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From Tuto1 Require Import Loader.
(*** Printing user inputs ***)
Definition definition := 5.
What's definition.
What kind of term is definition.
What kind of identifier is definition.
What is 1 2 3 a list of.
What is a list of. (* no arguments = empty list *)
Is 1 2 3 nonempty.
(* Is nonempty *) (* does not parse *)
And is 1 provided.
And is provided.
(*** Interning terms ***)
Intern 3.
Intern definition.
Intern (fun (x : Prop) => x).
Intern (fun (x : Type) => x).
Intern (forall (T : Type), T).
Intern (fun (T : Type) (t : T) => t).
Intern _.
Intern (Type : Type).
(*** Defining terms ***)
MyDefine n := 1.
Print n.
MyDefine f := (fun (x : Type) => x).
Print f.
(*** Printing terms ***)
MyPrint f.
MyPrint n.
Fail MyPrint nat.
DefineLookup n' := 1.
DefineLookup f' := (fun (x : Type) => x).
(*** Checking terms ***)
Check1 3.
Check1 definition.
Check1 (fun (x : Prop) => x).
Check1 (fun (x : Type) => x).
Check1 (forall (T : Type), T).
Check1 (fun (T : Type) (t : T) => t).
Check1 _.
Check1 (Type : Type).
Check2 3.
Check2 definition.
Check2 (fun (x : Prop) => x).
Check2 (fun (x : Type) => x).
Check2 (forall (T : Type), T).
Check2 (fun (T : Type) (t : T) => t).
Check2 _.
Check2 (Type : Type).
(*** Convertibility ***)
Convertible 1 1.
Convertible (fun (x : Type) => x) (fun (x : Type) => x).
Convertible Type Type.
Convertible 1 ((fun (x : nat) => x) 1).
Convertible 1 2.
Convertible (fun (x : Type) => x) (fun (x : Prop) => x).
Convertible Type Prop.
Convertible 1 ((fun (x : nat) => x) 2).
(*** Introducing variables ***)
Theorem foo:
forall (T : Set) (t : T), T.
Proof.
my_intro T. my_intro t. apply t.
Qed.
(*** Exploring proof state ***)
Fail ExploreProof. (* not in a proof *)
Theorem bar:
forall (T : Set) (t : T), T.
Proof.
ExploreProof. my_intro T. ExploreProof. my_intro t. ExploreProof. apply t.
Qed.
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