منابع مشابه
Dependent Cartesian Closed Categories
We present a generalization of cartesian closed categories (CCCs) for dependent types, called dependent cartesian closed categories (DCCCs), which also provides a reformulation of categories with families (CwFs), an abstract semantics for Martin-Löf type theory (MLTT) which is very close to the syntax. Thus, DCCCs accomplish mathematical elegance as well as a direct interpretation of the syntax...
متن کاملClosed Freyd- and -categories
We give two classes of sound and complete models for the computational-calculus, or c-calculus. For the rst, we generalise the notion of cartesian closed category to that of closed Freyd-category. For the second, we generalise simple indexed categories. The former gives a direct semantics for the computational-calculus. The latter corresponds to an idealisation of stack-based intermediate langu...
متن کاملCartesian closed Dialectica categories
When Gödel developed his functional interpretation, also known as the Dialectica interpretation, his aim was to prove (relative) consistency of first order arithmetic by reducing it to a quantifier-free theory with finite types. Like other functional interpretations (e.g. Kleene’s realizability interpretation and Kreisel’s modified realizability) Gödel’s Dialectica interpretation gives rise to ...
متن کاملOn Closed Categories of Functors
Brian Day Received November 7, 19~9 The purpose of the present paper is to develop in further detail the remarks, concerning the relationship of Kan functor extensions to closed structures on functor categories, made in "Enriched functor categories" | 1] §9. It is assumed that the reader is familiar with the basic results of closed category theory, including the representation theorem. Apart fr...
متن کاملClosed Categories and Categorial Grammar
Inspired by Lambek's work on categorial grammar, we examine the proposal that the theory of biclosed monoidal categories can serve as a foundation for a formal theory of natural language. The emphasis throughout is on the derivation of the axioms for these categories from linguistic intuitions. When Montague's principle that there is a homomorphism between syntax and semantics is reened to the ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Fundamenta Mathematicae
سال: 1977
ISSN: 0016-2736,1730-6329
DOI: 10.4064/fm-94-2-129-143