[SOLVED] CS ocaml interpreter Create the file interpreter.ml with the following data type:

Create the file interpreter.ml with the following data type:

type exp =
| True
| False
| If of exp * exp * exp
| Num of int
| IsZero of exp
| Plus of exp * exp
| Mult of exp * exp

and exception

exception Eval_error

Create the two functions:
step : exp -> exp
multi-step : exp -> exp

let rec step (e : exp) = insert code
let rec multi-step (e : exp) = insert code

The function step takes in input an expression and returns the expression that results from computing one step of the expression in input, or raises the OCaml exception Eval_error if the computation fails.

The function multi-step takes in input an expression and iterates the function step in order to evaluate the expression one step at a time until it returns a value, or raises the OCaml exception Eval_error if the computation fails.

Test multi-step with the following inputs:

1) true => true
(multi-step True)
Output: True

2) false => false
(multi-step False)
Output: False

3) 0 => 0
(multi-step (Num 0))
Output: (Num 0)

4) iszero(0) => true
(multi-step (IsZero (Num 0)))
Output: True

5) iszero(1 + 1) => false
(multi-step (IsZero (Plus (Num 1, Num 1))))
Output: False

6) iszero((2 + -1) + 1) => false
(multi-step (IsZero (Plus (Plus (Num 2, Num (-1)), Num 1))))
Output: False

7) (-1 + 1) + (-1 + 1) => 0
(multi-step (Plus (Plus (Num (-1), Num 1), Plus (Num (-1), Num 1))))
Output: (Num 0)

8) -1 + ((2 * 2) + 1) => 4
(multi-step (Plus (Num (-1), Plus (Mult (Num 2, Num 2), Num 1))))
Output: (Num 4)

9) (((2 + -1) + 1) + -1) => 1
(multi-step (Plus (Plus (Plus (Num 2, Num (-1)), Num 1), Num (-1))))
Output: (Num 1)

10) iszero(-1 + 1) + 1 => Eval_error
(multi-step (Plus (IsZero (Plus (Num (-1), Num 1)), Num 1)))
Output:Eval_error

11) iszero(if iszero(0) then true else 0) => Eval_error
(multi-step (IsZero (If (IsZero (Num 0), True, Num 0))))
Output:Eval_error

12) iszero(if iszero(5 * 0) then (if false then 0 else iszero(-1 + 0)) else 0) => Eval_error
(multi-step
(IsZero
(If
( IsZero (Mult (Num 5, Num 0))
, If (False, Num 0, IsZero (Plus (Num (-1), Num 0)))
, Num 0 ))))
Output:Eval_error

13) if iszero(-1 + 1) then 2 else true => 2
(multi-step (If (IsZero (Plus (Num (-1), Num 1)), Num 2, True)))
Output:(Num 2)

14) if (if iszero((1 + -1) * 1) then false else true) then 1 * 2 else true => true
(multi-step
(If
( If (IsZero (Mult (Plus (Num 1, Num (-1)), Num 1)), False, True)
, Mult (Num 1, Num 2)
, True )))
Output:True

15) if (if iszero(0 * 0) then iszero(2) else 0) then 2 * (1 * 1) else ((((if iszero(0) then 1 else 0) + -1) + 1) + -1) + 1 => 1
(multi-step
(If
( If (IsZero (Mult (Num 0, Num 0)), IsZero (Num 2), Num 0)
, Mult (Num 2, Mult (Num 1, Num 1))
, Plus
( Plus
( Plus
( Plus (If (IsZero (Num 0), Num 1, Num 0), Num (-1))
, Num 1 )
, Num (-1) )
, Num 1 ) )))
Output:(Num 1)

16) if true then (if true then (if false then 0 else 1) * 1 else 5) else (4 * 1) + 1 => 1
(multi-step
(If
( True
, If (True, Mult (If (False, Num 0, Num 1), Num 1), Num 5)
, Plus (Mult (Num 4, Num 1), Num 1) )))
Output:(Num 1)

17) if iszero(if iszero(-1 + 2) then 0 else 1) then (if true then (if false then 0 * 6) else 5) else 5 => 5
(multi-step
(If
( IsZero (If (IsZero (Plus (Num (-1), Num 2)), Num 0, Num 1))
, If
( True
, If (False, Mult (Num 0, Num 6), Plus (Num 0, Num 1))
, Num 5 )
, Num 5 )))
Output:(Num 5)

18) if iszero(-1 + (1 + (-1 + 1))) then iszero(true) else 1 => Eval_error
(multi-step
(If
( IsZero (Plus (Num (-1), Plus (Num 1, Plus (Num (-1), Num 1))))
, IsZero True
, Num 1 )))
Output:Eval_error

19) 1 + (-1 + (if iszero(1 + (if true then 1 else 2)) then 1 + 2 else 2 * 2)) => 4
(multi-step
(Plus
( Num 1
, Plus
( Num (-1)
, If
( IsZero (Plus (Num 1, If (True, Num 1, Num 2)))
, Plus (Num 1, Num 2)
, Mult (Num 2, Num 2) ) ) )))
Output:(Num 4)

20) -1 + (if iszero(5 + -4) then 123 * (5 + -4) else iszero(0)) => Eval_error
(multi-step
(Plus
( Num (-1)
, If
( IsZero (Plus (Num 5, Num (-4)))
, Mult (Num 123, Plus (Num 5, Num (-4)))
, IsZero (Num 0) ) )))
Output:Eval_error