Do-it-yourself type theory

Abstract

Abstract This paper provides a tutorial introduction to a constructive theory of types based on, but incorporating some extensions to, that originally developed by Per Martin-Löf. The emphasis is on the relevance of the theory to the construction of computer programs and, in particular, on the formal relationship between program and data structure. Topics discussed include the principle of propositions as types, free types, congruence types, types with information loss and mutually recursive types. Several examples of program development within the theory are also discussed in detail.