Provable isomorphisms and domain equations in models of typed languages
STOC '85 Proceedings of the seventeenth annual ACM symposium on Theory of computing
Principal type scheme and unification for intersection type discipline
Theoretical Computer Science - International Joint Conference on Theory and Practice of Software Development, P
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
Classical isomorphisms of types
Mathematical Structures in Computer Science
Intersection-types à la Church
Information and Computation
A typed lambda calculus with intersection types
Theoretical Computer Science
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The study of type isomorphisms for different λ-calculi started over twenty years ago, and a very wide body of knowledge has been established, both in terms of results and in terms of techniques. A notable missing piece of the puzzle was the characterization of type isomorphisms in the presence of intersection types. While, at first thought, this may seem to be a simple exercise, it turns out that not only finding the right characterization is not simple, but that the very notion of isomorphism in intersection types is an unexpectedly original element in the previously known landscape, breaking most of the known properties of isomorphisms of the typed λ-calculus. In particular, isomorphism is not a congruence and types that are equal in the standard models of intersection types may be nonisomorphic.