Move `group` stuff to its own file.

_CoqProject

@@ -4,6 +4,7 @@ theories/utils/auth_excl.v
 theories/utils/llist.v
 theories/utils/compare.v
 theories/utils/contribution.v
+theories/utils/group.v
 theories/channel/channel.v
 theories/channel/proto_model.v
 theories/channel/proto_channel.v

theories/examples/map_reduce.v

-From stdpp Require Import sorting.
 From actris.channel Require Import proto_channel proofmode.
 From iris.heap_lang Require Import proofmode notation.
-From actris.utils Require Import llist compare contribution.
+From actris.utils Require Import llist compare contribution group.
 From actris.examples Require Import map sort_fg_client.
 From iris.algebra Require Import gmultiset.
-From Coq Require Import SetoidPermutation.
 
 (** Functional version of map reduce (aka the specification) *)
-Fixpoint group_insert {A} `{EqDecision K} (i : K) (x : A)
-    (ixss : list (K * list A)) : list (K * list A) :=
-  match ixss with
-  | [] => [(i,[x])]
-  | (j,xs) :: ixss =>
-     if decide (i = j) then (j,x::xs) :: ixss else (j,xs) :: group_insert i x ixss
-  end.
-
-Fixpoint group {A} `{EqDecision K} (ixs : list (K * A)) : list (K * list A) :=
-  match ixs with
-  | [] => []
-  | (i,x) :: ixs => group_insert i x (group ixs)
-  end.
-
 Definition map_reduce {A B C} `{EqDecision K}
     (map : A → list (K * B)) (red : K → list B → list C) : list A → list C :=
   mbind (curry red) ∘ group ∘ mbind map.
-
-Instance: Params (@group_insert) 5.
-Instance: Params (@group) 3.
-Instance: Params (@group) 7.
-
+Instance: Params (@map_reduce) 7.
 
 (** Distributed version *)
 Definition par_map_reduce_map : val :=
@@ -91,101 +71,6 @@ Definition par_map_reduce : val := λ: "n" "map" "red" "xs",
 
