Lambda Calculus

Alonzo Church in 1930’s introduced lambda-calculus as an alternative (with respect to recursive functions) model of computation. • Lambda Terms • Variables: x, y,... (discrete, denumerable-infinite set) • Application: if T and U are lambda-terms then (T)U is a lambda-term • Abstraction: if x ia a variable and U is a lambda term then λx.U is a lambda term • Term reduction as computing device: (λx.U)V →β U [V /x] Lambda Calculus Alonzo Church in 1930’s introduced lambda-calculus as an alternative (with respect to recursive functions) model of computation. • Lambda Terms • Variables: x, y,... (discrete, denumerable-infinite set) • Application: if T and U are lambda-terms then (T)U is a lambda-term • Abstraction: if x ia a variable and U is a lambda term then λx.U is a lambda term • Term reduction as computing device: (λx.U)V →β U [V /x] Lambda Calculus Alonzo Church in 1930’s introduced lambda-calculus as an alternative (with respect to recursive functions) model of computation. • Lambda Terms • Variables: x, y,... (discrete, denumerable-infinite set) • Application: if T and U are lambda-terms then (T)U is a lambda-term • Abstraction: if x ia a variable and U is a lambda term then λx.U is a lambda term • Term reduction as computing device: (λx.U)V →β U [V /x] Lambda Calculus Alonzo Church in 1930’s introduced lambda-calculus as an alternative (with respect to recursive functions) model of computation