Linear Higher-Order Pre-Unification
Abstract
We develop a pre-unification algorithm in the style of Huet for the linear lambda-calculus lambda(->-o&T) which includes intuitionistic functions (->) linear functions (-o) additive pairing (&), and additive unit (T). This procedure conveniently operates on an efficient representation of lambda(->-o&T) the spine calculus S(->-o&T) for which we define the concept of weak head-normal form. We prove the soundness and completeness of our algorithm with respect to the proper notion of definitional equality for S(->-o&T), and illustrate the distinctive aspects of linear higher-order unification by means of examples. We also show that surprisingly, a similar pre-unification algorithm does not exist for certain sublanguages. Applications lie in proof search, logic programming, and logical frameworks based on linear type theories.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jul 20, 1997
- Accession Number
- ADA332093
Entities
People
- Frank Pfenning
- Iliano Cervesato
Organizations
- Carnegie Mellon University