Type-inference by yourself

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OCaml programs

Type-inference by yourself

To check your solution enter an Objective Caml toplevel from a directory containing the files  List_1.cmi  and  List_1.cmo  (in other words: the module  List_1 ) to be extracted from  this archive . Then in this toplevel first evaluate this Caml code:

All the following Caml phrases are syntactically correct. They are assumed to be evaluated in order. Consider each of them. Is it a value definition let ... = e or an expression e? Has e a value? If it has a value then which one and of which type? Else why? let li_1 = cons_list (7, cons_list (3, cons_list (11, empty_list ()))) ;; cons_list (2, 3) ;; cons_list (empty_list (), 7) ;; let li_2 = cons_list (9, li_1) in li_2 ;; li_1 ;; li_2 ;; empty_list () ;; empty_list ;; let li_2 = cons_list (6, cons_list (5, cons_list (9, empty_list ()))) ;; cons_list (li_2, cons_list (li_1, empty_list ())) ;; cons_list (6, cons_list (li_1, empty_list ())) ;; let li_3 = cons_list (6, cons_list (5.3, cons_list (9, empty_list ()))) ;; let li_4 = cons_list ("bear", cons_list ("cow", cons_list ("fox", empty_list ()))) ;; let li_5 = cons_list ("honey", cons_list ("grass", cons_list ("hen", empty_list ()))) ;; cons_list (li_4, li_5) ;; tail (tail (cons_list ("yes", empty_list ()))) ;; cons_list ("yes", empty_list ()) ;; cons_list ((2, 3.5), cons_list ((0, 4.), empty_list ())) ;; head (tail (cons_list ((if 4 > 2 then 3 < 5 else 3 > 5), l empty_list ()))) ;; cons_list ((if 4 > 2 then 3 < 5 else 3 > 5), empty_list ()) ;; cons_list (li_1, (cons_list (empty_list (), cons_list (cons_list (4, li_2), empty_list ())))) ;; tail (cons_list (5, empty_list ())) ;; let rec f1 = function li -> if is_empty_list (tail (li)) then head (li) else f1 (tail (li)) ;; let rec f2 = function (li, n) -> if n = 1 then head (li) else f2 (tail (li), n - 1) ;; cons_list (empty_list (), empty_list ()) ;; cons_list (cons_list (empty_list (), empty_list ()), empty_list ()) ;; cons_list (sqrt, cons_list (log, cons_list (exp, empty_list ()))) ;; cons_list (empty_list, empty_list ()) ;; cons_list (empty_list (), empty_list) ;; cons_list (empty_list, empty_list) ;; let rec f3 = function (li, li1) -> if is_empty_list (li) then li1 else if is_empty_list (li1) then li else if head (li) <= head (li1) then cons_list (head (li), f3 (tail (li), li1)) else cons_list (head (li1), f3 (li, tail (li1))) ;; let rec f4 = function li -> if is_empty_list (li) then (li, empty_list ()) else if is_empty_list (tail (li)) then (li, empty_list ()) else let (h1, h2) = f4 (tail (tail (li))) in (cons_list (head (li), h1), cons_list (head (tail (li)), h2)) ;; let rec f5 = function li -> if is_empty_list (li) then li else if is_empty_list (tail (li)) then li else let (h1, h2) = f4 (li) in f3 (f5 (h1), f5 (h2)) ;; let rec f6 = function (li, li1 ) -> if is_empty_list (li) & is_empty_list (li1) then empty_list () else cons_list ((head (li), head (li1)), f6 (tail (li), tail (li1))) ;; let rec f7 = function li -> if is_empty_list (li) then f7 (cons_list (0, li)) else f7 (li) ;; f7 (cons_list (2, empty_list ())) ;; let rec f8 = function li -> if is_empty_list (li) then tail (li) else f8 (tail (li)) ;; f8 (cons_list (2, empty_list ())) ;; let rec f9 = function li -> if is_empty_list (li) then empty_list () else if is_empty_list (tail (li)) then head (li) else tail (li) ;; f9 (cons_list (2, empty_list ())) ;; let rec f10 = function li -> if is_empty_list (li) then li else cons_list (head (li), f10 (tail (li))) ;; f10 (cons_list (3, cons_list (2, empty_list ()))) ;; head (tail (tail (li_1))) ;; is_empty_list (cons_list (3.5, empty_list ())) ;; is_empty_list (tail (tail (tail (li_4)))) ;; is_empty_list (empty_list ()) ;; (f1 (li_1), f1 (li_4)) ;; let li = f5 (f3 (li_1, li_2)) in (f2 (li, 1), f2 (li, 2), f2 (li, 3), f2 (li, 4), f2 (li, 5), f2 (li, 6)) ;; li ;; let li = f5 (f3 (li_4, li_5)) in (f2 (li, 1), f2 (li, 2), f2 (li, 3), f2 (li, 4), f2 (li, 5), f2 (li, 6)) ;; let li = f6 (li_4, li_5) in (f2 (li, 1), f2 (li, 2), f2 (li, 3)) ;;

Type-inference by yourself

Documentation and user's manual

Table of contents

OCaml programs