Formalized metatheory with terms represented by an indexed family of types
Paper in proceedings, 2006

It is possible to represent the terms of a syntax with binding constructors by a family of types, indexed by the free variables that may occur. This approach has been used several times for the study of syntax and substitution, but never for the formalization of the metatheory of a typing system. We describe a recent formalization of the metatheory of Pure Type Systems in Coq as an example of such a formalization. In general, careful thought is required as to how each definition and theorem should be stated, usually in an unfamiliar ‘big-step’ form; but, once the correct form has been found, the proofs are very elegant and direct.

syntax with binding

type theory

formalisation of mathematics


Robin Adams

Chalmers, Computer Science and Engineering (Chalmers), Computing Science (Chalmers)

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

03029743 (ISSN) 16113349 (eISSN)

Vol. 3839 1-16

Types for Proofs and Programs International Workshop, TYPES 2004
Jouy-en-Josas, France,

Subject Categories

Algebra and Logic

Computer Science

Areas of Advance

Information and Communication Technology


Basic sciences



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