Decidability of fourth-order matching

Authors:
Vincent Padovani
Affiliations:
Université PARIS VII-C.N.R.S U.R.A. 753, Equipe Preuves, Programmes et Systèmes, 2 Place Jussieu 75251 PARIS CEDEX 05 FRANCE. Email: padovani@pps.jussieu.fr
Venue:
Mathematical Structures in Computer Science
Year:
2000

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Abstract

Higher Order Matching consists of solving finite sets of equations of the form u = βη v, where u, v are simply typed terms of λ-calculus, and v is a closed term. Whether this problem is decidable is an open question. In this paper its decidability is proved when the free variables of all equations are of order at most 4 – we actually extend this result to a more general situation in which in addition to equations, disequations are also considered.