An Introduction to Functional Programming Through Lambda Calculus

- 93 -def MAKE_LIST = make_obj listtypedef CONS H T =if islist Tthen MAKE_LIST λs.(s H T)else LIST_ERRORFor example:and:CONS 1 NIL => ... =>MAKE_LIST λs.(s 1 NIL) => ... =>λs.(s listtypeλs.(s 1 NIL))CONS 2 (CONS 1 NIL) => ... =>MAKE_LIST λs.(s 2 (CONS 1 NIL)) => ... =>λs.(s listtypeλs.(s 2 (CONS 1 NIL))) => ... =>λs.(s listtypeλs.(s 2 λs.(s listtypeλs.(s 1 NIL))))The empty list will have both head and tail set to LIST_ERROR:so NIL is:def NIL = MAKE_LIST λs.(s LIST_ERROR LIST_ERROR)λs.(s listtypeλs.(s LIST_ERROR LIST_ERROR))Now we can use the pair selectors to extract the head and tail:def HEAD L =if islist Lthen (value L) select_firstelse LIST_ERRORdef TAIL L =if islist Lthen (value L) select_secondelse LIST_ERRORFor example:HEAD (CONS 1 (CONS 2 NIL)) ==(value (CONS 1 (CONS 2 NIL))) select_first ==(value λs.(s listtypeλs.(s 1 (CONS 2 NIL)))) select_first => ... =>