diff options
Diffstat (limited to 'test-suite')
35 files changed, 592 insertions, 26 deletions
diff --git a/test-suite/bugs/closed/3612.v b/test-suite/bugs/closed/3612.v index 73709268a4..33e5d532ad 100644 --- a/test-suite/bugs/closed/3612.v +++ b/test-suite/bugs/closed/3612.v @@ -39,7 +39,6 @@ Axiom path_path_sigma : forall {A : Type} (P : A -> Type) (u v : sigT P) p = q. Declare ML Module "ltac_plugin". -Declare ML Module "coretactics". Set Default Proof Mode "Classic". diff --git a/test-suite/bugs/closed/3649.v b/test-suite/bugs/closed/3649.v index 179f81e668..a664a1ef1d 100644 --- a/test-suite/bugs/closed/3649.v +++ b/test-suite/bugs/closed/3649.v @@ -3,7 +3,6 @@ (* coqc version trunk (September 2014) compiled on Sep 18 2014 21:0:5 with OCaml 4.01.0 coqtop version cagnode16:/afs/csail.mit.edu/u/j/jgross/coq-trunk,trunk (07e4438bd758c2ced8caf09a6961ccd77d84e42b) *) Declare ML Module "ltac_plugin". -Declare ML Module "coretactics". Set Default Proof Mode "Classic". Reserved Notation "x -> y" (at level 99, right associativity, y at level 200). Reserved Notation "x = y" (at level 70, no associativity). @@ -14,7 +13,6 @@ Axiom admit : forall {T}, T. Notation "A -> B" := (forall (_ : A), B) : type_scope. Reserved Infix "o" (at level 40, left associativity). Inductive paths {A : Type} (a : A) : A -> Type := idpath : paths a a where "x = y" := (@paths _ x y) : type_scope. -Ltac constr_eq a b := let test := constr:(@idpath _ _ : a = b) in idtac. Global Set Primitive Projections. Delimit Scope morphism_scope with morphism. Record PreCategory := diff --git a/test-suite/bugs/closed/4250.v b/test-suite/bugs/closed/4250.v new file mode 100644 index 0000000000..74cacf559a --- /dev/null +++ b/test-suite/bugs/closed/4250.v @@ -0,0 +1,11 @@ +Require Import FunInd. +Require Vector. +Generalizable All Variables. + +Definition f `{n:nat , u:Vector.t A n} := n. + +Function f2 {A:Type} {n:nat} {v:Vector.t A n} : nat := n. + +(* fails with "The reference A was not found in the current environment." *) +Function f3 `{n:nat , u:Vector.t A n} := u. +Check R_f3_complete.
\ No newline at end of file diff --git a/test-suite/bugs/closed/5205.v b/test-suite/bugs/closed/5205.v new file mode 100644 index 0000000000..406f37a4b1 --- /dev/null +++ b/test-suite/bugs/closed/5205.v @@ -0,0 +1,6 @@ +Definition foo (n : nat) (m : nat) : nat := m. + +Arguments foo {_} _, _ _. + +Check foo 1 1. +Check foo (n:=1) 1. diff --git a/test-suite/bugs/closed/5365.v b/test-suite/bugs/closed/5365.v new file mode 100644 index 0000000000..be360d24d2 --- /dev/null +++ b/test-suite/bugs/closed/5365.v @@ -0,0 +1,13 @@ + +Inductive TupleT : nat -> Type := +| nilT : TupleT 0 +| consT {n} A : (A -> TupleT n) -> TupleT (S n). + +Inductive Tuple : forall n, TupleT n -> Type := + nil : Tuple _ nilT +| cons {n A} (x : A) (F : A -> TupleT n) : Tuple _ (F x) -> Tuple _ (consT A F). + +Inductive TupleMap : forall n, TupleT n -> TupleT n -> Type := + tmNil : TupleMap _ nilT nilT +| tmCons {n} {A B : Type} (F : A -> TupleT n) (G : B -> TupleT n) + : (forall x, sigT (fun y => TupleMap _ (F x) (G y))) -> TupleMap _ (consT A F) (consT B G). diff --git a/test-suite/bugs/closed/5618.v b/test-suite/bugs/closed/5618.v new file mode 100644 index 0000000000..ab88a88f44 --- /dev/null +++ b/test-suite/bugs/closed/5618.v @@ -0,0 +1,9 @@ +Require Import FunInd. + +Function test {T} (v : T) (x : nat) : nat := + match x with + | 0 => 0 + | S x' => test v x' + end. + +Check R_test_complete.
