Use new Import/Export syntax everywhere.

Also, make our redefinition of done more robust under different
orders of Importing modules.

algebra/agree.v

-Require Export algebra.cmra.
-Require Import algebra.functor.
+From algebra Require Export cmra.
+From algebra Require Import functor.
 Local Hint Extern 10 (_ ≤ _) => omega.
 
 Record agree (A : Type) : Type := Agree {

algebra/auth.v

-Require Export algebra.excl.
-Require Import algebra.functor.
+From algebra Require Export excl.
+From algebra Require Import functor.
 Local Arguments validN _ _ _ !_ /.
 
 Record auth (A : Type) : Type := Auth { authoritative : excl A ; own : A }.

algebra/base.v

-Require Export mathcomp.ssreflect.ssreflect.
-Require Export prelude.prelude.
+From mathcomp.ssreflect Require Export ssreflect.
+From prelude Require Export prelude.
 Global Set Bullet Behavior "Strict Subproofs".
-Global Open Scope general_if_scope.
\ No newline at end of file
+Global Open Scope general_if_scope.
+Ltac done := prelude.tactics.done.
\ No newline at end of file

algebra/cmra.v

-Require Export algebra.cofe.
+From algebra Require Export cofe.
 
 Class Unit (A : Type) := unit : A → A.
 Instance: Params (@unit) 2.

algebra/cmra_big_op.v

-Require Export algebra.cmra.
-Require Import prelude.fin_maps.
+From algebra Require Export cmra.
+From prelude Require Import fin_maps.
 
 Fixpoint big_op {A : cmraT} `{Empty A} (xs : list A) : A :=
   match xs with [] => ∅ | x :: xs => x ⋅ big_op xs end.

algebra/cmra_tactics.v

-Require Export algebra.cmra.
-Require Import algebra.cmra_big_op.
+From algebra Require Export cmra.
+From algebra Require Import cmra_big_op.
 
 (** * Simple solver for validity and inclusion by reflection *)
 Module ra_reflection. Section ra_reflection.

algebra/cofe.v

-Require Export algebra.base.
+From algebra Require Export base.
 
 (** Unbundeled version *)
 Class Dist A := dist : nat → relation A.

algebra/cofe_solver.v

-Require Export algebra.cofe.
+From algebra Require Export cofe.
 
 Record solution (F : cofeT → cofeT → cofeT) := Solution {
   solution_car :> cofeT;

algebra/dra.v

-Require Export algebra.cmra.
+From algebra Require Export cmra.
 
 (** From disjoint pcm *)
 Record validity {A} (P : A → Prop) : Type := Validity {

algebra/excl.v

-Require Export algebra.cmra.
-Require Import algebra.functor.
+From algebra Require Export cmra.
+From algebra Require Import functor.
 Local Arguments validN _ _ _ !_ /.
 Local Arguments valid _ _  !_ /.
 

algebra/fin_maps.v

-Require Export algebra.cmra prelude.gmap algebra.option.
-Require Import algebra.functor.
+From algebra Require Export cmra option.
+From prelude Require Export gmap.
+From algebra Require Import functor.
 
 Section cofe.
 Context `{Countable K} {A : cofeT}.

algebra/functor.v

-Require Export algebra.cmra.
+From algebra Require Export cmra.
 
 (** * Functors from COFE to CMRA *)
 (* TODO RJ: Maybe find a better name for this? It is not PL-specific any more. *)

algebra/iprod.v

-Require Export algebra.cmra.
-Require Import algebra.functor.
+From algebra Require Export cmra.
+From algebra Require Import functor.
 
 (** * Indexed product *)
 (** Need to put this in a definition to make canonical structures to work. *)

algebra/option.v

-Require Export algebra.cmra.
-Require Import algebra.functor.
+From algebra Require Export cmra.
+From algebra Require Import functor.
 
 (* COFE *)
 Section cofe.

algebra/sts.v

-Require Export algebra.cmra.
-Require Import prelude.sets algebra.dra.
+From algebra Require Export cmra.
+From prelude Require Import sets.
+From algebra Require Import dra.
 Local Arguments valid _ _ !_ /.
 Local Arguments op _ _ !_ !_ /.
 Local Arguments unit _ _ !_ /.

algebra/upred.v

-Require Export algebra.cmra.
+From algebra Require Export cmra.
 Local Hint Extern 1 (_ ≼ _) => etransitivity; [eassumption|].
 Local Hint Extern 1 (_ ≼ _) => etransitivity; [|eassumption].
 Local Hint Extern 10 (_ ≤ _) => omega.

heap_lang/derived.v

-Require Export heap_lang.lifting.
+From heap_lang Require Export lifting.
 Import uPred.
 
