chore(tests/lean): add untracked tests

This commit is contained in:
Leonardo de Moura 2014-09-09 16:21:30 -07:00
parent 9b9adf8831
commit efb14d906b
5 changed files with 81 additions and 0 deletions

7
tests/lean/run/abs.lean Normal file
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import data.int
open int
variable abs : int → int
notation `|`:40 A:40 `|` := abs A
variables a b c : int
check |a + |b| + c|

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import logic
inductive category (ob : Type) (mor : ob → ob → Type) : Type :=
mk : Π (comp : Π⦃A B C : ob⦄, mor B C → mor A B → mor A C)
(id : Π {A : ob}, mor A A),
(Π {A B C D : ob} {f : mor A B} {g : mor B C} {h : mor C D},
comp h (comp g f) = comp (comp h g) f) →
(Π {A B : ob} {f : mor A B}, comp f id = f) →
(Π {A B : ob} {f : mor A B}, comp id f = f) →
category ob mor
class category
namespace category
section sec_cat
parameter A : Type
inductive foo :=
mk : A → foo
class foo
parameters {ob : Type} {mor : ob → ob → Type} {Cat : category ob mor}
abbreviation compose := rec (λ comp id assoc idr idl, comp) Cat
abbreviation id := rec (λ comp id assoc idr idl, id) Cat
infixr `∘`:60 := compose
end sec_cat
end category

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/- tests -/

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tests/lean/run/ctx.lean Normal file
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import data.nat logic.classes.inhabited
open nat inhabited
variable N : Type.{1}
variable a : N
section s1
set_option pp.implicit true
definition f (a b : nat) := a
theorem nat_inhabited [instance] : inhabited nat :=
inhabited.mk zero
definition to_N [coercion] (n : nat) : N := a
infixl `$$`:65 := f
end s1
theorem tst : inhabited nat
variables n m : nat
check n = a

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tests/lean/run/lift.lean Normal file
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import data.nat
open nat
inductive lift .{l} (A : Type.{l}) : Type.{l+1} :=
up : A → lift A
namespace lift
definition down {A : Type} (a : lift A) : A :=
rec (λ a, a) a
theorem down_up {A : Type} (a : A) : down (up a) = a :=
rfl
theorem induction_on [protected] {A : Type} {P : lift A → Prop} (a : lift A) (H : ∀ (a : A), P (up a)) : P a :=
rec H a
theorem up_down {A : Type} (a' : lift A) : up (down a') = a' :=
induction_on a' (λ a, rfl)
end lift
set_option pp.universes true
check nat
check lift nat
open lift
definition one1 : lift nat := up 1