-(* calc3,ml, enhanced with Mutable Pairs *)
+(* 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 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 index = int;;
type bound_value = Nonrecursive of expressed_value | Recursive_Closure of char * char * term * assignment
- and assignment = (char * bound_value) list
+ 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;;
+ 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
+ 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 *)
+ (* 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
+ ), 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
+ 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 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
+ 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
+ | 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'
+ 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 (new_value, s'') = eval t2 g s'
- (* now we create a list which is just like s'' except it has new_value in index1 *)
+ 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 -> new_value :: xs
+ | 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''')