\ No newline at end of file diff --git a/test-suite/failure/Tauto.v b/test-suite/failure/Tauto.v index d91d159d9c..19976b41bd 100644 --- a/test-suite/failure/Tauto.v +++ b/test-suite/failure/Tauto.v @@ -1,6 +1,6 @@ (************************************************************************) (* v * The Coq Proof Assistant / The Coq Development Team *) -(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2016 *) +(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *) (* \VV/ **************************************************************) (* // * This file is distributed under the terms of the *) (* * GNU Lesser General Public License Version 2.1 *) diff --git a/test-suite/failure/clash_cons.v b/test-suite/failure/clash_cons.v index b3fbff680b..1761cc437d 100644 --- a/test-suite/failure/clash_cons.v +++ b/test-suite/failure/clash_cons.v @@ -1,6 +1,6 @@ (************************************************************************) (* v * The Coq Proof Assistant / The Coq Development Team *) -(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2016 *) +(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *) (* \VV/ **************************************************************) (* // * This file is distributed under the terms of the *) (* * GNU Lesser General Public License Version 2.1 *) diff --git a/test-suite/failure/fixpoint1.v b/test-suite/failure/fixpoint1.v index c2b521c214..0739982442 100644 --- a/test-suite/failure/fixpoint1.v +++ b/test-suite/failure/fixpoint1.v @@ -1,6 +1,6 @@ (************************************************************************) (* v * The Coq Proof Assistant / The Coq Development Team *) -(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2016 *) +(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *) (* \VV/ **************************************************************) (* // * This file is distributed under the terms of the *) (* * GNU Lesser General Public License Version 2.1 *) diff --git a/test-suite/failure/guard.v b/test-suite/failure/guard.v index 8db2785837..312dc48bea 100644 --- a/test-suite/failure/guard.v +++ b/test-suite/failure/guard.v @@ -1,6 +1,6 @@ (************************************************************************) (* v * The Coq Proof Assistant / The Coq Development Team *) -(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2016 *) +(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *) (* \VV/ **************************************************************) (* // * This file is distributed under the terms of the *) (* * GNU Lesser General Public License Version 2.1 *) diff --git a/test-suite/failure/illtype1.v b/test-suite/failure/illtype1.v index 8ed3af1ce4..fdd1bddd88 100644 --- a/test-suite/failure/illtype1.v +++ b/test-suite/failure/illtype1.v @@ -1,6 +1,6 @@ (************************************************************************) (* v * The Coq Proof Assistant / The Coq Development Team *) -(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2016 *) +(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *) (* \VV/ **************************************************************) (* // * This file is distributed under the terms of the *) (* * GNU Lesser General Public License Version 2.1 *) diff --git a/test-suite/failure/positivity.v b/test-suite/failure/positivity.v index 8089de2bf0..b21204b9e4 100644 --- a/test-suite/failure/positivity.v +++ b/test-suite/failure/positivity.v @@ -1,6 +1,6 @@ (************************************************************************) (* v * The Coq Proof Assistant / The Coq Development Team *) -(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2016 *) +(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *) (* \VV/ **************************************************************) (* // * This file is distributed under the terms of the *) (* * GNU Lesser General Public License Version 2.1 *) diff --git a/test-suite/failure/redef.v b/test-suite/failure/redef.v index c8dc6303f7..c49dbd7cae 100644 --- a/test-suite/failure/redef.v +++ b/test-suite/failure/redef.v @@ -1,6 +1,6 @@ (************************************************************************) (* v * The Coq Proof Assistant / The Coq Development Team *) -(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2016 *) +(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *) (* \VV/ **************************************************************) (* // * This file is distributed under the terms of the *) (* * GNU Lesser General Public License Version 2.1 *) diff --git a/test-suite/failure/search.v b/test-suite/failure/search.v index 648ab0820c..fae6cd6f3b 100644 --- a/test-suite/failure/search.v +++ b/test-suite/failure/search.v @@ -1,6 +1,6 @@ (************************************************************************) (* v * The Coq Proof Assistant / The Coq Development Team *) -(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2016 *) +(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *) (* \VV/ **************************************************************) (* // * This file is distributed under the terms of the *) (* * GNU Lesser General Public License Version 2.1 *) diff --git a/test-suite/ideal-features/Apply.v b/test-suite/ideal-features/Apply.v index c8e9af216e..85680e94b9 100644 --- a/test-suite/ideal-features/Apply.v +++ b/test-suite/ideal-features/Apply.v @@ -1,6 +1,6 @@ (************************************************************************) (* v * The Coq Proof Assistant / The Coq Development Team *) -(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2016 *) +(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *) (* \VV/ **************************************************************) (* // * This file is distributed under the terms of the *) (* * GNU Lesser General Public License Version 2.1 *) diff --git a/test-suite/misc/deps-checksum.sh b/test-suite/misc/deps-checksum.sh index 1e2afb7540..e07612b84c 100755 --- a/test-suite/misc/deps-checksum.sh +++ b/test-suite/misc/deps-checksum.sh @@ -1,4 +1,4 @@ -rm -f misc/deps/*/*.vo +rm -f misc/deps/A/*.vo misc/deps/B/*.vo $coqc -R misc/deps/A A misc/deps/A/A.v $coqc -R misc/deps/B A misc/deps/B/A.v $coqc -R misc/deps/B A misc/deps/B/B.v diff --git a/test-suite/misc/deps-order.sh b/test-suite/misc/deps-order.sh index 375b706f0a..00c5eb1bd5 100755 --- a/test-suite/misc/deps-order.sh +++ b/test-suite/misc/deps-order.sh @@ -1,7 +1,7 @@ # Check that both coqdep and coqtop/coqc supports -R # Check that both coqdep and coqtop/coqc takes the later -R # See bugs 2242, 2337, 2339 -rm -f misc/deps/*/*.vo +rm -f misc/deps/lib/*.vo misc/deps/client/*.vo tmpoutput=`mktemp /tmp/coqcheck.XXXXXX` $coqdep -R misc/deps/lib lib -R misc/deps/client client misc/deps/client/bar.v 2>&1 | head -n 1 > $tmpoutput diff -u misc/deps/deps.out $tmpoutput 2>&1 diff --git a/test-suite/output/Notations.v b/test-suite/output/Notations.v index 2ccca829d6..b9985a594f 100644 --- a/test-suite/output/Notations.v +++ b/test-suite/output/Notations.v @@ -1,3 +1,14 @@ +(* Bug 5568, don't warn for notations in repeated module import *) + +Module foo. +Notation compose := (fun g f => g f). +Notation "g & f" := (compose g f) (at level 10). +End foo. + +Import foo. +Import foo. +Import foo. + (**********************************************************************) (* Notations for if and let (submitted by Roland Zumkeller) *) diff --git a/test-suite/output/RecognizePluginWarning.out b/test-suite/output/RecognizePluginWarning.out new file mode 100644 index 0000000000..e69de29bb2 --- /dev/null +++ b/test-suite/output/RecognizePluginWarning.out diff --git a/test-suite/output/RecognizePluginWarning.v b/test-suite/output/RecognizePluginWarning.v new file mode 100644 index 0000000000..cd667bbd00 --- /dev/null +++ b/test-suite/output/RecognizePluginWarning.v @@ -0,0 +1,5 @@ +(* -*- mode: coq; coq-prog-args: ("-emacs" "-w" "extraction-logical-axiom") -*- *) + +(* Test