Abstract not found

Abstract not found

A straightforward proof of the Coherence theorem for monoidal categories is presented in [2]. Here we describe the its formalisation within Martin-Löf type theory. The paper is organised as a commentary to the ALF proof files (recapitulated complete). In the current version the necessary categories and functors are constructed, and the main lemma (nat) is proved for all cases, except mult and inverse arrows. The case mult was already proved in the version 3a (which used different definitions incompatible with version 4)

The theory we will be concerned with in this paper is Martin-Löf's polymorphic type theory with intensional equality and the universe of small sets. We will give a different proof of normalization for this theory.

This paper deals with the problem of a program that is essentially the same over any of several types but which, in the older imperative languages must be rewritten for each separate type. For example, a sort routine may be written with essentially the same code except for the types for integers, booleans, and strings. It is clearly desirable to have a method of writing a piece of code that can accept the specific type as an argument. Milner developed his ideas in terms of type assignment to lambda-terms. It is based on a result due originally to Curry (Curry 1969) and Hindley (Hindley 1969) known as the principal type-scheme theorem, which says that (assuming that the typing assumptions are sufficiently wellbehaved) every term has a principal type-scheme, which is a type-scheme such that every other type-scheme which can be proved for the given term is obtained by a substitution of types for type variables. This use of type schemes allows a kind of generality over all types, which is known as polymorphism.