 
 (** Properties about the functional version *)
-Local Infix "≡ₚₚ" :=
-  (PermutationA (prod_relation (=) (≡ₚ))) (at level 70, no associativity) : stdpp_scope.
-Notation "(≡ₚₚ)" := (PermutationA (prod_relation (=) (≡ₚ))) (only parsing) : stdpp_scope.
-
-Section group.
-  Context {A : Type} `{EqDecision K}.
-  Implicit Types i : K.
-  Implicit Types xs : list A.
-  Implicit Types ixs : list (K * A).
-  Implicit Types ixss : list (K * list A).
-
-  Lemma elem_of_group_insert j i x ixss :
-    j ∈ (group_insert i x ixss).*1 → i = j ∨ j ∈ ixss.*1.
-  Proof.
-    induction ixss as [|[i' x'] ixss IH];
-      repeat (simplify_eq/= || case_decide); set_solver.
-  Qed.
-
-  Lemma group_insert_commute i1 i2 x1 x2 ixss :
-    group_insert i1 x1 (group_insert i2 x2 ixss) ≡ₚₚ group_insert i2 x2 (group_insert i1 x1 ixss).
-  Proof.
-    induction ixss as [|[j x] ixss IH]; repeat (simplify_eq/= || case_decide);
-      repeat constructor; done.
- Qed.
-
-  Lemma group_insert_nodup i x ixss :
-    NoDup ixss.*1 → NoDup (group_insert i x ixss).*1.
-  Proof.
-    pose proof @elem_of_group_insert.
-    induction ixss as [|[j xs] ixss IH]; csimpl; inversion_clear 1;
-      repeat (simplify_eq/= || case_decide); repeat constructor; set_solver.
-  Qed.
-  Lemma group_nodup ixs : NoDup (group ixs).*1.
-  Proof.
-    induction ixs as [|[i x] ixs IH]; csimpl;
-      auto using group_insert_nodup, NoDup_nil_2.
-  Qed.
-
-  Lemma grouped_permutation_elem_of ixss1 ixss2 i :
-    ixss1 ≡ₚₚ ixss2 → i ∈ ixss1.*1 → i ∈ ixss2.*1.
-  Proof.
-    induction 1 as [|[i1 xs1] [i2 xs2] ixss1 ixss2 [??]|[i1 xs1] [i2 xs2] ixss|];
-      set_solver.
-  Qed.
-
-  Lemma grouped_permutation_nodup ixss1 ixss2 :
-    ixss1 ≡ₚₚ ixss2 → NoDup ixss1.*1 → NoDup ixss2.*1.
-  Proof.
-    pose proof @grouped_permutation_elem_of.
-    induction 1 as [|[i1 xs1] [i2 xs2] ixss1 ixss2 [??]|[i1 xs1] [i2 xs2] ixss|];
-      csimpl; rewrite ?NoDup_cons; try set_solver.
-  Qed.
-
-  Lemma group_insert_perm ixss1 ixss2 i x :
-    NoDup ixss1.*1 →
-    ixss1 ≡ₚₚ ixss2 → group_insert i x ixss1 ≡ₚₚ group_insert i x ixss2.
-  Proof.
-    induction 2 as [|[i1 xs1] [i2 xs2] ixss1 ixss2 [??]|[i1 xs1] [i2 xs2] ixss|];
-      repeat match goal with
-      | _ => progress (simplify_eq/= || case_decide)
-      | H : NoDup (_ :: _) |- _ => inversion_clear H
-      end; first [repeat constructor; by auto
-                 |set_solver
-                 |etrans; eauto using grouped_permutation_nodup].
-  Qed.
-
-  Global Instance group_perm : Proper ((≡ₚ) ==> (≡ₚₚ)) (@group A K _).
-  Proof.
-    induction 1; repeat (simplify_eq/= || case_decide || case_match);
-      first [by etrans|auto using group_insert_perm, group_nodup, group_insert_commute].
-  Qed.
-
-  Lemma group_fmap (i : K) xs : xs ≠ [] → group ((i,) <$> xs) ≡ₚₚ [(i, xs)].
-  Proof.
-    induction xs as [|x1 [|x2 xs] IH]; intros; simplify_eq/=; try done.
-    etrans.
-    { apply group_insert_perm, IH; auto using group_insert_nodup, group_nodup. }
-    simpl; by case_decide.
-  Qed.
-  Lemma group_insert_snoc ixss i x j ys :
-    i ≠ j →
-    group_insert i x (ixss ++ [(j, ys)]) ≡ₚₚ group_insert i x ixss ++ [(j,ys)].
-  Proof.
-    intros. induction ixss as [|[i' xs'] ixss IH];
-      repeat (simplify_eq/= || case_decide); repeat constructor; by auto.
-  Qed.
-  Lemma group_snoc ixs j ys :
-    j ∉ ixs.*1 → ys ≠ [] → group (ixs ++ ((j,) <$> ys)) ≡ₚₚ group ixs ++ [(j,ys)].
-  Proof.
-    induction ixs as [|[i x] ixs IH]; csimpl; first by auto using group_fmap.
-    rewrite ?not_elem_of_cons=> -[??]. etrans; last by apply group_insert_snoc.
-    apply group_insert_perm, IH; auto using group_nodup.
-  Qed.
-End group.
-
 Section map_reduce.
   Context {A B C} `{EqDecision K} (map : A → list (K * B)) (red : K → list B → list C).
   Context `{!∀ j, Proper ((≡ₚ) ==> (≡ₚ)) (red j)}.
@@ -202,7 +87,6 @@ Section map_reduce.
   Proof. intros xs1 xs2 Hxs. by rewrite /map_reduce /= Hxs. Qed.
 End map_reduce.
 
-
 (** Correctness proofs of the distributed version *)
 Class map_reduceG Σ A B `{Countable A, Countable B} := {
   map_reduce_mapG :> mapG Σ A;

theories/examples/sort_fg.v

-From stdpp Require Import sorting.
+From stdpp Require Export sorting.
 From actris.channel Require Import proto_channel proofmode.
 From iris.heap_lang Require Import proofmode notation.
 From iris.heap_lang Require Import assert.

