Some Lambda Calculi With Categorical Sums and Products (1993)
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@MISC{Dougherty93somelambda,
author = {Daniel J. Dougherty},
title = {Some Lambda Calculi With Categorical Sums and Products},
year = {1993}
}
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Abstract
. We consider the simply typed -calculus with primitive recursion operators and types corresponding to categorical products and coproducts.. The standard equations corresponding to extensionality and to surjectivity of pairing and its dual are oriented as expansion rules. Strong normalization and ground (base-type) confluence is proved for the full calculus; full confluence is proved for the calculus omitting the rule for strong sums. In the latter case, fixed-point constructors may be added while retaining confluence. 1 Introduction The systems investigated here are simply typed -caluli whose types include pairs, unit, sums, an empty type, and a type of natural numbers supporting constructions by primitive recursion. In the core system the types behave as categorical product and coproducts, so the subject at hand is equivalently ([LS86]) the equational theory of the free bicartesian closed category (generated by objects for the base types) with weak natural numbers object. Su...
