Lambda calculus

Deductive lambda calculus

Deductive lambda calculus considers what happens when lambda terms are regarded as mathematical expressions. One interpretation of the untyped lambda calculus is as a programming language where evaluation proceeds by performing reductions on an expression until it is in normal form. In this interpretation, if the expression never reduces to normal form then the program never terminates, and the value is undefined. Considered as a mathematical deductive system, each reduction would not alter the value of the expression. The expression would equal the reduction of the expression. (Wikipedia).

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Haskell Curry | Alonzo Church | Church encoding | Typed lambda calculus | Lambda calculus | Extensionality | Curry's paradox | Richard's paradox | Universal instantiation | Mathematics | Real number | Church–Rosser theorem | Distributive property | Fixed-point combinator | Let expression | Universal quantification | Canonical form | Boolean algebra | Kleene–Rosser paradox | Arithmetic | Combinatory logic | Boolean algebra (structure)