Summary: Extensional Normalization in the Logical Framework with
Proof Irrelevant Equality
Andreas Abel
Department of Computer Science
Ludwig­Maximilians­University Munich
Abstract
We extend the Logical Framework by proof irrelevant
equality types and present an algorithm that computes
unique long normal forms. The algorithm is inspired by
normalization­by­evaluation. Equality proofs which are not
reflexivity are erased to a single object #. The algorithm
decides judgmental equality, its completeness is established
by a PER model.
1. Introduction
In intensional Martin­L˜of type theory (ITT), but also
in the Calculus of Inductive Constructions which underlies
the Coq proof assistant, we distinguish between definitional
equality of terms t and t # of type T , given by the judgement
# # t = t # : T , and propositional equality which is estab­
lished by providing an inhabitant of the identity set Id T t t # .

Source: Abel, Andreas - Theoretische Informatik, Ludwig-Maximilians-Universität München

Collections: Computer Technologies and Information Sciences