An Introduction to Functional Programming Through Lambda Calculus

- 234 -iii) rec DTRAVERSE TEMPTY = []or DTRAVERSE [V,L,R] = APPEND (DTRAVERSE R) (V::(DTRAVERSE L))3)rec EVAL [E1,OP,E2] =let R1 = EVAL E1inlet R2 = EVAL E2inIF STRING_EQUAL OP "+"THEN R1 + R2ELSEIF STRING_EQUAL OP "-"THEN R1 - R2ELSEIF STRING_EQUAL OP "*"THEN R1 * R2ELSE R1 / R2or EVAL N = NChapter 81)i)Normal orderλs.(s s) (λf.λa.(f a) λx.x λy.y) =>(λf.λa.(f a) λx.x λy.y) (λf.λa.(f a) λx.x λy.y) =>(λa.(λx.x a) λy.y) (λf.λa.(f a) λx.x λy.y) =>(λx.x λy.y) (λf.λa.(f a) λx.x λy.y) =>λy.y (λf.λa.(f a) λx.x λy.y) =>λf.λa.(f a) λx.x λy.y =>λa.(λx.x a) λy.y =>λx.x λy.y =>λy.y8 reductionsλf.λa.(f a) λx.x λy.y reduced twiceApplicative orderλs.(s s) (λf.λa.(f a) λx.x λy.y) ->λs.(s s) (λa.(λx.x a) λy.y) ->λs.(s s) (λx.x λy.y) ->λs.(s s) λy.y ->λy.y λy.y ->λy.y5 reductionsλf.λa.(f a) λx.x λy.y reduced onceLazyλs.(s s) (λf.λa.(f a) λx.x λy.y) 1=>(λf.λa.(f a) λx.x λy.y) 1(λf.λa.(f a) λx.x λy.y) 1=>(λa.(λx.x a) λy.y) 2(λa.(λx.x a) λy.y) 2=>(λx.x λy.y) 3(λx.x λy.y) 3=>λy.y λy.y =>