Intersection Type Matching with Subtyping

Type matching problems occur in a number of contexts, including library search, component composition, and inhabitation. We consider the intersection type matching problem under the standard notion of subtyping for intersection types: Given intersection types τ and σ, where σ is a constant type, doe...

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Bibliographic Details
Published inTyped Lambda Calculi and Applications pp. 125 - 139
Main Authors Düdder, Boris, Martens, Moritz, Rehof, Jakob
Format Book Chapter
LanguageEnglish
Published Berlin, Heidelberg Springer Berlin Heidelberg
SeriesLecture Notes in Computer Science
Subjects
Combinatory Logic
Intersection Type
Match Problem
Organize Type
Type Variable
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Summary:Type matching problems occur in a number of contexts, including library search, component composition, and inhabitation. We consider the intersection type matching problem under the standard notion of subtyping for intersection types: Given intersection types τ and σ, where σ is a constant type, does there exist a type substitution S such that S(τ) is a subtype of σ? We show that the matching problem is NP-complete. NP-hardness holds already for the restriction to atomic substitutions. The main contribution is an NP-algorithm which is engineered for efficiency by minimizing nondeterminism and running in Ptime on deterministic input problems. Our algorithm is based on a nondeterministic polynomial time normalization procedure for subtype constraint systems with intersection types. We have applied intersection type matching in optimizations of an inhabitation algorithm.
ISBN:9783642389450
3642389457
ISSN:0302-9743
1611-3349
DOI:10.1007/978-3-642-38946-7_11