Stream: Coq users

Topic: Random selection


view this post on Zulip zohaze (Jan 22 2023 at 12:25):

I am writing a function which gives true in case of existence of same values between two provided indexes of list nat.
For example index[3] ,index[7] & l=[4,8,1,2,2,2,2,2,2,2,8]. I am performing patteren matching on list and function work well only for index 0 & index 1 because list start from head position. How i can select indexed randomly ?

view this post on Zulip Lessness (Jan 22 2023 at 12:55):

Imho, you don't. Because Coq has no built-in randomness.

view this post on Zulip Karl Palmskog (Jan 22 2023 at 13:52):

as a pure language, Coq indeed has no built-in random selection, but most people do it via some probability monad like Haskell, some examples:

view this post on Zulip Paolo Giarrusso (Jan 22 2023 at 19:20):

I am writing a function which gives true in case of existence of same values between two provided indexes of list nat.

it's hard to tell, but the question might be about deciding exists i1 i2 v. nth_error i1 l = Some v /\ nth_error i2 l = Some v — if so, the point is not that i1 and i2 must be random, but that one needs a complete search.

view this post on Zulip Pierre Castéran (Jan 23 2023 at 08:03):

Not clear what "provided index" means.
If only lis given, as Paolo says, you may want to prove that the following predicate is decidable:

Definition has_duplicates (l: list nat) :=
   exists i1 i2 v: nat, nth_error l i1 = Some v /\ nth_error l i2 = Some v /\ i1 <> i2.

If l, i1 and i2are "provided", you just have to compare nth_error l i1with nth_error l i2.

view this post on Zulip Michael Soegtrop (Jan 23 2023 at 08:03):

Maybe "random" is meant here in the sense of "random access memory" and not in the sense of "random number generator". In this case: accessing lists e.g. via the nth function is always O(n), but since a while Coq has support for native arrays which have O(1) access. This comes at the price of a few axioms.

view this post on Zulip Laurent Théry (Jan 23 2023 at 13:13):

Here it is

Require Import List.

Definition index (n : nat) (l : list nat) := nth 0 l n.

Definition check_index n1 n2 l :=  Nat.eqb (index n1 l) (index n2 l).

Compute check_index 3 7 (4 :: 8 :: 1 :: 2 :: 2 :: 2 :: 2 :: 2 :: 2 :: 2 ::8 :: nil).

view this post on Zulip zohaze (Jan 24 2023 at 13:29):

sorry, i have not clearly mentioned it. l[i][j] i shows index which is 0 and j shows value that is 4, next 1 index and value is 8.... (above Laurent Thery's example)

view this post on Zulip Laurent Théry (Jan 24 2023 at 14:09):

Yes

Compute index 0 (4 :: 8 :: 1 :: 2 :: 2 :: 2 :: 2 :: 2 :: 2 :: 2 ::8 :: nil).

returns 4
and

Compute index 1 (4 :: 8 :: 1 :: 2 :: 2 :: 2 :: 2 :: 2 :: 2 :: 2 ::8 :: nil).

returns 8

view this post on Zulip zohaze (Jan 24 2023 at 14:27):

Above definition checks two values at two provided indexes. But i want to find true when values between two provided index is same. Like l[i][j] for i=3 to i=7(index) l[3] , l[7] (4 :: 8 :: 1 :: 2 :: 2 :: 2 :: 2 :: 2 :: 2 :: 2 ::8 :: nil)=true
l[3] ,l[7] (4 :: 8 :: 1 :: 2 :: 2 :: 2 :: 22 :: 2 :: 2 :: 2 ::8 :: nil)=false. Secondly,in two dimentional array i should omit j for finding equal values between two indexes.

view this post on Zulip Laurent Théry (Jan 24 2023 at 15:22):

Something like this?

Require Import List.

Definition index (n : nat) (l : list nat) := nth 0 l n.

Definition check_index n1 n2 l := Nat.eqb (index n1 l) (index n2 l).

(* Build m :: m + 1 :: m + n *)
Fixpoint iota (m n : nat) : list nat :=
  match n with
  | 0 => nil
  | S n' => m :: iota (S m) n'
  end.

Compute iota 3 5.

(* Build m :: m + 1 :: n *)
Definition range m n := iota m (S n - m).

Compute range 3 7.

(* Build list of list of pairs *)
Definition all_pairs (l1 l2 : list nat) :=
  map (fun x => map (fun y => (x, y)) l1) l2.

(* Build list of list for range *)
Definition range_pairs m n := all_pairs (range m n) (range m n).

Compute range_pairs 3 7.

Definition check_range_pairs m n l :=
  map (fun l1  =>
            filter (fun p : (nat * nat) => let (x, y) := p in
                        andb (Nat.ltb x y) (check_index x y l)) l1)
    (range_pairs m n).

Compute check_range_pairs 3 7 (4 :: 8 :: 1 :: 2 :: 2 :: 2 :: 2 :: 2 :: 2 :: 2 ::8 :: nil).

Definition test m n l := Nat.ltb 0 (length (check_range_pairs m n l)).

Compute test 3 7 (4 :: 8 :: 1 :: 2 :: 2 :: 2 :: 2 :: 2 :: 2 :: 2 ::8 :: nil).

view this post on Zulip Pierre Castéran (Jan 24 2023 at 16:02):

Another solution (with Laurent's helpers):

Definition select from to (l : list nat) :=
  map (fun i =>  nth_error l i) (range from to).

Compute select 3 7 (4 :: 8 :: 1 :: 2 :: 2 :: 2 :: 2 :: 2 :: 2 :: 2 ::8 :: nil).

Fixpoint same_value (n : nat) (l: list (option nat)) : bool :=
  match l with
  | nil => true
  | Some m  :: l' =>  andb (Nat.eqb n m) (same_value n l')
  | _ => false
  end.


Definition test from to l :=
  match    select from to l with
    nil => true
  | Some n :: l' => same_value n l'
  | _ => false
  end.

Compute test 3 7 (4 :: 8 :: 1 :: 2 :: 2 :: 2 :: 2 :: 2 :: 2 :: 2 ::8 :: nil).

Compute test 2 7 (4 :: 8 :: 1 :: 2 :: 2 :: 2 :: 2 :: 2 :: 2 :: 2 ::8 :: nil).

Compute test 3 7 (4 :: 8 :: 1 :: 2 :: 2 :: 22 :: 2 :: 2 :: 2 :: 2 ::8 :: nil).

Note there was a misunderstanding on the initial specification :
"existence of same values between two provided indexes of list nat."
It would have been better to say "all the values between index i and j are equal".
Or did you mean "there exist at least two equal values between index i and j" ?

If I take the example with 3 7 (4 :: 8 :: 1 :: 2 :: 2 :: 22 :: 2 :: 2 :: 2 :: 2 ::8 :: nil)., I could say there exist some equal values between index 3 and 7.

view this post on Zulip zohaze (Jan 25 2023 at 04:22):

Yes. "all the values between index i and j are equal".

view this post on Zulip Laurent Théry (Jan 25 2023 at 04:27):

ok so Pierre solution is the right one :wink:


Last updated: Jun 24 2024 at 00:02 UTC