## Ramified Higher-Order Unification (1996)

by
Jean Goubault-Larrecq

Citations: | 1 - 0 self |

### BibTeX

@MISC{Goubault-Larrecq96ramifiedhigher-order,

author = {Jean Goubault-Larrecq},

title = {Ramified Higher-Order Unification },

year = {1996}

}

### OpenURL

### Abstract

While unification in the simple theory of types (a.k.a. higher-order logic) is undecidable, we show that unification in the pure ramified theory of types with integer levels is decidable. Since pure ramified type theory is not very expressive, we examine the impure case, which has an undecidable unification problem even at order 2. However, the decidability result for the pure subsystem indicates that unification terminates more often than general higher-order unification. We present an application to ACA 0 and other expressive subsystems of second-order Peano arithmetic.