Category Theory and the Simply-Typed lambda-Calculus

Category Theory and the Simply-Typed lambda-Calculus (1996)

by Alfio Martini , Alfio Martini

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Datum	Value	Source
TITLE	Category Theory and the Simply-Typed lambda-Calculus	user correction - Legacy Corrections
AUTHOR NAME	Alfio Martini	SVM HeaderParse 0.1
AUTHOR NAME	Alfio Martini	SVM HeaderParse 0.1
ABSTRACT	This report deals with the question on how to provide a categorical model for the simply-typed -calculus. We first introduce cartesian closed categories and work in detail a number of results concerning this construction. Next, we present the basic concepts related with the typed -calculus, i.e., concrete syntax for -terms, occurrence of variables, context substitution and equivalence of -terms. Then we present the typing rules and an equational proof system together with reduction rules that model the execution of expressions (programs). The chapter ends with the presentation of a categorical semantics for the calculus and a soundness proof for the equational proof system. The main technical result of this proof is the substitution lemma, which says, basically, that the (operational) concept of substitution can be understood (algebraically) as a composition of two suitable morphisms in a (cartesian closed) category. Contents 1 Cartesian closed categories 2 1.1 Exponentials . . . . ....	user correction - Legacy Corrections
YEAR	1996	user correction - Legacy Corrections
CITATIONS	20 found	ParsCit 1.0