(* calc7.ml: calc6.ml enhanced with Aliases and Passing by Reference *) 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) | Change of (char * term * term) | Alias of (char * char * term) | Applyalias of (term * char) ;; type index = int;; type bound_value = index;; type assignment = (char * bound_value) list;; type expressed_value = Int of int | Bool of bool | Pair of expressed_value * expressed_value | Closure of char * term * assignment;; 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 *) let index = List.assoc var g (* get value stored at location index in s *) in let value = List.nth s index in (value, s) | Let (var_to_bind, t2, t3) -> let (value2, s') = eval t2 g s (* note that s' may be different from s, if t2 itself contained any mutation operations *) (* get next free index in s' *) in let new_index = List.length s' (* now we want to insert value2 there; the following is an easy but inefficient way to do it *) in let s'' = List.append s' [value2] (* bind var_to_bind to location new_index in the store *) in let g' = ((var_to_bind, new_index) :: 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 a new location containing value2 *) in let new_index = List.length s'' in let s''' = List.append s'' [value2] in let savedg' = (arg_var, new_index) :: 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 in let new_index = List.length s' in let savedg' = (var_to_bind, new_index) :: savedg in let new_closure = Closure (arg_var, body, savedg') in let s'' = List.append s' [new_closure] in let g' = (var_to_bind, new_index) :: g in eval t3 g' s'' | Change (var, t2, t3) -> (* we don't handle cases where g doesn't bind var to any value *) let index = List.assoc var g in let (value2, s') = eval t2 g s (* note that s' may be different from s, if t2 itself contained any mutation operations *) (* now we create a list which is just like s' except it has value2 at index *) 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' index (* evaluate t3 using original assignment function and new store *) in eval t3 g s'' | Alias (var_to_bind, orig_var, t3) -> (* we don't handle cases where g doesn't bind orig_var to any value *) let index = List.assoc orig_var g (* bind var_to_bind to the same index in the store *) in let g' = ((var_to_bind, index) :: g) in eval t3 g' s | Applyalias (t1, var) -> (* 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 (* we don't handle cases where g doesn't bind var to any value *) in let index = List.assoc var g (* evaluate body under savedg, except with arg_var bound to existing index *) in let savedg' = (arg_var, index) :: savedg in eval body savedg' s' ;;