that mentioning a warning defined in plugins works. The failure +mode here is that these result in a warning about unknown warnings, since the +plugins are not known at command line parsing time. *) diff --git a/test-suite/output/UsePluginWarning.out b/test-suite/output/UsePluginWarning.out new file mode 100644 index 0000000000..47409f3ec5 --- /dev/null +++ b/test-suite/output/UsePluginWarning.out @@ -0,0 +1 @@ +type foo = __ diff --git a/test-suite/output/UsePluginWarning.v b/test-suite/output/UsePluginWarning.v new file mode 100644 index 0000000000..c6e0054641 --- /dev/null +++ b/test-suite/output/UsePluginWarning.v @@ -0,0 +1,7 @@ +(* -*- mode: coq; coq-prog-args: ("-emacs" "-w" "-extraction-logical-axiom") -*- *) + +Require Extraction. +Axiom foo : Prop. + +Extraction foo. + diff --git a/test-suite/success/Check.v b/test-suite/success/Check.v index e4ee351c3a..0f677a8495 100644 --- a/test-suite/success/Check.v +++ b/test-suite/success/Check.v @@ -1,6 +1,6 @@ (************************************************************************) (* v * The Coq Proof Assistant / The Coq Development Team *) -(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2016 *) +(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *) (* \VV/ **************************************************************) (* // * This file is distributed under the terms of the *) (* * GNU Lesser General Public License Version 2.1 *) diff --git a/test-suite/success/Field.v b/test-suite/success/Field.v index 438e461357..018b22c489 100644 --- a/test-suite/success/Field.v +++ b/test-suite/success/Field.v @@ -1,6 +1,6 @@ (************************************************************************) (* v * The Coq Proof Assistant / The Coq Development Team *) -(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2016 *) +(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *) (* \VV/ **************************************************************) (* // * This file is distributed under the terms of the *) (* * GNU Lesser General Public License Version 2.1 *) diff --git a/test-suite/success/FunindExtraction_compat86.v b/test-suite/success/FunindExtraction_compat86.v new file mode 100644 index 0000000000..8912197d2f --- /dev/null +++ b/test-suite/success/FunindExtraction_compat86.v @@ -0,0 +1,506 @@ +(* -*- coq-prog-args: ("-compat" "8.6") -*- *) + +Definition iszero (n : nat) : bool := + match n with + | O => true + | _ => false + end. + +Functional Scheme iszero_ind := Induction for iszero Sort Prop. + +Lemma toto : forall n : nat, n = 0 -> iszero n = true. +intros x eg. + functional induction iszero x; simpl. +trivial. +inversion eg. +Qed. + + +Function ftest (n m : nat) : nat := + match n with + | O => match m with + | O => 0 + | _ => 1 + end + | S p => 0 + end. +(* MS: FIXME: apparently can't define R_ftest_complete. Rest of the file goes through. *) + +Lemma test1 : forall n m : nat, ftest n m <= 2. +intros n m. + functional induction ftest n m; auto. +Qed. + +Lemma test2 : forall m n, ~ 2 = ftest n m. +Proof. +intros n m;intro H. +functional inversion H ftest. +Qed. + +Lemma test3 : forall n m, ftest n m = 0 -> (n = 0 /\ m = 0) \/ n <> 0. +Proof. +functional inversion 1 ftest;auto. +Qed. + + +Require Import Arith. +Lemma test11 : forall m : nat, ftest 0 m <= 2. +intros m. + functional induction ftest 0 m. +auto. +auto. +auto with *. +Qed. + +Function lamfix (m n : nat) {struct n } : nat := + match n with + | O => m + | S p => lamfix m p + end. + +(* Parameter v1 v2 : nat. *) + +Lemma lamfix_lem : forall v1 v2 : nat, lamfix v1 v2 = v1. +intros v1 v2. + functional induction lamfix v1 v2. +trivial. +assumption. +Defined. + + + +(* polymorphic function *) +Require Import List. + +Functional Scheme app_ind := Induction for app Sort Prop. + +Lemma appnil : forall (A : Set) (l l' : list A), l' = nil -> l = l ++ l'. +intros A l l'. + functional induction app A l l'; intuition. + rewrite <- H0; trivial. +Qed. + + + + + +Require Export Arith. + + +Function trivfun (n : nat) : nat := + match n with + | O => 0 + | S m => trivfun m + end. + + +(* essaie de parametre variables non locaux:*) + +Parameter varessai : nat. + +Lemma first_try : trivfun varessai = 0. + functional induction trivfun varessai. +trivial. +assumption. +Defined. + + + Functional Scheme triv_ind := Induction for trivfun Sort Prop. + +Lemma bisrepetita : forall n' : nat, trivfun n' = 0. +intros n'. + functional induction trivfun n'. +trivial. +assumption. +Qed. + + + + + + + +Function iseven (n : nat) : bool := + match n with + | O => true + | S (S m) => iseven m + | _ => false + end. + + +Function funex (n : nat) : nat := + match iseven n with + | true => n + | false => match n with + | O => 0 + | S r => funex r + end + end. + + +Function nat_equal_bool (n m : nat) {struct n} : bool := + match n with + | O => match m with + | O => true + | _ => false + end + | S p => match m with + | O => false + | S q => nat_equal_bool p q + end + end. + + +Require Export Div2. +Require Import Nat. +Functional Scheme div2_ind := Induction for div2 Sort Prop. +Lemma div2_inf : forall n : nat, div2 n <= n. +intros n. + functional induction div2 n. +auto. +auto. + +apply le_S. +apply le_n_S. +exact IHn0. +Qed. + +(* reuse this lemma as a scheme:*) + +Function nested_lam (n : nat) : nat -> nat := + match n with + | O => fun m : nat => 0 + | S n' => fun m : nat => m + nested_lam n' m + end. + + +Lemma nest : forall n m : nat, nested_lam n m = n * m. +intros n m. + functional induction nested_lam n m; simpl;auto. +Qed. + + +Function essai (x : nat) (p : nat * nat) {struct x} : nat := + let (n, m) := (p: nat*nat) in + match n with + | O => 0 + | S q => match x with + | O => 1 + | S r => S (essai r (q, m)) + end + end. + +Lemma essai_essai : + forall (x : nat) (p : nat * nat), let (n, m) := p in 0 < n -> 0 < essai x p. +intros x p. + functional induction essai x p; intros. +inversion H. +auto with arith. + auto with arith. +Qed. + +Function plus_x_not_five'' (n m : nat) {struct n} : nat := + let x := nat_equal_bool m 5 in + let y := 0 in + match n with + | O => y + | S q => + let recapp := plus_x_not_five'' q m in + match x with + | true => S recapp + | false => S recapp + end + end. + +Lemma notplusfive'' : forall x y : nat, y = 5 -> plus_x_not_five'' x y = x. +intros a b. + functional induction plus_x_not_five'' a b; intros hyp; simpl; auto. +Qed. + +Lemma iseq_eq : forall n m : nat, n = m -> nat_equal_bool n m = true. +intros n m. + functional induction nat_equal_bool n m; simpl; intros hyp; auto. +rewrite <- hyp in y; simpl in y;tauto. +inversion hyp. +Qed. + +Lemma iseq_eq' : forall n m : nat, nat_equal_bool n m = true -> n = m. +intros n m. + functional induction nat_equal_bool n m; simpl; intros eg; auto. +inversion eg. +inversion eg. +Qed. + + +Inductive istrue : bool -> Prop := + istrue0 : istrue true. + +Functional Scheme add_ind := Induction for add Sort Prop. + +Lemma inf_x_plusxy' : forall x y : nat, x <= x + y. +intros n m. + functional induction add n m; intros. +auto with arith. +auto with arith. +Qed. + + +Lemma inf_x_plusxy'' : forall x : nat, x <= x + 0. +intros n. +unfold plus. + functional induction plus n 0; intros. +auto with arith. +apply le_n_S. +assumption. +Qed. + +Lemma inf_x_plusxy''' : forall x : nat, x <= 0 + x. +intros n. + functional induction plus 0 n; intros; auto with arith. +Qed. + +Function mod2 (n : nat) : nat := + match n with + | O => 0 + | S (S m) => S (mod2 m) + | _ => 0 + end. + +Lemma princ_mod2 : forall n : nat, mod2 n <= n. +intros n. + functional induction mod2 n; simpl; auto with