An introduction to functional programming through lambda calculus

An introduction to functional programming through lambda calculus

Lambda-Calculus and Functional Programming

ion operator; this is because [x]M is an abbreviation for a term in which M and its subterms do not occur. On the other hand, in the natural reduction for lambda-calculus, replacements inside the scope of an abstraction are extremely natural. Thus, what is now called λβ -reduction satisfies a scheme which weak reduction does not, namely (ξ): if M reduces to N, then λx.M reduces to λx.N. (The sa...

Introduction to Lambda Calculus

ion is said to bind the free variable x in M . E.g. we say that λx.yx has x as bound and y as free variable. Substitution [x := N ] is only performed in the free occurrences of x: yx(λx.x)[x := N ] ≡ yN(λx.x). In calculus there is a similar variable binding. In ∫ b a f(x, y)dx the variable x is bound and y is free. It does not make sense to substitute 7 for x: ∫ b a f(7, y)d7; but substitution ...

An Introduction to the Clocked Lambda Calculus

We give a brief introduction to the clocked λ-calculus, an extension of the classical λ-calculus with a unary symbol τ used to witness the β-steps. In contrast to the classical λ-calculus, this extension is infinitary strongly normalising and infinitary confluent. The infinitary normal forms are enriched Lévy–Longo Trees, which we call clocked Lévy–Longo Trees. 1998 ACM Subject Classification D...

An Introduction to the Lambda Calculus

It is surprising that despite the simplicity of its syntax, the λ-calculus hosts a large body of notation, abbreviations, naming conventions, etc. Our aim, as far as the notation throughout this work is concerned, is to remain consistent, clear and unambiguous as much as possible. By and large we adhere to the notation set down in Church’s Calculi of Lambda Conversion [4], and Barendregt’s The ...