Singly-linked list/Traversal: Difference between revisions
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iMagicNumber: .int 0xCCCCCCCD
</lang>
=={{header|ATS}}==
<lang ATS>(*------------------------------------------------------------------*)
(* The Rosetta Code linear list type can contain any vt@ype.
(The ‘@’ means it doesn’t have to be the size of a pointer.
You can read {0 <= n} as ‘for all non-negative n’. *)
dataviewtype rclist_vt (vt : vt@ype+, n : int) =
| rclist_vt_nil (vt, 0)
| {0 <= n} rclist_vt_cons (vt, n + 1) of (vt, rclist_vt (vt, n))
(* A lemma one will need: lists never have negative lengths. *)
extern prfun {vt : vt@ype}
lemma_rclist_vt_param
{n : int}
(lst : !rclist_vt (vt, n)) :<prf> [0 <= n] void
(* Proof of the lemma. *)
primplement {vt}
lemma_rclist_vt_param lst =
case+ lst of
| rclist_vt_nil () => ()
| rclist_vt_cons _ => ()
(*------------------------------------------------------------------*)
(* For simplicity, the Rosetta Code linear list traverse-and-print
routine will be specifically for lists of ‘int’. *)
(* Some things that will be needed. *)
#include "share/atspre_staload.hats"
(* The list is passed by value and will be preserved with the same
type. *)
extern fun
rclist_int_traverse_and_print
{m : int} (* ‘for all list lengths m’ *)
(lst : !rclist_vt (int, m) >> (* ! = pass by value *)
(* The new type will be the same as the old
type. *)
rclist_vt (int, m)) : void
implement
rclist_int_traverse_and_print {m} (lst) =
{
(* A recursive nested function that traverses the list, printing
elements along the way. *)
fun
traverse {k : int | 0 <= k}
.<k>. (* Means: ‘k must uniformly decrease towards zero.’
If so, that is proof that ‘find’ terminates. *)
(lst : !rclist_vt (int, k) >> rclist_vt (int, k)) :
void =
case+ lst of
| rclist_vt_nil () => () (* End of list. *)
| rclist_vt_cons (head, tail) =>
begin
println! (head);
traverse tail
end
(* The following is needed to prove that the initial k above
satisfies 0 <= k. *)
prval _ = lemma_rclist_vt_param lst
val _ = traverse lst
}
(* Now let’s try it. *)
(* Some convenient notation. *)
#define NIL rclist_vt_nil ()
#define :: rclist_vt_cons
overload traverse_and_print with rclist_int_traverse_and_print
val A = 123
val B = 789
val C = 456
val lst = A :: C :: B :: NIL
val () = traverse_and_print lst
(*------------------------------------------------------------------*)
implement
main0 () = ()</lang>
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