(* calc4.ml: calc3.ml enhanced with Mutable Cells *) 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) | Newref of term | Deref of term | Setref of (term * term) ;; type index = int;; 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 | Mutcell of index;; type store = expressed_value list;; let rec eval (t : term) (g : assignment) (s : store) = match t with Intconstant x -> (Int x, s) | Multiplication (t1, t2) -> (* we don't handle cases where the subterms don't evaluate to Ints *) let (Int i1, s') = eval t1 g s in let (Int i2, s'') = eval t2 g s' (* Multiplication (t1, t2) should evaluate to an Int *) in (Int (i1 * i2), s'') | Addition (t1, t2) -> let (Int i1, s') = eval t1 g s in let (Int i2, s'') = eval t2 g s' in (Int (i1 + i2), s'') | 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') ), s) | 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, s') = eval t2 g s (* we have to wrap value2 in Nonrecursive *) in let g' = (var_to_bind, Nonrecursive value2) :: g in eval t3 g' s' | Iszero (t1) -> (* we don't handle cases where t1 doesn't evaluate to an Int *) let (Int i1, s') = eval t1 g s (* Iszero t1 should evaluate to a Bool *) in (Bool (i1 = 0), s') | If (t1, t2, t3) -> (* we don't handle cases where t1 doesn't evaluate to a boolean *) let (Bool b1, s') = eval t1 g s (* note we thread s' through only one of the then/else clauses *) in if b1 then eval t2 g s' else eval t3 g s' | Makepair (t1, t2) -> let (value1, s') = eval t1 g s in let (value2, s'') = eval t2 g s' in (Pair (value1, value2), s'') | First (t1) -> (* we don't handle cases where t1 doesn't evaluate to a Pair *) let (Pair (value1, value2), s') = eval t1 g s in (value1, s') | Lambda (arg_var, t2) -> (Closure (arg_var, t2, g), s) | Apply (t1, t2) -> (* we don't handle cases where t1 doesn't evaluate to a function value *) let (Closure (arg_var, body, savedg), s') = eval t1 g s in let (value2, s'') = eval t2 g s' (* evaluate body under savedg, except with arg_var bound to Nonrecursive value2 *) in let savedg' = (arg_var, Nonrecursive value2) :: savedg in eval body savedg' s'' | 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), s') = eval t2 g s (* 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' s' | Newref (t1) -> let (value1, s') = eval t1 g s (* note that s' may be different from s, if t1 itself contained any mutation operations *) (* now we want to retrieve the next free index in s' *) in let new_index = List.length s' (* now we want to insert value1 there; the following is an easy but inefficient way to do it *) in let s'' = List.append s' [value1] (* now we return a pair of a wrapped new_index, and the new store *) in (Mutcell new_index, s'') | Deref (t1) -> (* we don't handle cases where t1 doesn't evaluate to a Mutcell *) let (Mutcell index1, s') = eval t1 g s (* note that s' may be different from s, if t1 itself contained any mutation operations *) in (List.nth s' index1, s') | Setref (t1, t2) -> (* we don't handle cases where t1 doesn't evaluate to a Mutcell *) let (Mutcell index1, s') = eval t1 g s (* note that s' may be different from s, if t1 itself contained any mutation operations *) in let (value2, s'') = eval t2 g s' (* now we create a list which is just like s'' except it has value2 in index1 *) in let rec replace_nth lst m = match lst with | [] -> failwith "list too short" | x::xs when m = 0 -> value2 :: xs | x::xs -> x :: replace_nth xs (m - 1) in let s''' = replace_nth s'' index1 (* we'll arbitrarily return Int 42 as the expressed_value of a Setref operation *) in (Int 42, s''') ;;