arith. +Qed. + +Function isfour (n : nat) : bool := + match n with + | S (S (S (S O))) => true + | _ => false + end. + +Function isononeorfour (n : nat) : bool := + match n with + | S O => true + | S (S (S (S O))) => true + | _ => false + end. + +Lemma toto'' : forall n : nat, istrue (isfour n) -> istrue (isononeorfour n). +intros n. + functional induction isononeorfour n; intros istr; simpl; + inversion istr. +apply istrue0. +destruct n. inversion istr. +destruct n. tauto. +destruct n. inversion istr. +destruct n. inversion istr. +destruct n. tauto. +simpl in *. inversion H0. +Qed. + +Lemma toto' : forall n m : nat, n = 4 -> istrue (isononeorfour n). +intros n. + functional induction isononeorfour n; intros m istr; inversion istr. +apply istrue0. +rewrite H in y; simpl in y;tauto. +Qed. + +Function ftest4 (n m : nat) : nat := + match n with + | O => match m with + | O => 0 + | S q => 1 + end + | S p => match m with + | O => 0 + | S r => 1 + end + end. + +Lemma test4 : forall n m : nat, ftest n m <= 2. +intros n m. + functional induction ftest n m; auto with arith. +Qed. + +Lemma test4' : forall n m : nat, ftest4 (S n) m <= 2. +intros n m. +assert ({n0 | n0 = S n}). +exists (S n);reflexivity. +destruct H as [n0 H1]. +rewrite <- H1;revert H1. + functional induction ftest4 n0 m. +inversion 1. +inversion 1. + +auto with arith. +auto with arith. +Qed. + +Function ftest44 (x : nat * nat) (n m : nat) : nat := + let (p, q) := (x: nat*nat) in + match n with + | O => match m with + | O => 0 + | S q => 1 + end + | S p => match m with + | O => 0 + | S r => 1 + end + end. + +Lemma test44 : + forall (pq : nat * nat) (n m o r s : nat), ftest44 pq n (S m) <= 2. +intros pq n m o r s. + functional induction ftest44 pq n (S m). +auto with arith. +auto with arith. +auto with arith. +auto with arith. +Qed. + +Function ftest2 (n m : nat) {struct n} : nat := + match n with + | O => match m with + | O => 0 + | S q => 0 + end + | S p => ftest2 p m + end. + +Lemma test2' : forall n m : nat, ftest2 n m <= 2. +intros n m. + functional induction ftest2 n m; simpl; intros; auto. +Qed. + +Function ftest3 (n m : nat) {struct n} : nat := + match n with + | O => 0 + | S p => match m with + | O => ftest3 p 0 + | S r => 0 + end + end. + +Lemma test3' : forall n m : nat, ftest3 n m <= 2. +intros n m. + functional induction ftest3 n m. +intros. +auto. +intros. +auto. +intros. +simpl. +auto. +Qed. + +Function ftest5 (n m : nat) {struct n} : nat := + match n with + | O => 0 + | S p => match m with + | O => ftest5 p 0 + | S r => ftest5 p r + end + end. + +Lemma test5 : forall n m : nat, ftest5 n m <= 2. +intros n m. + functional induction ftest5 n m. +intros. +auto. +intros. +auto. +intros. +simpl. +auto. +Qed. + +Function ftest7 (n : nat) : nat := + match ftest5 n 0 with + | O => 0 + | S r => 0 + end. + +Lemma essai7 : + forall (Hrec : forall n : nat, ftest5 n 0 = 0 -> ftest7 n <= 2) + (Hrec0 : forall n r : nat, ftest5 n 0 = S r -> ftest7 n <= 2) + (n : nat), ftest7 n <= 2. +intros hyp1 hyp2 n. + functional induction ftest7 n; auto. +Qed. + +Function ftest6 (n m : nat) {struct n} : nat := + match n with + | O => 0 + | S p => match ftest5 p 0 with + | O => ftest6 p 0 + | S r => ftest6 p r + end + end. + + +Lemma princ6 : + (forall n m : nat, n = 0 -> ftest6 0 m <= 2) -> + (forall n m p : nat, + ftest6 p 0 <= 2 -> ftest5 p 0 = 0 -> n = S p -> ftest6 (S p) m <= 2) -> + (forall n m p r : nat, + ftest6 p r <= 2 -> ftest5 p 0 = S r -> n = S p -> ftest6 (S p) m <= 2) -> + forall x y : nat, ftest6 x y <= 2. +intros hyp1 hyp2 hyp3 n m. +generalize hyp1 hyp2 hyp3. +clear hyp1 hyp2 hyp3. + functional induction ftest6 n m; auto. +Qed. + +Lemma essai6 : forall n m : nat, ftest6 n m <= 2. +intros n m. + functional induction ftest6 n m; simpl; auto. +Qed. + +(* Some tests with