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From computation to foundations via functions and application: The λ-calculus and its webbed models by Chantal Berline is a Computer Science article available to read on EtoBox.
What is From computation to foundations via functions and application: The λ-calculus and its webbed models about?
Church's -calculus is an enthralling object of mathematical and logical study, born in 1930 as the mathematical theory of functions as rules, and invented for foundational purposes. -calculus gave rise to the ÿrst (and the most elegant) mathematical deÿnition of computable functions and inspired the main theorems of recursion theory. It came back on the scene in the 1960s with the development of programming theory. A capital contribution of -calculus to this subject is that it allows the mathematical expression and development of the Curry-Howard correspondence between proofs and programs, which generates deep and active research. The ÿrst aim of this paper is to introduce -calculus to a mathematical audience with no previous knowledge of it. After giving a brief insight to the conceptual and practical importance of typed calculi we will concentrate on untyped -calculus, which is logic free, has the most powerful expressive power and can be more easily described. In the second and main part of the paper we give an elementary, algebraic, and bottom-up presentation of its useful classes of models, which are powersets built from adequate "webs". We focus on two methods: completion of
Who reads From computation to foundations via functions and application: The λ-calculus and its webbed models?
It is typically read by researchers, students, and practitioners in Computer Science.
- Author
- Chantal Berline
- Publisher
- Elsevier Science; Elsevier ; Elsevier BV (ISSN 0304-3975)
- Published
- 2000
- Language
- EN
- Field
- Computer Science (Physical Sciences)