Decidability of higher-order matching

Decidability of higher-order matching

We show that the higher-order matching problem is decidable using a game-

Introduction to Decidability of Higher-Order Matching

Higher-order unification is the problem given an equation t = u containing free variables is there a solution substitution θ such that tθ and uθ have the same normal form? The terms t and u are from the simply typed lambda calculus and the same normal form is with respect to βη-equivalence. Higher-order matching is the particular instance when the term u is closed; can t be pattern matched to u...

An Introduction to Decidability of Higher-Order Matching

Higher-Order Concurrency: Expressiveness and Decidability Results

ion is an expression of the form (x)Pit is a parameterized process. An abstraction has a functional type. Applying an abstraction (x)P of type T → ♦ (where ♦ is the type of all processes) to an argument W of type T yields the process P{W/x}. The argument W can itself be an abstraction; therefore the order of an abstraction, that is, the level of arrow nesting in its type, can be arbitrarily hi...

Higher-Order Concurrency: Expressiveness and Decidability Results

ion is an expression of the form (x)Pit is a parameterized process. An abstraction has a functional type. Applying an abstraction (x)P of type T → ♦ (where ♦ is the type of all processes) to an argument W of type T yields the process P{W/x}. The argument W can itself be an abstraction; therefore the order of an abstraction, that is, the level of arrow nesting in its type, can be arbitrarily hi...