 (** Define some derived forms, and derived lemmas about them. *)

heap_lang/heap_lang.v

-Require Export program_logic.language prelude.strings.
-Require Import prelude.gmap.
+From program_logic Require Export language.
+From prelude Require Export strings.
+From prelude Require Import gmap.
 
 Module heap_lang.
 Open Scope Z_scope.

heap_lang/lifting.v

-Require Export program_logic.weakestpre heap_lang.heap_lang.
-Require Import program_logic.lifting.
-Require Import program_logic.ownership. (* for ownP *)
-Require Import heap_lang.tactics.
+From program_logic Require Export weakestpre.
+From heap_lang Require Export heap_lang.
+From program_logic Require Import lifting.
+From program_logic Require Import ownership. (* for ownP *)
+From heap_lang Require Import tactics.
 Export heap_lang. (* Prefer heap_lang names over language names. *)
 Import uPred.
 Local Hint Extern 0 (language.reducible _ _) => do_step ltac:(eauto 2).

heap_lang/notation.v

-Require Export heap_lang.derived.
+From heap_lang Require Export derived.
 
 (* What about Arguments for hoare triples?. *)
 Arguments wp {_ _} _ _%L _.
@@ -62,4 +62,4 @@ Notation "'rec:' f x y := e" := (RecV f x (Lam y e%L))
 Notation "'rec:' f x y z := e" := (Rec f x (Lam y (Lam z e%L)))
   (at level 102, f, x, y, z at level 1, e at level 200) : lang_scope.
 Notation "'rec:' f x y z := e" := (RecV f x (Lam y (Lam z e%L)))
-  (at level 102, f, x, y, z at level 1, e at level 200) : lang_scope.
\ No newline at end of file
+  (at level 102, f, x, y, z at level 1, e at level 200) : lang_scope.

heap_lang/substitution.v

-Require Export heap_lang.derived.
+From heap_lang Require Export derived.
 
 (** We define an alternative notion of substitution [gsubst e x ev] that
 preserves the expression [e] syntactically in case the variable [x] does not

heap_lang/tactics.v

-Require Export heap_lang.heap_lang.
-Require Import prelude.fin_maps.
+From heap_lang Require Export heap_lang.
+From prelude Require Import fin_maps.
 Import heap_lang.
 
 (** The tactic [inv_step] performs inversion on hypotheses of the shape

heap_lang/tests.v

 (** This file is essentially a bunch of testcases. *)
-Require Import program_logic.ownership.
+From program_logic Require Import ownership.
 From heap_lang Require Import substitution tactics notation.
 Import uPred.
 

prelude/base.v

@@ -7,7 +7,7 @@ structures. *)
 Global Generalizable All Variables.
 Global Set Automatic Coercions Import.
 Global Set Asymmetric Patterns.
-Require Export Morphisms RelationClasses List Bool Utf8 Program Setoid.
+From Coq Require Export Morphisms RelationClasses List Bool Utf8 Program Setoid.
 Obligation Tactic := idtac.
 
 (** * General *)

prelude/bsets.v

 (* Copyright (c) 2012-2015, Robbert Krebbers. *)
 (* This file is distributed under the terms of the BSD license. *)
 (** This file implements bsets as functions into Prop. *)
-Require Export prelude.prelude.
+From prelude Require Export prelude.
 
 Record bset (A : Type) : Type := mkBSet { bset_car : A → bool }.
 Arguments mkBSet {_} _.

prelude/co_pset.v

@@ -2,8 +2,8 @@
 (* This file is distributed under the terms of the BSD license. *)
 (** This files implements an efficient implementation of finite/cofinite sets
 of positive binary naturals [positive]. *)
-Require Export prelude.collections.
-Require Import prelude.pmap prelude.gmap prelude.mapset.
+From prelude Require Export collections.
+From prelude Require Import pmap gmap mapset.
 Local Open Scope positive_scope.
 
 (** * The tree data structure *)

prelude/collections.v

@@ -3,7 +3,7 @@
 (** This file collects definitions and theorems on collections. Most
 importantly, it implements some tactics to automatically solve goals involving
 collections. *)
-Require Export prelude.base prelude.tactics prelude.orders.
+From prelude Require Export base tactics orders.
 
