Algorithmic aspects of type-based program synthesis release_eizzv5sgwrgl3os5bal27h437q

by Andrej Dudenhefner, Technische Universität Dortmund, Technische Universität Dortmund

Published by Technische Universität Dortmund.

2019  

Abstract

In the area of type-based program synthesis, the decision problem of inhabitation (given a type environment Gamma and a type tau, is there a term M such that M can be assigned the type tau in Gamma?) corresponds to existence of a program (term M) that satisfies the given specification (type tau) under additional assumptions (type environment Gamma). Inhabitation in typed lambda-calculi can be seen as functional program synthesis from scratch. Complementarily, inhabitation in combinatory logic can be seen as domain-specific program synthesis. Further restrictions on inhabitant search, such as principality and relevance restrictions, yield inhabitants that are more closely tied to given specifications. Alternatively, dimension, rank, order, and arity restrictions provide means to control the complexity of inhabitant search. This work provides an overview over following results in type-based program synthesis: PSpace-completeness of principal inhabitation in the simply typed lambda-calculus, undecidability of inhabitation in lambda-calculus with intersection types, undecidability of inhabitation in lambda-calculus with intersection types in bounded dimension, undecidability of inhabitation in subintuitionistic combinatory logic, (o+2)-ExpTime-completeness of inhabitation in combinatory logic with intersection types with instantiation of bounded order o, and ExpTime-hardness of intersection type unification.
In text/plain format

Archived Files and Locations

application/pdf  1.8 MB
file_tcxbosdbtvfyfhjy5mnhltzzme
eldorado.tu-dortmund.de (web)
web.archive.org (webarchive)
Read Archived PDF
Preserved and Accessible
Type  article-journal
Stage   published
Date   2019-07-10
Language   en ?
Work Entity
access all versions, variants, and formats of this works (eg, pre-prints)
Catalog Record
Revision: 9ade483e-2783-4d04-8fc8-fe83f0f77c0a
API URL: JSON