A simple semantics for ML polymorphism

Research output: Chapter in Book/Report/Conference proceedingConference contribution

22 Citations (Scopus)

Abstract

We give a framework for denotational semantics for the polymorphic "core" of the programming language ML. This framework requires no more semantic material than what is needed for modeling the simple type discipline. In our view, terms of ML are pairs consisting of a raw (untyped) lambda term and a type-scheme that ML's type inference system can derive for the raw term. We interpret a type-scheme as a set of simple types. Then, given any model M of the simply typed lambda calculus, the meaning of an ML term will be a set of pairs, each consisting of a simple type r and an element of M of type T. Hence, there is no need to interpret all raw terms, as was done in Milner's original semantic framework. In comparison to Mitchell and Harper's analysis, we avoid having to provide a very large type universe in which generic type-schemes are interpreted. Also, we show how to give meaning to ML terms rather than to derivations in the ML type inference system (which can be infinitely many for a single ML term). We give an axiomatization for the equational theory that corresponds to our semantic framework and prove the analogs of the completeness theorems that Friedman proved for the simply typed lambda calculus. The framework can be extended to languages with constants, type constructors and recursive types (via regular trees). For the extended language, we prove a theorem that allows the transfer of certain full abstraction results from languages based on the typed lambda calculus to ML-like languages.

Original languageEnglish
Title of host publicationProceedings of the 4th International Conference on Functional Programming Languages and Computer Architecture, FPCA 1989
PublisherAssociation for Computing Machinery, Inc
Pages281-292
Number of pages12
ISBN (Electronic)0897913280, 9780897913287
DOIs
Publication statusPublished - 1989 Nov 1
Externally publishedYes
Event4th International Conference on Functional Programming Languages and Computer Architecture, FPCA 1989 - London, United Kingdom
Duration: 1989 Sep 111989 Sep 13

Publication series

NameProceedings of the 4th International Conference on Functional Programming Languages and Computer Architecture, FPCA 1989

Other

Other4th International Conference on Functional Programming Languages and Computer Architecture, FPCA 1989
CountryUnited Kingdom
CityLondon
Period89/9/1189/9/13

ASJC Scopus subject areas

  • Computer Science(all)

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