 Instance collection_subseteq `{ElemOf A C} : SubsetEq C := λ X Y,
   ∀ x, x ∈ X → x ∈ Y.

prelude/countable.v

 (* Copyright (c) 2012-2015, Robbert Krebbers. *)
 (* This file is distributed under the terms of the BSD license. *)
-Require Export prelude.list.
+From prelude Require Export list.
 Local Open Scope positive.
 
 Class Countable A `{∀ x y : A, Decision (x = y)} := {

prelude/decidable.v

@@ -3,7 +3,7 @@
 (** This file collects theorems, definitions, tactics, related to propositions
 with a decidable equality. Such propositions are collected by the [Decision]
 type class. *)
-Require Export prelude.proof_irrel.
+From prelude Require Export proof_irrel.
 
 Hint Extern 200 (Decision _) => progress (lazy beta) : typeclass_instances.
 

prelude/error.v

 (* Copyright (c) 2012-2015, Robbert Krebbers. *)
 (* This file is distributed under the terms of the BSD license. *)
-Require Export prelude.list.
+From prelude Require Export list.
 
 Definition error (S E A : Type) : Type := S → E + (A * S).
 

prelude/fin_collections.v

@@ -3,8 +3,9 @@
 (** This file collects definitions and theorems on finite collections. Most
 importantly, it implements a fold and size function and some useful induction
 principles on finite collections . *)
-Require Import Permutation prelude.relations prelude.listset.
-Require Export prelude.numbers prelude.collections.
+From Coq Require Import Permutation.
+From prelude Require Import relations listset.
+From prelude Require Export numbers collections.
 
 Instance collection_size `{Elements A C} : Size C := length ∘ elements.
 Definition collection_fold `{Elements A C} {B}

prelude/fin_map_dom.v

@@ -3,7 +3,7 @@
 (** This file provides an axiomatization of the domain function of finite
 maps. We provide such an axiomatization, instead of implementing the domain
 function in a generic way, to allow more efficient implementations. *)
-Require Export prelude.collections prelude.fin_maps.
+From prelude Require Export collections fin_maps.
 
 Class FinMapDom K M D `{FMap M,
     ∀ A, Lookup K A (M A), ∀ A, Empty (M A), ∀ A, PartialAlter K A (M A),

prelude/fin_maps.v

@@ -4,8 +4,8 @@
 finite maps and collects some theory on it. Most importantly, it proves useful
 induction principles for finite maps and implements the tactic
 [simplify_map_equality] to simplify goals involving finite maps. *)
-Require Import Permutation.
-Require Export prelude.relations prelude.vector prelude.orders.
+From Coq Require Import Permutation.
+From prelude Require Export relations vector orders.
 
 (** * Axiomatization of finite maps *)
 (** We require Leibniz equality to be extensional on finite maps. This of

prelude/finite.v

 (* Copyright (c) 2012-2015, Robbert Krebbers. *)
 (* This file is distributed under the terms of the BSD license. *)
-Require Export prelude.countable prelude.list.
+From prelude Require Export countable list.
 
 Class Finite A `{∀ x y : A, Decision (x = y)} := {
   enum : list A;

prelude/gmap.v

@@ -2,8 +2,8 @@
 (* This file is distributed under the terms of the BSD license. *)
 (** This file implements finite maps and finite sets with keys of any countable
 type. The implementation is based on [Pmap]s, radix-2 search trees. *)
-Require Export prelude.countable prelude.fin_maps prelude.fin_map_dom.
-Require Import prelude.pmap prelude.mapset.
+From prelude Require Export countable fin_maps fin_map_dom.
+From prelude Require Import pmap mapset.
 
 (** * The data structure *)
 (** We pack a [Pmap] together with a proof that ensures that all keys correspond

prelude/hashset.v

@@ -3,8 +3,8 @@
 (** This file implements finite set using hash maps. Hash sets are represented
 using radix-2 search trees. Each hash bucket is thus indexed using an binary
 integer of type [Z], and contains an unordered list without duplicates. *)
-Require Export prelude.fin_maps prelude.listset.
-Require Import prelude.zmap.
+From prelude Require Export fin_maps listset.
+From prelude Require Import zmap.
 
 Record hashset {A} (hash : A → Z) := Hashset {
   hashset_car : Zmap (list A);

prelude/lexico.v

@@ -2,7 +2,7 @@
 (* This file is distributed under the terms of the BSD license. *)
 (** This files defines a lexicographic order on various common data structures
 and proves that it is a partial order having a strong variant of trichotomy. *)
-Require Import prelude.numbers.
+From prelude Require Import numbers.
 