theories/utils/group.v

+From stdpp Require Export prelude.
+From Coq Require Export SetoidPermutation.
+
+Fixpoint group_insert {A} `{EqDecision K} (i : K) (x : A)
+    (ixss : list (K * list A)) : list (K * list A) :=
+  match ixss with
+  | [] => [(i,[x])]
+  | (j,xs) :: ixss =>
+     if decide (i = j) then (j,x::xs) :: ixss else (j,xs) :: group_insert i x ixss
+  end.
+
+Fixpoint group {A} `{EqDecision K} (ixs : list (K * A)) : list (K * list A) :=
+  match ixs with
+  | [] => []
+  | (i,x) :: ixs => group_insert i x (group ixs)
+  end.
+
+Instance: Params (@group_insert) 5.
+Instance: Params (@group) 3.
+
+Local Infix "≡ₚₚ" :=
+  (PermutationA (prod_relation (=) (≡ₚ))) (at level 70, no associativity) : stdpp_scope.
+Notation "(≡ₚₚ)" := (PermutationA (prod_relation (=) (≡ₚ))) (only parsing) : stdpp_scope.
+
+Section group.
+  Context {A : Type} `{EqDecision K}.
+  Implicit Types i : K.
+  Implicit Types xs : list A.
+  Implicit Types ixs : list (K * A).
+  Implicit Types ixss : list (K * list A).
+
+  Lemma elem_of_group_insert j i x ixss :
+    j ∈ (group_insert i x ixss).*1 → i = j ∨ j ∈ ixss.*1.
+  Proof.
+    induction ixss as [|[i' x'] ixss IH];
+      repeat (simplify_eq/= || case_decide); set_solver.
+  Qed.
+
+  Lemma group_insert_commute i1 i2 x1 x2 ixss :
+    group_insert i1 x1 (group_insert i2 x2 ixss) ≡ₚₚ group_insert i2 x2 (group_insert i1 x1 ixss).
+  Proof.
+    induction ixss as [|[j x] ixss IH]; repeat (simplify_eq/= || case_decide);
+      repeat constructor; done.
+ Qed.
+
+  Lemma group_insert_nodup i x ixss :
+    NoDup ixss.*1 → NoDup (group_insert i x ixss).*1.
+  Proof.
+    pose proof @elem_of_group_insert.
+    induction ixss as [|[j xs] ixss IH]; csimpl; inversion_clear 1;
+      repeat (simplify_eq/= || case_decide); repeat constructor; set_solver.
+  Qed.
+  Lemma group_nodup ixs : NoDup (group ixs).*1.
+  Proof.
+    induction ixs as [|[i x] ixs IH]; csimpl;
+      auto using group_insert_nodup, NoDup_nil_2.
+  Qed.
+
+  Lemma grouped_permutation_elem_of ixss1 ixss2 i :
+    ixss1 ≡ₚₚ ixss2 → i ∈ ixss1.*1 → i ∈ ixss2.*1.
+  Proof.
+    induction 1 as [|[i1 xs1] [i2 xs2] ixss1 ixss2 [??]|[i1 xs1] [i2 xs2] ixss|];
+      set_solver.
+  Qed.
+
+  Lemma grouped_permutation_nodup ixss1 ixss2 :
+    ixss1 ≡ₚₚ ixss2 → NoDup ixss1.*1 → NoDup ixss2.*1.
+  Proof.
+    pose proof @grouped_permutation_elem_of.
+    induction 1 as [|[i1 xs1] [i2 xs2] ixss1 ixss2 [??]|[i1 xs1] [i2 xs2] ixss|];
+      csimpl; rewrite ?NoDup_cons; try set_solver.
+  Qed.
+
+  Lemma group_insert_perm ixss1 ixss2 i x :
+    NoDup ixss1.*1 →
+    ixss1 ≡ₚₚ ixss2 → group_insert i x ixss1 ≡ₚₚ group_insert i x ixss2.
+  Proof.
+    induction 2 as [|[i1 xs1] [i2 xs2] ixss1 ixss2 [??]|[i1 xs1] [i2 xs2] ixss|];
+      repeat match goal with
+      | _ => progress (simplify_eq/= || case_decide)
+      | H : NoDup (_ :: _) |- _ => inversion_clear H
+      end; first [repeat constructor; by auto
+                 |set_solver
+                 |etrans; eauto using grouped_permutation_nodup].
+  Qed.
+
+  Global Instance group_perm : Proper ((≡ₚ) ==> (≡ₚₚ)) (@group A K _).
+  Proof.
+    induction 1; repeat (simplify_eq/= || case_decide || case_match);
+      first [by etrans|auto using group_insert_perm, group_nodup, group_insert_commute].
+  Qed.
+
+  Lemma group_fmap (i : K) xs : xs ≠ [] → group ((i,) <$> xs) ≡ₚₚ [(i, xs)].
+  Proof.
+    induction xs as [|x1 [|x2 xs] IH]; intros; simplify_eq/=; try done.
+    etrans.
+    { apply group_insert_perm, IH; auto using group_insert_nodup, group_nodup. }
+    simpl; by case_decide.
+  Qed.
+  Lemma group_insert_snoc ixss i x j ys :
+    i ≠ j →
+    group_insert i x (ixss ++ [(j, ys)]) ≡ₚₚ group_insert i x ixss ++ [(j,ys)].
+  Proof.
+    intros. induction ixss as [|[i' xs'] ixss IH];
+      repeat (simplify_eq/= || case_decide); repeat constructor; by auto.
+  Qed.
+  Lemma group_snoc ixs j ys :
+    j ∉ ixs.*1 → ys ≠ [] → group (ixs ++ ((j,) <$> ys)) ≡ₚₚ group ixs ++ [(j,ys)].
+  Proof.
+    induction ixs as [|[i x] ixs IH]; csimpl; [by auto using group_fmap|].
+    rewrite ?not_elem_of_cons; intros [??]. etrans; [|by apply group_insert_snoc].
+    apply group_insert_perm, IH; auto using group_nodup.
+  Qed.
+End group.