Abstract

. We present a case study on the formal development of a non trivial (meta)theory in the Theory of Contexts using the Coq proof assistant. The methodology underlying the Theory of Contexts for reasoning on systems presented in HOAS is based on an axiomatic syntactic standpoint. We feel that one of the main advantages of this approach, is that it requires a very low logical overhead. The object logic we focus on is the lazy, call-by-name #-calculus (#cbn ), both untyped and simply typed. We will see that the formal, fully detailed development of the theory of #cbn in the Theory of Contexts introduces a small, sustainable overhead with respect to the proofs "on the paper". Moreover, this will allow for comparison with similar case studies developed in other approaches to the metatheoretical reasoning in higher-order abstract syntax. Keywords: higher-order abstract syntax, induction, logical frameworks.

Citations

997	The Lambda Calculus, its Syntax and Semantics - Barendregt - 1984
128	Full Abstraction in the Lazy Lambda Calculus - Abramsky, Ong - 1993
78	Using typed lambda calculus to implement formal systems on a machine - Avron, Honsell, et al. - 1992
56	A meta-mathematical investigation of a Calculus of Constructions. Private Communication - Coquand - 1987
12	Consistency of the theory of contexts - Bucalo, Honsell, et al.
11	Automating Inversion of Inductive Predicates in Coq - Cornes, Terrasse - 1996