Proofs and types
A rewriting system for categorical combinators with multiple arguments
SIAM Journal on Computing
On ground-confluence of term rewriting systems
Information and Computation
Computational aspects of an order-sorted logic with term declarations
Computational aspects of an order-sorted logic with term declarations
A framework for defining logics
Journal of the ACM (JACM)
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
Categorical abstract machines for higher-order typed &lgr;-calculi
MFPS '92 Selected papers of the meeting on Mathematical foundations of programming semantics. Part II : lambda calculus and domain theory: lambda calculus and domain theory
Confluence properties of weak and strong calculi of explicit substitutions
Journal of the ACM (JACM)
The Barendregt cube with definitions and generalised reduction
Information and Computation
Pure Type Systems with Definitions
LFCS '94 Proceedings of the Third International Symposium on Logical Foundations of Computer Science
Typed lambda-calculi with explicit substitutions may not terminate
TLCA '95 Proceedings of the Second International Conference on Typed Lambda Calculi and Applications
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
A short and flexible proof of Strong Normalization for the Calculus of Constructions
TYPES '94 Selected papers from the International Workshop on Types for Proofs 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
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
Strong Normalization of Explicit Substitutions via Cut Elimination in Proof Nets
LICS '97 Proceedings of the 12th Annual IEEE Symposium on Logic in Computer Science
Termination Of Term Rewriting By Semantic Labelling
Fundamenta Informaticae
ACM Transactions on Computational Logic (TOCL)
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We present a dependent-type system for a λ-calculus with explicit substitutions. In this system, meta-variables, as well as substitutions, are first-class objects. We show that the system enjoys properties like type uniqueness, subject reduction, soundness, confluence, and weak normalization.