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Diffstat (limited to 'test-suite/kernel/vm-univ.v')
-rw-r--r-- | test-suite/kernel/vm-univ.v | 145 |
1 files changed, 0 insertions, 145 deletions
diff --git a/test-suite/kernel/vm-univ.v b/test-suite/kernel/vm-univ.v deleted file mode 100644 index 1bdba3c6..00000000 --- a/test-suite/kernel/vm-univ.v +++ /dev/null @@ -1,145 +0,0 @@ -(* Basic tests *) -Polymorphic Definition pid {T : Type} (x : T) : T := x. -(* -Definition _1 : pid true = true := - @eq_refl _ true <: pid true = true. - -Polymorphic Definition a_type := Type. - -Definition _2 : a_type@{i} = Type@{i} := - @eq_refl _ Type@{i} <: a_type@{i} = Type@{i}. - -Polymorphic Definition FORALL (T : Type) (P : T -> Prop) : Prop := - forall x : T, P x. - -Polymorphic Axiom todo : forall {T:Type}, T -> T. - -Polymorphic Definition todo' (T : Type) := @todo T. - -Definition _3 : @todo'@{Set} = @todo@{Set} := - @eq_refl _ (@todo@{Set}) <: @todo'@{Set} = @todo@{Set}. -*) - -(* Inductive Types *) -Inductive sumbool (A B : Prop) : Set := -| left : A -> sumbool A B -| right : B -> sumbool A B. - -Definition x : sumbool True False := left _ _ I. - -Definition sumbool_copy {A B : Prop} (H : sumbool A B) : sumbool A B := - match H with - | left _ _ x => left _ _ x - | right _ _ x => right _ _ x - end. - -Definition _4 : sumbool_copy x = x := - @eq_refl _ x <: sumbool_copy x = x. - -(* Polymorphic Inductive Types *) -Polymorphic Inductive poption (T : Type@{i}) : Type@{i} := -| PSome : T -> poption@{i} T -| PNone : poption@{i} T. - -Polymorphic Definition poption_default {T : Type@{i}} (p : poption@{i} T) (x : T) : T := - match p with - | @PSome _ y => y - | @PNone _ => x - end. - -Polymorphic Inductive plist (T : Type@{i}) : Type@{i} := -| pnil -| pcons : T -> plist@{i} T -> plist@{i} T. - -Arguments pnil {_}. -Arguments pcons {_} _ _. - -Section pmap. - Context {T : Type@{i}} {U : Type@{j}} (f : T -> U). - - Polymorphic Fixpoint pmap (ls : plist@{i} T) : plist@{j} U := - match ls with - | @pnil _ => @pnil _ - | @pcons _ l ls => @pcons@{j} U (f l) (pmap@{i j} ls) - end. -End pmap. - -Universe Ubool. -Inductive tbool : Type@{Ubool} := ttrue | tfalse. - - -Eval vm_compute in pmap pid (pcons true (pcons false pnil)). -Eval vm_compute in pmap (fun x => match x with - | pnil => true - | pcons _ _ => false - end) (pcons pnil (pcons (pcons false pnil) pnil)). -Eval vm_compute in pmap (fun x => x -> Type) (pcons tbool (pcons (plist tbool) pnil)). - -Polymorphic Inductive Tree (T : Type@{i}) : Type@{i} := -| Empty -| Branch : plist@{i} (Tree@{i} T) -> Tree@{i} T. - -Section pfold. - Context {T : Type@{i}} {U : Type@{u}} (f : T -> U -> U). - - Polymorphic Fixpoint pfold (acc : U) (ls : plist@{i} T) : U := - match ls with - | pnil => acc - | pcons a b => pfold (f a acc) b - end. -End pfold. - -Polymorphic Inductive nat : Type@{i} := -| O -| S : nat -> nat. - -Fixpoint nat_max (a b : nat) : nat := - match a , b with - | O , b => b - | a , O => a - | S a , S b => S (nat_max a b) - end. - -Polymorphic Fixpoint height {T : Type@{i}} (t : Tree@{i} T) : nat := - match t with - | Empty _ => O - | Branch _ ls => S (pfold nat_max O (pmap height ls)) - end. - -Polymorphic Fixpoint repeat {T : Type@{i}} (n : nat) (v : T) : plist@{i} T := - match n with - | O => pnil - | S n => pcons v (repeat n v) - end. - -Polymorphic Fixpoint big_tree (n : nat) : Tree@{i} nat := - match n with - | O => @Empty nat - | S n' => Branch _ (repeat n' (big_tree n')) - end. - -Eval compute in height (big_tree (S (S (S O)))). - -Let big := S (S (S (S (S O)))). -Polymorphic Definition really_big := (S@{i} (S (S (S (S (S (S (S (S (S O)))))))))). - -Time Definition _5 : height (@Empty nat) = O := - @eq_refl nat O <: height (@Empty nat) = O. - -Time Definition _6 : height@{Set} (@Branch nat pnil) = S O := - @eq_refl nat@{Set} (S@{Set} O@{Set}) <: height@{Set} (@Branch nat pnil) = S O. - -Time Definition _7 : height (big_tree big) = big := - @eq_refl nat big <: height (big_tree big) = big. - -Time Definition _8 : height (big_tree really_big) = really_big := - @eq_refl nat@{Set} (S@{Set} - (S@{Set} - (S@{Set} - (S@{Set} - (S@{Set} - (S@{Set} (S@{Set} (S@{Set} (S@{Set} (S@{Set} O@{Set})))))))))) - <: - @eq nat@{Set} - (@height nat@{Set} (big_tree really_big@{Set})) - really_big@{Set}. |