Commit 11790649 authored by Robbert Krebbers's avatar Robbert Krebbers

Now compiles with 8.5 beta 3.

parent ebcb867c
PREREQUISITES
-------------
This version is known to compile with:
- Coq 8.4pl5
- SCons 2.0
- Ocaml 4.01.0
- GNU C preprocessor 4.7
BUILDING INSTRUCTIONS
---------------------
Say "scons" to build the full library, or "scons some_module.vo" to just
build some_module.vo (and its dependencies).
In addition to common Make options like -j N and -k, SCons supports some
useful options of its own, such as --debug=time, which displays the time
spent executing individual build commands.
scons -c replaces Make clean
......@@ -656,7 +656,7 @@ Lemma map_choose {A} (m : M A) : m ≠ ∅ → ∃ i x, m !! i = Some x.
Proof.
intros Hemp. destruct (map_to_list m) as [|[i x] l] eqn:Hm.
{ destruct Hemp; eauto using map_to_list_empty_inv. }
exists i x. rewrite <-elem_of_map_to_list, Hm. by left.
exists i, x. rewrite <-elem_of_map_to_list, Hm. by left.
Qed.
(** Properties of the imap function *)
......@@ -777,7 +777,7 @@ Proof.
split; [|intros (i&x&?&?) Hm; specialize (Hm i x); tauto].
rewrite map_Forall_to_list. intros Hm.
apply (not_Forall_Exists _), Exists_exists in Hm.
destruct Hm as ([i x]&?&?). exists i x. by rewrite <-elem_of_map_to_list.
destruct Hm as ([i x]&?&?). exists i, x. by rewrite <-elem_of_map_to_list.
Qed.
End map_Forall.
......
......@@ -85,7 +85,7 @@ Proof.
rewrite elem_of_list_intersection in Hx; naive_solver. }
intros [(l&?&?) (k&?&?)]. assert (x list_intersection l k)
by (by rewrite elem_of_list_intersection).
exists (list_intersection l k); split; [exists l k|]; split_ands; auto.
exists (list_intersection l k); split; [exists l, k|]; split_ands; auto.
by rewrite option_guard_True by eauto using elem_of_not_nil.
* unfold elem_of, hashset_elem_of, intersection, hashset_intersection.
intros [m1 ?] [m2 ?] x; simpl.
......@@ -95,7 +95,7 @@ Proof.
intros [(l&?&?) Hm2]; destruct (m2 !! hash x) as [k|] eqn:?; eauto.
destruct (decide (x k)); [destruct Hm2; eauto|].
assert (x list_difference l k) by (by rewrite elem_of_list_difference).
exists (list_difference l k); split; [right; exists l k|]; split_ands; auto.
exists (list_difference l k); split; [right; exists l,k|]; split_ands; auto.
by rewrite option_guard_True by eauto using elem_of_not_nil.
* unfold elem_of at 2, hashset_elem_of, elements, hashset_elems.
intros [m Hm] x; simpl. setoid_rewrite elem_of_list_bind. split.
......
......@@ -487,8 +487,8 @@ Lemma list_lookup_other l i x :
length l ≠ 1 → l !! i = Some x → ∃ j y, j ≠ i ∧ l !! j = Some y.
Proof.
intros. destruct i, l as [|x0 [|x1 l]]; simplify_equality'.
* by exists 1 x1.
* by exists 0 x0.
* by exists 1, x1.
* by exists 0, x0.
Qed.
Lemma alter_app_l f l1 l2 i :
i < length l1 → alter f i (l1 ++ l2) = alter f i l1 ++ l2.
......@@ -604,7 +604,7 @@ Proof. induction 1; rewrite ?elem_of_nil, ?elem_of_cons; intuition. Qed.
Lemma elem_of_list_split l x : x ∈ l → ∃ l1 l2, l = l1 ++ x :: l2.
Proof.
induction 1 as [x l|x y l ? [l1 [l2 ->]]]; [by eexists [], l|].
by exists (y :: l1) l2.
by exists (y :: l1), l2.
Qed.
Lemma elem_of_list_lookup_1 l x : x ∈ l → ∃ i, l !! i = Some x.
Proof.
......@@ -1621,7 +1621,7 @@ Proof.
split.
* intros Hlk. induction k as [|y k IH]; inversion Hlk.
+ eexists [], k. by repeat constructor.
+ destruct IH as (k1&k2&->&?); auto. by exists (y :: k1) k2.
+ destruct IH as (k1&k2&->&?); auto. by exists (y :: k1), k2.
* intros (k1&k2&->&?). by apply sublist_inserts_l, sublist_skip.
Qed.
Lemma sublist_app_r l k1 k2 :
......@@ -1633,9 +1633,9 @@ Proof.
