Applying Universal Algebra to Lambda Calculus
نویسندگان
چکیده
منابع مشابه
Applying Universal Algebra to Lambda Calculus
The aim of this paper is double. From one side we survey the knowledge we have acquired these last ten years about the lattice of all λ-theories (= equational extensions of untyped λ-calculus) and the models of lambda calculus via universal algebra. This includes positive or negative answers to several questions raised in these years as well as several independent results, the state of the art ...
متن کاملFrom lambda-Calculus to Universal Algebra and Back
We generalize to universal algebra concepts originating from lambda calculus and programming in order first to prove a new result on the lattice of λ-theories, and second a general theorem of pure universal algebra which can be seen as a meta version of the Stone Representation Theorem. The interest of a systematic study of the lattice λT of λ-theories grows out of several open problems on lamb...
متن کاملClone Theory: Its Syntax and Semantics, Applications to Universal Algebra, Lambda Calculus and Algebraic Logic
The primary goal of this paper is to present a unified way to transform the syntax of a logic system into certain initial algebraic structure so that it can be studied algebraically. The algebraic structures which one may choose for this purpose are various clones over a full subcategory of a category. We show that the syntax of equational logic, lambda calculus and first order logic can be rep...
متن کاملAlgebra and Topology in Lambda Calculus
The untyped lambda calculus was introduced around 1930 by Church [11] as part of an investigation in the formal foundations of mathematics and logic. Although lambda calculus is a very basic language, it is sufficient to express all the computable functions. The process of application and evaluation reflects the computational behavior of many modern functional programming languages, which expla...
متن کاملFrom λ-calculus to Universal Algebra and Back
We generalize to universal algebra concepts originating from λ-calculus and programming to prove a new result on the lattice λT of λ-theories, and a general theorem of pure universal algebra which can be seen as a meta version of the Stone Representation Theorem. In this paper we introduce the class of Church algebras (which includes all Boolean algebras, combinatory algebras, rings with unit a...
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ژورنال
عنوان ژورنال: Journal of Logic and Computation
سال: 2008
ISSN: 0955-792X,1465-363X
DOI: 10.1093/logcom/exn085