(* calc5.ml: calc3,ml enhanced with Mutable Pairs *)
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)
| Setfirst 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 index * index | 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 *)
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'
(* now we want to retrieve the next free index in s'' *)
in let new_index = List.length s''
(* now we want to insert value1 and value2 there; the following is an easy but inefficient way to do it *)
in let s''' = List.append s'' [value1; value2]
in (Pair (new_index, new_index + 1), s''')
| First (t1) ->
(* we don't handle cases where t1 doesn't evaluate to a Pair *)
let (Pair (index1, index2), 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')
| 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'
| Setfirst (t1, t2) ->
(* we don't handle cases where t1 doesn't evaluate to a Pair *)
let (Pair (index1, index2), 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
in (Int 42, s''')
;;