modules *) +Module M. +Function test_m (n:nat) : nat := + match n with + | 0 => 0 + | S n => S (S (test_m n)) + end. + +Lemma test_m_is_double : forall n, div2 (test_m n) = n. +Proof. +intros n. +functional induction (test_m n). +reflexivity. +simpl;rewrite IHn0;reflexivity. +Qed. +End M. +(* We redefine a new Function with the same name *) +Function test_m (n:nat) : nat := + pred n. + +Lemma test_m_is_pred : forall n, test_m n = pred n. +Proof. +intro n. +functional induction (test_m n). (* the test_m_ind to use is the last defined saying that test_m = pred*) +reflexivity. +Qed. + +(* Checks if the dot notation are correctly treated in infos *) +Lemma M_test_m_is_double : forall n, div2 (M.test_m n) = n. +intro n. +(* here we should apply M.test_m_ind *) +functional induction (M.test_m n). +reflexivity. +simpl;rewrite IHn0;reflexivity. +Qed. + +Import M. +(* Now test_m is the one which defines double *) + +Lemma test_m_is_double : forall n, div2 (M.test_m n) = n. +intro n. +(* here we should apply M.test_m_ind *) +functional induction (test_m n). +reflexivity. +simpl;rewrite IHn0;reflexivity. +Qed. + +Extraction iszero. diff --git a/test-suite/success/Tauto.v b/test-suite/success/Tauto.v index 767f15be72..bffd96044d 100644 --- a/test-suite/success/Tauto.v +++ b/test-suite/success/Tauto.v @@ -1,6 +1,6 @@ (************************************************************************) (* v * The Coq Proof Assistant / The Coq Development Team *) -(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2016 *) +(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *) (* \VV/ **************************************************************) (* // * This file is distributed under the terms of the *) (* * GNU Lesser General Public License Version 2.1 *) diff --git a/test-suite/success/TestRefine.v b/test-suite/success/TestRefine.v index 023cb5f59d..87296744c4 100644 --- a/test-suite/success/TestRefine.v +++ b/test-suite/success/TestRefine.v @@ -1,6 +1,6 @@ (************************************************************************) (* v * The Coq Proof Assistant / The Coq Development Team *) -(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2016 *) +(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *) (* \VV/ **************************************************************) (* // * This file is distributed under the terms of the *) (* * GNU Lesser General Public License Version 2.1 *) diff --git a/test-suite/success/eauto.v b/test-suite/success/eauto.v index 160f2d9deb..9b0ff1c8fe 100644 --- a/test-suite/success/eauto.v +++ b/test-suite/success/eauto.v @@ -1,6 +1,6 @@ (************************************************************************) (* v * The Coq Proof Assistant / The Coq Development Team *) -(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2016 *) +(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *) (* \VV/ **************************************************************) (* // * This file is distributed under the terms of the *) (* * GNU Lesser General Public License Version 2.1 *) diff --git a/test-suite/success/eqdecide.v b/test-suite/success/eqdecide.v index 724e2998ef..055434df01 100644 --- a/test-suite/success/eqdecide.v +++ b/test-suite/success/eqdecide.v @@ -1,6 +1,6 @@ (************************************************************************) (* v * The Coq Proof Assistant / The Coq Development Team *) -(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2016 *) +(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *) (* \VV/ **************************************************************) (* // * This file is distributed under the terms of the *) (* * GNU Lesser General Public License Version 2.1 *) diff --git a/test-suite/success/extraction.v b/test-suite/success/extraction.v index 89be144152..4a509da89e 