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Category theory and the simply-typed lambda-calculus (1996).
| Content Provider | CiteSeerX |
|---|---|
| Author | Martini, Alfio |
| 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 . . . . .... |
| File Format | |
| Publisher Date | 1996-01-01 |
| Access Restriction | Open |
| Subject Keyword | Category Theory Simply-typed Lambda-calculus Equational Proof System Main Technical Result Reduction Rule Typed Calculus Soundness Proof Categorical Semantics Basic Concept Simply-typed Calculus Context Substitution Categorical Model Concrete Syntax Suitable Morphisms Typing Rule Substitution Lemma |
| Content Type | Text |
