An Introduction to Functional Programming Through Lambda Calculus

- 37 -Bound variablesi) is bound in λ.if is or is bound in .ii) is bound in ( )if is bound in or is bound in .Normal order β reductionFor ( )i) normal order β reduce to ii)if is λ.then replace all free occurences of in with and normal order β reduce the new oriii)if is not a functionthen normal order β reduce to and return ( )Normal order reduction notationDefinitions=> - normal order β reduction=> ... => - multiple normal order β reductiondef = Replace all subsequent occurences of with before evaluation.Replacement notation== - defined name replacementα conversionTo rename as in λ.if is not free in λ.then replace all free occurences of in with and replace in λ.η reduction(λ.( ) ) =>