Journal of Symbolic Logic

On the Unification Problem for Cartesian Closed Categories

Paliath Narendran, Frank Pfenning, and Richard Statman

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Abstract

Cartesian closed categories (CCCs) have played and continue to play an important role in the study of the semantics of programming languages. An axiomatization of the isomorphisms which hold in all Cartesian closed categories discovered independently by Soloviev and Bruce, Di Cosmo and Longo leads to seven equalities. We show that the unification problem for this theory is undecidable, thus settling an open question. We also show that an important subcase, namely unification modulo the linear isomorphisms, is NP-complete. Furthermore, the problem of matching in CCCs is NP-complete when the subject term is irreducible. CCC-matching and unification form the basis for an elegant and practical solution to the problem of retrieving functions from a library indexed by types investigated by Rittri. It also has potential applications to the problem of polymorphic type inference and polymorphic higher-order unification, which in turn is relevant to theorem proving and logic programming.

Article information

Source
J. Symbolic Logic Volume 62, Issue 2 (1997), 636-647.

Dates
First available in Project Euclid: 6 July 2007

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1183745248

Mathematical Reviews number (MathSciNet)
MR1464118

Zentralblatt MATH identifier
0882.03044

JSTOR
links.jstor.org

Citation

Narendran, Paliath; Pfenning, Frank; Statman, Richard. On the Unification Problem for Cartesian Closed Categories. J. Symbolic Logic 62 (1997), no. 2, 636--647.https://projecteuclid.org/euclid.jsl/1183745248


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