An Introduction to Functional Programming Through Lambda Calculus

- 92 -The head of the tail of the tail of this list:HEAD (TAIL (TAIL (CONS 1 (CONS 2 (CONS 3 NIL)))))is:HEAD (TAIL (CONS 2 (CONS 3 NIL)))which is:HEAD (CONS 3 NIL)giving:3The tail of the tail of the tail of the list:TAIL (TAIL (TAIL (CONS 1 (CONS 2 (CONS 3 NIL)))))is:TAIL (TAIL (CONS 2 (CONS 3 NIL)))which is:TAIL (CONS 3 NIL)giving:NIL6.3. List representationFirst we define the list type:def list_type = threeand associated tests:def islist = istype list_typedef ISLIST L = MAKE_BOOL (islist L)and error object:def LIST_ERROR = MAKE_ERROR list_typeA list value will consist of a pair made from the list head and tail so the general form of a list object with head and tail will be:λs.(s listtypeλs.(s ))Thus, we define: