Constrained resolution: a complete method for higher-order logic.
Termination Of Term Rewriting By Semantic Labelling
Fundamenta Informaticae
IJCAR '01 Proceedings of the First International Joint Conference on Automated Reasoning
A sequent calculus for type theory
CSL'06 Proceedings of the 20th international conference on Computer Science Logic
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Typed λ-terms are used as a compact and linear representation of proofs in intuitionistic logic. This is possible since the Curry-Howard isomorphism relates proof-trees with typed λ-terms. The proofs-as-terms principle can be used to verify the validity of a proof by type checking the λ term extracted from the complete proof-tree. In this paper we present a proof synthesis method for dependent-type systems where typed open terms are built incrementally at the same time as proofs are done. This way, every construction step, not just the last one, may be type checked. The method is based on a suitable calculus where substitutions as well as meta-variables are first-class objects. Copyright 2001 Elsevier Science B.V.