Abstract

The higher order matching problem is the problem of determining whether a term is an instance of another in the simply typed -calculus, i.e. to solve the equation a = b where a and b are simply typed -terms and b is ground. The decidability of this problem is still open. We prove the decidability of the particular case in which the variables occurring in the problem are at most third order. Introduction The higher order matching problem is the problem of determining whether a term is an instance of another in the simply typed -calculus i.e. to solve the equation a = b where a and b are simply typed -terms and b is ground. Pattern matching algorithms are used to check if a proposition can be deduced from another by elimination of universal quantifiers or by introduction of existential quantifiers. In automated theorem proving, elimination of universal quantifiers and introduction of existential quantifiers are mixed and full unification is required, but in proof-checking and semi-aut...

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