The "Relevance" of Intersection and Union Types

Notre Dame Journal of Formal Logic 38 (2):246-269 (1997)

Abstract

The aim of this paper is to investigate a Curry-Howard interpretation of the intersection and union type inference system for Combinatory Logic. Types are interpreted as formulas of a Hilbert-style logic L, which turns out to be an extension of the intuitionistic logic with respect to provable disjunctive formulas (because of new equivalence relations on formulas), while the implicational-conjunctive fragment of L is still a fragment of intuitionistic logic. Moreover, typable terms are translated in a typed version, so that --typed combinatory logic terms are proved to completely codify the associated logical proofs

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References found in this work

A Propositional Calculus with Denumerable Matrix.Michael Dummett - 1959 - Journal of Symbolic Logic 24 (2):97-106.
The Semantics of Entailment — III.Richard Routley & Robert K. Meyer - 1972 - Journal of Philosophical Logic 1 (2):192 - 208.
Concerning Formulas of the Types a →B ∨C, a →(Ex)B(X).Ronald Harrop - 1960 - Journal of Symbolic Logic 25 (1):27-32.
Algebraic Analysis of Entailment I.Robert K. Meyer & Richard Routley - 1972 - Logique Et Analyse 15 (59/60):407-428.
Domain Theory in Logical Form.Samson Abramsky - 1991 - Annals of Pure and Applied Logic 51 (1-2):1-77.

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Citations of this work

The Emptiness Problem for Intersection Types.Paweł Urzyczyn - 1999 - Journal of Symbolic Logic 64 (3):1195-1215.

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