An Introduction to Functional Programming Through Lambda Calculus

- 116 -which is equivalent to the original:because:rec DOUBLE [] = []or DOUBLE (H::T) = (2*H)::(DOUBLE T)DOUBLE == MAPCAR λX.(2*X)For example:DOUBLE [1,2,3] => ... =>(λX.(2*X) 1):)::(MAPCAR λX.(2*X) [2,3]) -> ... ->2::(λX.(2*X) 2)::(MAPCAR λX.(2*X) [3]) -> ... ->2::4::(λX.(2*X) 3)::(MAPCAR λX.(2*X) []) -> ... ->2::4::6::[] ==[2,4,6]Similarly, we can redefine PLURAL as:def PLURAL = MAPCAR λW.(APPEND W "s")so expanding the definition gives:rec PLURAL [] = []or PLURAL (H::T) = (λW.(APPEND W "s") H)::(MAPCAR λW.(APPEND W "s") T)so, simplifying:def PLURAL [] = []or PLURAL (H::T) = (APPEND H "s")::(MAPCAR λW.(APPEND W "s") T)which is equivalent to:because:rec PLURAL [] = []or PLURAL (H::T) = (APPEND H "s")::(PLURAL T)PLURAL == MAPCAR λW.(APPEND W "s")For example:PLURAL ["cat","dog","pig"] => ... =>(λW.(APPEND W "s") "cat")::(MAPCAR λW.(APPEND W "s") ["dog","pig"]) -> ... ->"cats"::(λW.(APPEND W "s") "dog")::(MAPCAR λW.(APPEND W "s") ["pig"]) -> ... ->