For questions on the formal system in mathematical logic for expressing effective functions, programs and computation, and proofs, using abstract notions of functions and combining them through binding and substitution.
Its dynamics is a rewriting system representing computation by mean of the beta-reduction, that substitutes each occurrence of the variable with the argument term. From this operational point of view, it represents the ideal formal model of a functional programming language and it can be enriched with constant values and datatypes. Such a typed restriction constitutes the bridge across logic's proof-theory and computer science's theory of computability known as the Curry-Howard correspondence: a term is a proof of its type formula.
- Henk Barendregt, Lambda Calculus. Its Syntax and Semantics, 1981. The monograph of the subject.