An Introduction to Functional Programming Through Lambda Calculus

- 94 -λs.(s 1 (CONS 2 NIL)) select_first =>select_first 1 (CONS 2 NIL) => ... =>1and:TAIL (CONS 1 (CONS 2 NIL)) ==(value (CONS 1 (CONS 2 NIL))) select_second ==(value λs.(s listtypeλs.(s 1 (CONS 2 NIL)))) select_second => ... =>λs.(s 1 (CONS 2 NIL)) select_second =>select_second 1 (CONS 2 NIL) => ... =>(CONS 2 NIL)and:HEAD (TAIL (CONS 1 (CONS 2 NIL))) -> ... ->HEAD (CONS 2 NIL) ==(value (CONS 2 NIL)) select_first ==(value λs.(listtype λs.(s 2 NIL))) select_first => ... =>λs.(s 2 NIL) select_first => ... =>select_first 2 NIL => ... =>2Note that both HEAD and TAIL will return LIST_ERROR from the empty list. Thus:HEAD NIL ==(value NIL) select_first => ...=>λs.(s LIST_ERROR LIST_ERROR) select_first =>select_first LIST_ERROR LIST_ERROR => ... =>LIST_ERRORand:TAIL NIL ==(value NIL) select_second => ...=>λs.(s LIST_ERROR LIST_ERROR) select_second =>select_second LIST_ERROR LIST_ERROR => ... =>