{ eexists [], l. by repeat constructor. }
rewrite sublist_cons_r. intros [?|(l' & ? &?)]; subst.
+ destruct (IH l k2) as (l1&l2&?&?&?); trivial; subst.
exists l1 l2. auto using sublist_cons.
exists l1, l2. auto using sublist_cons.
+ destruct (IH l' k2) as (l1&l2&?&?&?); trivial; subst.
exists (y :: l1) l2. auto using sublist_skip.
exists (y :: l1), l2. auto using sublist_skip.
* intros (?&?&?&?&?); subst. auto using sublist_app.
Qed.
Lemma sublist_app_l l1 l2 k :
......@@ -1647,7 +1647,7 @@ Proof.
{ eexists [], k. by repeat constructor. }
rewrite sublist_cons_l. intros (k1 & k2 &?&?); subst.
destruct (IH l2 k2) as (h1 & h2 &?&?&?); trivial; subst.
exists (k1 ++ x :: h1) h2. rewrite <-(associative_L (++)).
exists (k1 ++ x :: h1), h2. rewrite <-(associative_L (++)).
auto using sublist_inserts_l, sublist_skip.
* intros (?&?&?&?&?); subst. auto using sublist_app.
Qed.
......@@ -1865,7 +1865,7 @@ Proof.
split.
* rewrite contains_sublist_r. intros (l'&E&Hl').
rewrite sublist_app_r in Hl'. destruct Hl' as (l1&l2&?&?&?); subst.
exists l1 l2. eauto using sublist_contains.
exists l1, l2. eauto using sublist_contains.
* intros (?&?&E&?&?). rewrite E. eauto using contains_app.
Qed.
Lemma contains_app_l l1 l2 k :
......@@ -1875,7 +1875,7 @@ Proof.
split.
* rewrite contains_sublist_l. intros (l'&Hl'&E).
rewrite sublist_app_l in Hl'. destruct Hl' as (k1&k2&?&?&?); subst.
exists k1 k2. split. done. eauto using sublist_contains.
exists k1, k2. split. done. eauto using sublist_contains.
* intros (?&?&E&?&?). rewrite E. eauto using contains_app.
Qed.
Lemma contains_app_inv_l l1 l2 k :
......@@ -2578,7 +2578,7 @@ Section fmap.
Proof.
revert l. induction k1 as [|y k1 IH]; simpl; [intros l ?; by eexists [],l|].
intros [|x l] ?; simplify_equality'.
destruct (IH l) as (l1&l2&->&->&->); [done|]. by exists (x :: l1) l2.
destruct (IH l) as (l1&l2&->&->&->); [done|]. by exists (x :: l1), l2.
Qed.
Lemma fmap_length l : length (f <$> l) = length l.
Proof. by induction l; f_equal'. Qed.
......@@ -3006,7 +3006,7 @@ Section zip_with.
{ intros l k ?. by eexists [], [], l, k. }
intros [|x l] [|y k] ?; simplify_equality'.
destruct (IH l k) as (l1&k1&l2&k2&->&->&->&->&?); [done |].
exists (x :: l1) (y :: k1) l2 k2; simpl; auto with congruence.
exists (x :: l1), (y :: k1), l2, k2; simpl; auto with congruence.
Qed.
Lemma zip_with_inj `{!Injective2 (=) (=) (=) f} l1 l2 k1 k2 :
length l1 = length k1 → length l2 = length k2 →
......
......@@ -19,7 +19,7 @@ Lemma natmap_wf_lookup {A} (l : natmap_raw A) :
Proof.
intros Hwf Hl. induction l as [|[x|] l IH]; simpl; [done| |].
{ exists 0. simpl. eauto. }
destruct IH as (i&x&?); eauto using natmap_wf_inv; [|by exists (S i) x].
destruct IH as (i&x&?); eauto using natmap_wf_inv; [|by exists (S i), x].
intros ->. by destruct Hwf.
Qed.
......
......@@ -114,9 +114,9 @@ Proof. by destruct i. Qed.
Lemma Pmap_ne_lookup {A} (t : Pmap_raw A) : Pmap_ne t i x, t !! i = Some x.
Proof.
induction 1 as [? x ?| l r ? IHl | l r ? IHr].
* intros. by exists 1 x.
* destruct IHl as [i [x ?]]. by exists (i~0) x.
* destruct IHr as [i [x ?]]. by exists (i~1) x.
* intros. by exists 1, x.
* destruct IHl as [i [x ?]]. by exists (i~0), x.
* destruct IHr as [i [x ?]]. by exists (i~1), x.
Qed.
Lemma Pmap_wf_eq_get {A} (t1 t2 : Pmap_raw A) :
......
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