-(* calc2.ml, enhanced with Recursive Function Values *)
+(* calc3.ml: calc2.ml enhanced with Recursive Function Values *)
- type term =
+ type term =
Intconstant of int
| Multiplication of (term * term)
| Addition of (term * term)
;;
type bound_value = Nonrecursive of expressed_value | Recursive_Closure of char * char * term * assignment
- and assignment = (char * bound_value) list
+ and assignment = (char * bound_value) list
and expressed_value = Int of int | Bool of bool | Pair of expressed_value * expressed_value | Closure of char * term * assignment;;
- let rec eval (t : term) (g : assignment) = match t with
- Intconstant x -> Int x
- | Multiplication (t1, t2) ->
- (* we don't handle cases where the subterms don't evaluate to Ints *)
- let Int i1 = eval t1 g
- in let Int i2 = eval t2 g
- (* Multiplication (t1, t2) should evaluate to an Int *)
- in Int (i1 * i2)
- | Addition (t1, t2) ->
- let Int i1 = eval t1 g
- in let Int i2 = eval t2 g
- in Int (i1 + i2)
- | Variable (var) -> (
- (* we don't handle cases where g doesn't bind var to any value *)
- match List.assoc var g with
+ let rec eval (t : term) (g : assignment) = match t with
+ Intconstant x -> Int x
+ | Multiplication (t1, t2) ->
+ (* we don't handle cases where the subterms don't evaluate to Ints *)
+ let Int i1 = eval t1 g
+ in let Int i2 = eval t2 g
+ (* Multiplication (t1, t2) should evaluate to an Int *)
+ in Int (i1 * i2)
+ | Addition (t1, t2) ->
+ let Int i1 = eval t1 g
+ in let Int i2 = eval t2 g
+ in Int (i1 + i2)
+ | Variable (var) -> (
+ (* we don't handle cases where g doesn't bind var to any value *)
+ match List.assoc var g with
| Nonrecursive value -> value
| Recursive_Closure (self_var, arg_var, body, savedg) as rec_closure ->
- (* we update savedg to bind self_var to rec_closure here *)
+ (* we update savedg to bind self_var to rec_closure here *)
let savedg' = (self_var, rec_closure) :: savedg
in Closure (arg_var, body, savedg')
)
- | Let (var_to_bind, t2, t3) ->
- (* evaluate t3 under a new assignment where var_to_bind has been bound to
+ | Let (var_to_bind, t2, t3) ->
+ (* evaluate t3 under a new assignment where var_to_bind has been bound to
the result of evaluating t2 under the current assignment *)
- let value2 = eval t2 g
- (* we have to wrap value2 in Nonrecursive *)
- in let g' = (var_to_bind, Nonrecursive value2) :: g
- in eval t3 g'
- | Iszero (t1) ->
- (* we don't handle cases where t1 doesn't evaluate to an Int *)
- let Int i1 = eval t1 g
- (* Iszero t1 should evaluate to a Bool *)
- in Bool (i1 = 0)
- | If (t1, t2, t3) ->
- (* we don't handle cases where t1 doesn't evaluate to a boolean *)
- let Bool b1 = eval t1 g
- in if b1 then eval t2 g
- else eval t3 g
- | Makepair (t1, t2) ->
- let value1 = eval t1 g
- in let value2 = eval t2 g
- in Pair (value1, value2)
- | First (t1) ->
- (* we don't handle cases where t1 doesn't evaluate to a Pair *)
- let Pair (value1, value2) = eval t1 g
- in value1
- | Lambda (arg_var, t2) -> Closure (arg_var, t2, g)
- | Apply (t1, t2) ->
- (* we don't handle cases where t1 doesn't evaluate to a function value *)
- let Closure (arg_var, body, savedg) = eval t1 g
- in let value2 = eval t2 g
- (* evaluate body under savedg, except with arg_var bound to Nonrecursive value2 *)
- in let savedg' = (arg_var, Nonrecursive value2) :: savedg
- in eval body savedg'
- | Letrec (var_to_bind, t2, t3) ->
- (* we don't handle cases where t2 doesn't evaluate to a function value *)
- let Closure (arg_var, body, savedg) = eval t2 g
+ let value2 = eval t2 g
+ (* we have to wrap value2 in Nonrecursive *)
+ in let g' = (var_to_bind, Nonrecursive value2) :: g
+ in eval t3 g'
+ | Iszero (t1) ->
+ (* we don't handle cases where t1 doesn't evaluate to an Int *)
+ let Int i1 = eval t1 g
+ (* Iszero t1 should evaluate to a Bool *)
+ in Bool (i1 = 0)
+ | If (t1, t2, t3) ->
+ (* we don't handle cases where t1 doesn't evaluate to a boolean *)
+ let Bool b1 = eval t1 g
+ in if b1 then eval t2 g
+ else eval t3 g
+ | Makepair (t1, t2) ->
+ let value1 = eval t1 g
+ in let value2 = eval t2 g
+ in Pair (value1, value2)
+ | First (t1) ->
+ (* we don't handle cases where t1 doesn't evaluate to a Pair *)
+ let Pair (value1, value2) = eval t1 g
+ in value1
+ | Lambda (arg_var, t2) -> Closure (arg_var, t2, g)
+ | Apply (t1, t2) ->
+ (* we don't handle cases where t1 doesn't evaluate to a function value *)
+ let Closure (arg_var, body, savedg) = eval t1 g
+ in let value2 = eval t2 g
+ (* evaluate body under savedg, except with arg_var bound to Nonrecursive value2 *)
+ in let savedg' = (arg_var, Nonrecursive value2) :: savedg
+ in eval body savedg'
+ | Letrec (var_to_bind, t2, t3) ->
+ (* we don't handle cases where t2 doesn't evaluate to a function value *)
+ let Closure (arg_var, body, savedg) = eval t2 g
(* evaluate t3 under a new assignment where var_to_bind has been recursively bound to that function value *)
- in let g' = (var_to_bind, Recursive_Closure (var_to_bind, arg_var, body, savedg)) :: g
- in eval t3 g'
+ in let g' = (var_to_bind, Recursive_Closure (var_to_bind, arg_var, body, savedg)) :: g
+ in eval t3 g'
;;