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Introduction to higher order categorical logic
Preface Part I. Introduction to Category Theory: Part II. Cartesian Closed Categories and Calculus: Part III. Type Theory and Toposes: Part IV. Representing Numerical Functions in Various CategoriesExpand
Bounded Linear Logic: A Modular Approach to Polynomial-Time Computability
TLDR
Usual typed lambda-calculi yield input/output specifications; in this paper the authors show how to extend this paradigm to complexity specifications. Expand
Functorial Polymorphism
Geometry of Interaction and linear combinatory algebras
TLDR
We present an axiomatic framework for Girard's Geometry of Interaction based on the notion of linear combinatory algebra. Expand
On the pi-Calculus and Linear Logic
TLDR
Abstract We detail Abramsky's “proofs-as-processes” paradigm for interpreting classical linear logic (CLL) into a “synchronous” version of the π-calculus recently proposed by Milner (1992, 1993). Expand
Normalization and the Yoneda Embedding
TLDR
We show how to solve the word problem for simply typed λβη-calculus by using a few well-known facts about categories of presheaves and the Yoneda embedding. Expand
Category theory for linear logicians
This paper presents an introduction to category theory with an emphasis on those aspects relevant to the analysis of the model theory of linear logic. With this in mind, we focus on the basicExpand
Normalization by evaluation for typed lambda calculus with coproducts
TLDR
Solves the decision problem for simply typed lambda calculus with a strong binary sum, or, equivalently, the word problem for free Cartesian closed categories with binary co-products. Expand
Normal Forms and Cut-Free Proofs as Natural Transformations
What equations can we guarantee that simple functional programs must satisfy, irrespective of their obvious defining equations? Equivalently, what non-trivial identifications must hold between lambdaExpand
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