Intersection Type Matching with Subtyping

  • Boris Düdder
  • Moritz Martens
  • Jakob Rehof
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7941)


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.


Type Variable Intersection Type Match Problem Organize Type Combinatory Logic 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Boris Düdder
    • 1
  • Moritz Martens
    • 1
  • Jakob Rehof
    • 1
  1. 1.Faculty of Computer ScienceTechnical University of DortmundGermany

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