100644 --- a/test-suite/success/extraction.v +++ b/test-suite/success/extraction.v @@ -1,6 +1,6 @@ (************************************************************************) (* v * The Coq Proof Assistant / The Coq Development Team *) -(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2016 *) +(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *) (* \VV/ **************************************************************) (* // * This file is distributed under the terms of the *) (* * GNU Lesser General Public License Version 2.1 *) diff --git a/test-suite/success/inds_type_sec.v b/test-suite/success/inds_type_sec.v index c729b23ce7..7e9095dfd7 100644 --- a/test-suite/success/inds_type_sec.v +++ b/test-suite/success/inds_type_sec.v @@ -1,6 +1,6 @@ (************************************************************************) (* v * The Coq Proof Assistant / The Coq Development Team *) -(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2016 *) +(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *) (* \VV/ **************************************************************) (* // * This file is distributed under the terms of the *) (* * GNU Lesser General Public License Version 2.1 *) diff --git a/test-suite/success/induct.v b/test-suite/success/induct.v index 1ed731f50f..35d7929877 100644 --- a/test-suite/success/induct.v +++ b/test-suite/success/induct.v @@ -1,6 +1,6 @@ (************************************************************************) (* v * The Coq Proof Assistant / The Coq Development Team *) -(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2016 *) +(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *) (* \VV/ **************************************************************) (* // * This file is distributed under the terms of the *) (* * GNU Lesser General Public License Version 2.1 *) diff --git a/test-suite/success/mutual_ind.v b/test-suite/success/mutual_ind.v index 45c1a5e584..c4c5623897 100644 --- a/test-suite/success/mutual_ind.v +++ b/test-suite/success/mutual_ind.v @@ -1,6 +1,6 @@ (************************************************************************) (* v * The Coq Proof Assistant / The Coq Development Team *) -(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2016 *) +(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *) (* \VV/ **************************************************************) (* // * This file is distributed under the terms of the *) (* * GNU Lesser General Public License Version 2.1 *) diff --git a/test-suite/success/unfold.v b/test-suite/success/unfold.v index d595cbc2b8..ce1c33fc40 100644 --- a/test-suite/success/unfold.v +++ b/test-suite/success/unfold.v @@ -1,6 +1,6 @@ (************************************************************************) (* v * The Coq Proof Assistant / The Coq Development Team *) -(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2016 *) +(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *) (* \VV/ **************************************************************) (* // * This file is distributed under the terms of the *) (* * GNU Lesser General Public License Version 2.1 *) diff --git a/test-suite/typeclasses/NewSetoid.v b/test-suite/typeclasses/NewSetoid.v index 49f20a23f5..37d197a15c 100644 --- a/test-suite/typeclasses/NewSetoid.v +++ b/test-suite/typeclasses/NewSetoid.v @@ -1,6 +1,6 @@ (************************************************************************) (* v * The Coq Proof Assistant / The Coq Development Team *) -(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2016 *) +(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *) (* \VV/ **************************************************************) (* // * This file is distributed under the terms of the *) (* * GNU Lesser General Public License Version 2.1 *) |