(* calc2.ml, enhanced with Recursive Function Values *)
type term =
Intconstant of int
| Multiplication of (term * term)
| Addition of (term * term)
| Variable of char
| Let of (char * term * term)
| Iszero of term
| If of (term * term * term)
| Makepair of (term * term)
| First of term
| Lambda of (char * term)
| Apply of (term * term)
| Letrec of (char * term * term)
;;
type bound_value = Nonrecursive of expressed_value | Recursive_Closure of char * char * term * assignment
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
| 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 *)
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
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
(* 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'
;;