 Notation cast_trichotomy T :=
   match T with

prelude/list.v

@@ -2,8 +2,8 @@
 (* This file is distributed under the terms of the BSD license. *)
 (** This file collects general purpose definitions and theorems on lists that
 are not in the Coq standard library. *)
-Require Export Permutation.
-Require Export prelude.numbers prelude.base prelude.decidable prelude.option.
+From Coq Require Export Permutation.
+From prelude Require Export numbers base decidable option.
 
 Arguments length {_} _.
 Arguments cons {_} _ _.

prelude/listset.v

@@ -2,7 +2,7 @@
 (* This file is distributed under the terms of the BSD license. *)
 (** This file implements finite set as unordered lists without duplicates
 removed. This implementation forms a monad. *)
-Require Export prelude.base prelude.decidable prelude.collections prelude.list.
+From prelude Require Export base decidable collections list.
 
 Record listset A := Listset { listset_car: list A }.
 Arguments listset_car {_} _.

prelude/listset_nodup.v

@@ -3,7 +3,7 @@
 (** This file implements finite as unordered lists without duplicates.
 Although this implementation is slow, it is very useful as decidable equality
 is the only constraint on the carrier set. *)
-Require Export prelude.base prelude.decidable prelude.collections prelude.list.
+From prelude Require Export base decidable collections list.
 
 Record listset_nodup A := ListsetNoDup {
   listset_nodup_car : list A; listset_nodup_prf : NoDup listset_nodup_car

prelude/mapset.v

@@ -3,7 +3,7 @@
 (** This files gives an implementation of finite sets using finite maps with
 elements of the unit type. Since maps enjoy extensional equality, the
 constructed finite sets do so as well. *)
-Require Export prelude.fin_map_dom.
+From prelude Require Export fin_map_dom.
 
 Record mapset (M : Type → Type) : Type :=
   Mapset { mapset_car: M (unit : Type) }.

prelude/natmap.v

@@ -3,7 +3,7 @@
 (** This files implements a type [natmap A] of finite maps whose keys range
 over Coq's data type of unary natural numbers [nat]. The implementation equips
 a list with a proof of canonicity. *)
-Require Import prelude.fin_maps prelude.mapset.
+From prelude Require Import fin_maps mapset.
 
 Notation natmap_raw A := (list (option A)).
 Definition natmap_wf {A} (l : natmap_raw A) :=

prelude/nmap.v

@@ -2,8 +2,8 @@
 (* This file is distributed under the terms of the BSD license. *)
 (** This files extends the implementation of finite over [positive] to finite
 maps whose keys range over Coq's data type of binary naturals [N]. *)
-Require Import prelude.pmap prelude.mapset.
-Require Export prelude.prelude prelude.fin_maps.
+From prelude Require Import pmap mapset.
+From prelude Require Export prelude fin_maps.
 
 Local Open Scope N_scope.
 

prelude/numbers.v

@@ -3,9 +3,9 @@
 (** This file collects some trivial facts on the Coq types [nat] and [N] for
 natural numbers, and the type [Z] for integers. It also declares some useful
 notations. *)
-Require Export Eqdep PArith NArith ZArith NPeano.
-Require Import QArith Qcanon.
-Require Export prelude.base prelude.decidable prelude.option.
+From Coq Require Export Eqdep PArith NArith ZArith NPeano.
+From Coq Require Import QArith Qcanon.
+From prelude Require Export base decidable option.
 Open Scope nat_scope.
 
 Coercion Z.of_nat : nat >-> Z.
@@ -50,7 +50,7 @@ Proof.
     * clear nat_le_pi. intros; exfalso; auto with lia.
     * injection 1. intros Hy. by case (nat_le_pi x y p y' q Hy). }
   intros x y p q.
-  by apply (eq_dep_eq_dec (λ x y, decide (x = y))), aux.
+  by apply (Eqdep_dec.eq_dep_eq_dec (λ x y, decide (x = y))), aux.
 Qed.
 Instance nat_lt_pi: ∀ x y : nat, ProofIrrel (x < y).
 Proof. apply _. Qed.

prelude/option.v

@@ -2,7 +2,7 @@
 (* This file is distributed under the terms of the BSD license. *)
 (** This file collects general purpose definitions and theorems on the option
 data type that are not in the Coq standard library. *)
-Require Export prelude.base prelude.tactics prelude.decidable.
+From prelude Require Export base tactics decidable.
 
