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replace prodLists with list_prod from stdlib #173

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Merged
mrhaandi merged 2 commits into from
Oct 14, 2022
Merged

replace prodLists with list_prod from stdlib #173

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8172c2a
replace prodLists with list_prod from stdlib
Oct 12, 2022
c615010
remove unused lemma prod_nil
Oct 13, 2022
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15 changes: 0 additions & 15 deletions theories/Shared/Libs/PSL/FiniteTypes/BasicDefinitions.v
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Original file line number Diff line number Diff line change
Expand Up @@ -19,21 +19,6 @@ Proof.
cbn. rewrite IH. unfold Dec. now destruct (HX x y); destruct (HX y x); congruence.
Qed.

(* Function that takes two lists and returns the list of all pairs of elements from the two lists *)
Fixpoint prodLists {X Y: Type} (A: list X) (B: list Y) {struct A} :=
match A with
| nil => nil
| cons x A' => map (fun y => (x,y)) B ++ prodLists A' B end.

(* Crossing any list with the empty list always yields the empty list *)
Lemma prod_nil (X Y: Type) (A: list X) :
prodLists A ([]: list Y) = [].
Proof.
induction A.
- reflexivity.
- cbn. assumption.
Qed.

(* This function takes a (A: list X) and yields a list (option X) which for every x in A contains Some x. The resultung list also contains None. The order is preserved. None is the first element of the resulting list. *)

Definition toOptionList {X: Type} (A: list X) :=
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5 changes: 2 additions & 3 deletions theories/Shared/Libs/PSL/FiniteTypes/CompoundFinTypes.v
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@@ -1,9 +1,8 @@
From Undecidability.Shared.Libs.PSL Require Import FinTypes.

(* * Definition of prod as finType *)

Lemma ProdCount (T1 T2: eqType) (A: list T1) (B: list T2) (a:T1) (b:T2) :
count (prodLists A B) (a,b) = count A a * count B b .
count (list_prod A B) (a,b) = count A a * count B b .
Proof.
induction A.
- reflexivity.
Expand All @@ -13,7 +12,7 @@ Proof.
Qed.

Lemma prod_enum_ok (T1 T2: finType) (x: T1 * T2):
count (prodLists (elem T1) (elem T2)) x = 1.
count (list_prod (elem T1) (elem T2)) x = 1.
Proof.
destruct x as [x y]. rewrite ProdCount. unfold elem.
now repeat rewrite enum_ok.
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