Type-inference by yourself

Documentation and user's manual

Table of contents

OCaml programs

Type-inference by yourself

1

All the following Caml expressions are syntactically correct. Consider each of them. Has it a value? If it has a value then which one and of which type? Else why? 5 * 4 * 3 * 2 * 1 ;; true ;; if 2 > 0 then "true" else "false" ;; if 2 > 0 then true else false ;; if 2 > 0 then "yes" else "no" ;; if 2 > 0 then yes else no ;; if 2 > 0 then true else "false" ;; 3.14 +. 2. ;; 3.14 +. 2 ;; 3.14 + 2.0 ;; 3.14 > 2. ;; 3.14 > 2 ;; int_of_float (3.14) > 2 ;; 3.14 > float_of_int (2) ;; 3 > 2 ;; "three" > "two" ;; "two" > "one" ;; 5 / 2 ;; 5. /. 2. ;; sqrt (4.) ;; sqrt (4) ;; sqrt ;; exp (1.) ;; log (exp (1.)) ;; 5 / 0 ;; if true then 5 / 0 else 3 ;; if true then 3 else 5 / 0 ;; if false then 5 / 0 else 3 ;; if false then 3 else 5 / 0 ;; "s" ^ "i" ;; `s` ^ "i" ;; `s` ^ `i` ;; "s" ^ i ;; si ;; "if" ;; function x -> x > 0 ;; (function x -> x > 0) (12) ;; function x -> 2 * x ;; (function x -> 2 * x) (7) ;; function (x, y) -> (x + y, x - y) ;; function x -> x / 0 ;; (function x -> x / 0) (12) ;; (function x -> x) (5) ;; (function x -> x) ("yes") ;; function x -> x ;; (function x -> 1) (5) ;; (function x -> 1) (5.) ;; function x -> 1 ;; (function (x, y) -> (y, x)) (1, 2) ;; (function (x, y) -> (y, x)) (1, "yes") ;; (function (x, y) -> (y, x)) ("yes", "yes") ;; function (x, y) -> (y, x) ;; function x -> (x, x) ;; (function x -> (x, x)) (1) ;;

2

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 absolute = function x -> if x >= 0 then x else - x ;; absolute (absolute (-12)) ;; let comp = function (x, y, z) -> (x <= y, y <= z) ;; (comp (3, 2, 4), comp (2, 3, 4)) ;; comp ("yellow", "red", "green") ;; let approx = function (a, b) -> let (b1, b2) = comp (a - 1, b, a + 1) in b1 & b2 ;; approx (12, 13) ;; approx ("purple", "violet") ;; let ff = function x -> x + 1 in ff ;; ff (5) ;; let ff = function x -> x + 1 ;; ff (5) ;; let ff = function x -> x + 1. ;; ff (5) ;; let ff = function x -> x +. 1. ;; ff (5) ;; (let ff = function x -> x + 1 in ff) (5) ;; ff (5) ;; ff ;;

3

Consider each of the following types. Write a value having this types (naming it is useless), evaluate it, then apply it: int -> int int * int -> bool string -> bool float * float -> string bool * bool -> bool int -> int * bool

4

Write values named  f  and  g  in such a manner that the following expression has a value: f (f (g (2, true), 4))

5

All the following Caml phrases are syntactically correct. They are assumed to be evaluated in order (those in the left column being evaluated first). 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 a = 5 in 2 * a ;; a ;; let a = 7 in (a, a) ;; let a = 1 and b = 3 and c = 4 in a + b + c ;; let (a, b, c) = (1, 3, 4) in a + b + c ;; let a = 5 ;; a ;; let a = 3 in 2 * a ;; a ;; let a = "yes" ;; a ;; let x = 5 ;; let x = 3 in 2 * x ;; let y = x + 1 ;; let x = 4 and y = 2 in x * y ;; y ;; let y = let x = 7 and y = 9 in y - x ;; let y = y = 9 ;; failwith ;;

6

Same question. let f = function x -> if x <> 0 then x / abs (x) else failwith ("f : requires a non-zero value as argument") ;; (f (-7), f (5)) ;; f (0) ;; let rec times = function (a, b) -> if b = 0 then 0 else a + times (a, b - 1) ;; times (5, 7) ;; let rec modulo_8 = function n -> if n < 0 then modulo_8 (n + 8) else if n >= 8 then modulo_8 (n - 8) else n ;; modulo_8 (-13) ;; let rec repeat = function (word, n) -> if n = 0 then "!" else word ^ repeat (word, n - 1) ;; repeat ("Ah ", 5) ;; let rec f = function x -> f (x) ;; f (3) ;; let rec power = function (x, n) -> if n = 0 then 1.0 else if n < 0 then 1.0 /. power (x, - n) else x *. power (x, n - 1) ;; power (1.2, 4) ;; power (5.0, -3) ;; let rec is_even = function n -> if n = 0 then true else is_even (n - 2) ;; is_even (12) ;; is_even (11) ;;

Type-inference by yourself

Documentation and user's manual

Table of contents

OCaml programs