Lambda calculus

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Haskell theoretical foundations

Mathematics - Category theory
Research - Curry/Howard/Lambek

Lambda calculus:
Alpha conversion - Beta reduction
Eta conversion - Lambda abstraction

Recursion - Combinatory logic
Chaitin's construction - Turing machine
Relational algebra

The lambda calculus is a formal mathematical system for expressing the notion of computation. Most functional programming languages are based upon the lambda calculus.

Wikipedia has more information on the matter: Lambda calculus.