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Set Universe Polymorphism.
Module Segfault.
Inductive decision_tree : Type := .
Fixpoint first_satisfying_helper {A B} (f : A -> option B) (ls : list A) : option B
:= match ls with
| nil => None
| cons x xs
=> match f x with
| Some v => Some v
| None => first_satisfying_helper f xs
end
end.
Axiom admit : forall {T}, T.
Definition dtree4 : option decision_tree :=
match first_satisfying_helper (fun pat : nat => Some pat) (cons 0 nil)
with
| Some _ => admit
| None => admit
end
.
Definition dtree'' := Eval vm_compute in dtree4. (* segfault *)
End Segfault.
Module OtherExample.
Definition bar@{i} := Type@{i}.
Definition foo@{i j} (x y z : nat) :=
@id Type@{j} bar@{i}.
Eval vm_compute in foo.
End OtherExample.
Module LocalClosure.
Definition bar@{i} := Type@{i}.
Definition foo@{i j} (x y z : nat) :=
@id (nat -> Type@{j}) (fun _ => Type@{i}).
Eval vm_compute in foo.
End LocalClosure.
Module QVar.
Definition bar@{q|i|} := Type@{q|i}.
Definition gbar@{q1 q2|i j|} := bar@{q2|i}.
Eval vm_compute in gbar.
Definition gprop := Eval vm_compute in gbar@{Type Prop|Set Set}.
Check eq_refl : gprop = Prop.
End QVar.
Require Import Hurkens.
Polymorphic Inductive unit := tt.
Polymorphic Definition foo :=
let x := id tt in (x, x, Type).
Lemma bad : False.
refine (TypeNeqSmallType.paradox (snd foo) _).
vm_compute.
Fail reflexivity.
Abort.
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