From 164c6861860e6b52818c031f901ffeff91fca16a Mon Sep 17 00:00:00 2001 From: Enrico Tassi Date: Tue, 26 Jan 2016 16:56:33 +0100 Subject: Imported Upstream version 8.5 --- test-suite/success/vm_univ_poly.v | 141 ++++++++++++++++++++++++++++++++++++++ 1 file changed, 141 insertions(+) create mode 100644 test-suite/success/vm_univ_poly.v (limited to 'test-suite/success/vm_univ_poly.v') diff --git a/test-suite/success/vm_univ_poly.v b/test-suite/success/vm_univ_poly.v new file mode 100644 index 00000000..58fa3974 --- /dev/null +++ b/test-suite/success/vm_univ_poly.v @@ -0,0 +1,141 @@ +(* 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@{i} (T : Type@{i}) : Type@{i} := +| PSome : T -> poption@{i} T +| PNone : poption@{i} T. + +Polymorphic Definition poption_default@{i} {T : Type@{i}} (p : poption@{i} T) (x : T) : T := + match p with + | @PSome _ y => y + | @PNone _ => x + end. + +Polymorphic Inductive plist@{i} (T : Type@{i}) : Type@{i} := +| pnil +| pcons : T -> plist@{i} T -> plist@{i} T. + +Arguments pnil {_}. +Arguments pcons {_} _ _. + +Polymorphic Definition pmap@{i j} + {T : Type@{i}} {U : Type@{j}} (f : T -> U) := + fix 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. + +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@{i} (T : Type@{i}) : Type@{i} := +| Empty +| Branch : plist@{i} (Tree@{i} T) -> Tree@{i} T. + +Polymorphic Definition pfold@{i u} + {T : Type@{i}} {U : Type@{u}} (f : T -> U -> U) := + fix pfold (acc : U) (ls : plist@{i} T) : U := + match ls with + | pnil => acc + | pcons a b => pfold (f a acc) b + end. + +Polymorphic Inductive nat@{i} : Type@{i} := +| O +| S : nat -> nat. + +Polymorphic Fixpoint nat_max@{i} (a b : nat@{i}) : nat@{i} := + match a , b with + | O , b => b + | a , O => a + | S a , S b => S (nat_max a b) + end. + +Polymorphic Fixpoint height@{i} {T : Type@{i}} (t : Tree@{i} T) : nat@{i} := + match t return nat@{i} with + | Empty _ => O + | Branch _ ls => S@{i} (pfold@{i i} nat_max O (pmap height ls)) + end. + +Polymorphic Fixpoint repeat@{i} {T : Type@{i}} (n : nat@{i}) (v : T) : plist@{i} T := + match n return plist@{i} T with + | O => pnil + | S n => pcons@{i} v (repeat n v) + end. + +Polymorphic Fixpoint big_tree@{i} (n : nat@{i}) : Tree@{i} nat@{i} := + match n with + | O => @Empty nat@{i} + | S n' => Branch@{i} nat@{i} (repeat@{i} n' (big_tree@{i} n')) + end. + +Eval compute in height (big_tree (S (S (S O)))). + +Let big := S (S (S (S (S O)))). +Polymorphic Definition really_big@{i} := (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}) <: @eq nat@{Set} (height@{Set} (@Branch@{Set} nat@{Set} (@pnil@{Set} (Tree@{Set} nat@{Set})))) (S@{Set} O@{Set}). + +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}. -- cgit v1.2.3