 Inductive option_reflect {A} (P : A → Prop) (Q : Prop) : option A → Type :=
   | ReflectSome x : P x → option_reflect P Q (Some x)

prelude/orders.v

@@ -2,8 +2,8 @@
 (* This file is distributed under the terms of the BSD license. *)
 (** This file collects common properties of pre-orders and semi lattices. This
 theory will mainly be used for the theory on collections and finite maps. *)
-Require Export Sorted.
-Require Export prelude.base prelude.decidable prelude.tactics prelude.list.
+From Coq Require Export Sorted.
+From prelude Require Export base decidable tactics list.
 
 (** * Arbitrary pre-, parial and total orders *)
 (** Properties about arbitrary pre-, partial, and total orders. We do not use

prelude/pmap.v

@@ -7,8 +7,9 @@ trees (uncompressed Patricia trees) and guarantees logarithmic-time operations.
 However, we extend Leroy's implementation by packing the trees into a Sigma
 type such that canonicity of representation is ensured. This is necesarry for
 Leibniz equality to become extensional. *)
-Require Import PArith prelude.mapset.
-Require Export prelude.fin_maps.
+From Coq Require Import PArith.
+From prelude Require Import mapset.
+From prelude Require Export fin_maps.
 
 Local Open Scope positive_scope.
 Local Hint Extern 0 (@eq positive _ _) => congruence.

prelude/prelude.v

 (* Copyright (c) 2012-2015, Robbert Krebbers. *)
 (* This file is distributed under the terms of the BSD license. *)
-Require Export
-  prelude.base
-  prelude.tactics
-  prelude.decidable
-  prelude.orders
-  prelude.option
-  prelude.vector
-  prelude.numbers
-  prelude.relations
-  prelude.collections
-  prelude.fin_collections
-  prelude.listset
-  prelude.list
-  prelude.lexico.
+From prelude Require Export
+  base
+  tactics
+  decidable
+  orders
+  option
+  vector
+  numbers
+  relations
+  collections
+  fin_collections
+  listset
+  list
+  lexico.

prelude/pretty.v

 (* Copyright (c) 2012-2015, Robbert Krebbers. *)
 (* This file is distributed under the terms of the BSD license. *)
-Require Export prelude.strings.
-Require Import prelude.relations.
-Require Import Ascii.
+From prelude Require Export strings.
+From prelude Require Import relations.
+From Coq Require Import Ascii.
 
 Class Pretty A := pretty : A → string.
 Definition pretty_N_char (x : N) : ascii :=

prelude/proof_irrel.v

 (* Copyright (c) 2012-2015, Robbert Krebbers. *)
 (* This file is distributed under the terms of the BSD license. *)
 (** This file collects facts on proof irrelevant types/propositions. *)
-Require Export Eqdep_dec prelude.tactics.
+From Coq Require Import Eqdep_dec.
+From prelude Require Export tactics.
 
 Hint Extern 200 (ProofIrrel _) => progress (lazy beta) : typeclass_instances.
 

prelude/relations.v

@@ -4,8 +4,8 @@
 These are particularly useful as we define the operational semantics as a
 small step semantics. This file defines a hint database [ars] containing
 some theorems on abstract rewriting systems. *)
-Require Import Wf_nat.
-Require Export prelude.tactics prelude.base.
+From Coq Require Import Wf_nat.
+From prelude Require Export tactics base.
 
 (** * Definitions *)
 Section definitions.

prelude/sets.v

 (* Copyright (c) 2012-2015, Robbert Krebbers. *)
 (* This file is distributed under the terms of the BSD license. *)
 (** This file implements sets as functions into Prop. *)
-Require Export prelude.prelude.
+From prelude Require Export prelude.
 
 Record set (A : Type) : Type := mkSet { set_car : A → Prop }.
 Arguments mkSet {_} _.

prelude/streams.v

 (* Copyright (c) 2012-2015, Robbert Krebbers. *)
 (* This file is distributed under the terms of the BSD license. *)
-Require Export prelude.tactics.
+From prelude Require Export tactics.
 
 CoInductive stream (A : Type) : Type := scons : A → stream A → stream A.
 Arguments scons {_} _ _.

prelude/stringmap.v

@@ -4,8 +4,8 @@
 range over Coq's data type of strings [string]. The implementation uses radix-2
 search trees (uncompressed Patricia trees) as implemented in the file [pmap]
 and guarantees logarithmic-time operations. *)
-Require Export prelude.fin_maps prelude.pretty.
-Require Import prelude.gmap.
+From prelude Require Export fin_maps pretty.
+From prelude Require Import gmap.
 
 Notation stringmap := (gmap string).
 Notation stringset := (gset string).
@@ -58,4 +58,4 @@ Fixpoint fresh_strings_of_set
   | S n =>
      let x := fresh_string_of_set s X in
      x