(* calc3.ml: 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' ;;