diff options
author | Stephane Glondu <steph@glondu.net> | 2012-06-04 12:07:52 +0200 |
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committer | Stephane Glondu <steph@glondu.net> | 2012-06-04 12:07:52 +0200 |
commit | 61dc740ed1c3780cccaec00d059a28f0d31d0052 (patch) | |
tree | d88d05baf35b9b09a034233300f35a694f9fa6c2 /test-suite/success/telescope_canonical.v | |
parent | 97fefe1fcca363a1317e066e7f4b99b9c1e9987b (diff) |
Imported Upstream version 8.4~gamma0+really8.4beta2upstream/8.4_gamma0+really8.4beta2
Diffstat (limited to 'test-suite/success/telescope_canonical.v')
-rw-r--r-- | test-suite/success/telescope_canonical.v | 70 |
1 files changed, 65 insertions, 5 deletions
diff --git a/test-suite/success/telescope_canonical.v b/test-suite/success/telescope_canonical.v index 8a607c93..73df5ca9 100644 --- a/test-suite/success/telescope_canonical.v +++ b/test-suite/success/telescope_canonical.v @@ -1,12 +1,72 @@ Structure Inner := mkI { is :> Type }. Structure Outer := mkO { os :> Inner }. - Canonical Structure natInner := mkI nat. Canonical Structure natOuter := mkO natInner. - Definition hidden_nat := nat. - Axiom P : forall S : Outer, is (os S) -> Prop. - -Lemma foo (n : hidden_nat) : P _ n. +Lemma test1 (n : hidden_nat) : P _ n. Admitted. + +Structure Pnat := mkP { getp : nat }. +Definition my_getp := getp. +Axiom W : nat -> Prop. + +(* Fix *) +Canonical Structure add1Pnat n := mkP (plus n 1). +Definition test_fix n := (refl_equal _ : W (my_getp _) = W (n + 1)). + +(* Case *) +Definition pred n := match n with 0 => 0 | S m => m end. +Canonical Structure predSS n := mkP (pred n). +Definition test_case x := (refl_equal _ : W (my_getp _) = W (pred x)). +Fail Definition test_case' := (refl_equal _ : W (my_getp _) = W (pred 0)). + +Canonical Structure letPnat' := mkP 0. +Definition letin := (let n := 0 in n). +Definition test4 := (refl_equal _ : W (getp _) = W letin). +Definition test41 := (refl_equal _ : W (my_getp _) = W letin). +Definition letin2 (x : nat) := (let n := x in n). +Canonical Structure letPnat'' x := mkP (letin2 x). +Definition test42 x := (refl_equal _ : W (my_getp _) = W (letin2 x)). +Fail Definition test42' x := (refl_equal _ : W (my_getp _) = W x). + +Structure Morph := mkM { f :> nat -> nat }. +Definition my_f := f. +Axiom Q : (nat -> nat) -> Prop. + +(* Lambda *) +Canonical Structure addMorh x := mkM (plus x). +Definition test_lam x := (refl_equal _ : Q (my_f _) = Q (plus x)). +Definition test_lam' := (refl_equal _ : Q (my_f _) = Q (plus 0)). + +(* Simple tests to justify Sort and Prod as "named". + They are already normal, so they cannot loose their names, + but still... *) +Structure Sot := mkS { T : Type }. +Axiom R : Type -> Prop. +Canonical Structure tsot := mkS (Type). +Definition test_sort := (refl_equal _ : R (T _) = R Type). +Canonical Structure tsot2 := mkS (nat -> nat). +Definition test_prod := (refl_equal _ : R (T _) = R (nat -> nat)). + +(* Var *) +Section Foo. +Variable v : nat. +Definition my_v := v. +Canonical Structure vP := mkP my_v. +Definition test_var := (refl_equal _ : W (getp _) = W my_v). +Canonical Structure vP' := mkP v. +Definition test_var' := (refl_equal _ : W (my_getp _) = W my_v). +End Foo. + +(* Rel *) +Definition test_rel v := (refl_equal _ : W (my_getp _) = W (my_v v)). +Goal True. +pose (x := test_rel 2). +match goal with x := _ : W (my_getp (vP 2)) = _ |- _ => idtac end. +apply I. +Qed. + + + + |