Introduction to higher order categorical logic
Introduction to higher order categorical logic
Isomorphisms of types: from &lgr;-calculus to information retrieval and language design
Isomorphisms of types: from &lgr;-calculus to information retrieval and language design
A Complete Axiom System for Isomorphism of Types in Closed Categories
LPAR '93 Proceedings of the 4th International Conference on Logic Programming and Automated Reasoning
A short survey of isomorphisms of types
Mathematical Structures in Computer Science
| Hi-index | 0.00 |
This paper presents a new and self-contained proof of a result characterizing objects isomorphic in the free symmetric monoidal closed category, i.e., objects isomorphic in every symmetric monoidal closed category. This characterization is given by a finitely axiomatizable and decidable equational calculus, which differs from the calculus that axiomatizes all arithmetical equalities in the language with 1, product and exponentiation by lacking 1c=1 and (a · b)c =ac · bc (the latter calculus characterizes objects isomorphic in the free cartesian closed category). Nevertheless, this calculus is complete for a certain arithmetical interpretation, and its arithmetical completeness plays an essential role in the proof given here of its completeness with respect to symmetric monoidal closed isomorphisms.