Information and Computation - Semantics of Data Types
Handbook of logic in computer science (vol. 2)
Checking algorithms for pure type systems
TYPES '93 Proceedings of the international workshop on Types for proofs and programs
Explicit substitution on the edge of strong normalization
Theoretical Computer Science
Permutability of proofs in intuitionistic sequent calculi
Theoretical Computer Science - Special issue: Gentzen
Proof-term synthesis on dependent-type systems via explicit substitutions
Theoretical Computer Science
A Lambda-Calculus Structure Isomorphic to Gentzen-Style Sequent Calculus Structure
CSL '94 Selected Papers from the 8th International Workshop on Computer Science Logic
Pure type systems with explicit substitution
Mathematical Structures in Computer Science
Expansion postponement for normalising pure type systems
Journal of Functional Programming
Continuation-passing style and strong normalisation for intuitionistic sequent calculi
TLCA'07 Proceedings of the 8th international conference on Typed lambda calculi and applications
The theory of calculi with explicit substitutions revisited
CSL'07/EACSL'07 Proceedings of the 21st international conference, and Proceedings of the 16th annuall conference on Computer Science Logic
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Based on natural deduction, Pure Type Systems (PTS) can express a wide range of type theories. In order to express proof-search in such theories, we introduce the Pure Type Sequent Calculi (PTSC) by enriching a sequent calculus due to Herbelin, adapted to proof-search and strongly related to natural deduction. PTSC are equipped with a normalisation procedure, adapted from Herbelin’s and defined by local rewrite rules as in Cut-elimination, using explicit substitutions. It satisfies Subject Reduction and it is confluent. A PTSC is logically equivalent to its corresponding PTS, and the former is strongly normalising if and only if the latter is. We show how the conversion rules can be incorporated inside logical rules (as in syntax-directed rules for type checking), so that basic proof-search tactics in type theory are merely the root-first application of our inference rules.