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Set Primitive Projections.
Set Nonrecursive Elimination Schemes.
Module Prim.
Record F := { a : nat; b : a = a }.
Record G (A : Type) := { c : A; d : F }.
Check c.
End Prim.
Module Univ.
Set Universe Polymorphism.
Set Implicit Arguments.
Record Foo (A : Type) := { foo : A }.
Record G (A : Type) := { c : A; d : c = c; e : Foo A }.
Definition Foon : Foo nat := {| foo := 0 |}.
Definition Foonp : nat := Foon.(foo).
Definition Gt : G nat := {| c:= 0; d:=eq_refl; e:= Foon |}.
Check (Gt.(e)).
Section bla.
Record bar := { baz : nat; def := 0; baz' : forall x, x = baz \/ x = def }.
End bla.
End Univ.
Set Primitive Projections.
Unset Elimination Schemes.
Set Implicit Arguments.
Check nat.
Inductive X (U:Type) := { k : nat; a: k = k -> X U; b : let x := a eq_refl in X U }.
Parameter x:X nat.
Check (a x : forall _ : @eq nat (k x) (k x), X nat).
Check (b x : X nat).
Inductive Y := { next : option Y }.
Check _.(next) : option Y.
Lemma eta_ind (y : Y) : y = Build_Y y.(next).
Proof. Fail reflexivity. Abort.
Inductive Fdef := { Fa : nat ; Fb := Fa; Fc : Fdef }.
Fail Scheme Fdef_rec := Induction for Fdef Sort Prop.
(*
Rules for parsing and printing of primitive projections and their eta expansions.
If r : R A where R is a primitive record with implicit parameter A.
If p : forall {A} (r : R A) {A : Set}, list (A * B).
*)
Record R {A : Type} := { p : forall {X : Set}, A * X }.
Arguments R : clear implicits.
Record R' {A : Type} := { p' : forall X : Set, A * X }.
Arguments R' : clear implicits.
Unset Printing All.
Parameter r : R nat.
Check (r.(p)).
Set Printing Projections.
Check (r.(p)).
Unset Printing Projections.
Set Printing All.
Check (r.(p)).
Unset Printing All.
(* Check (r.(p)).
Elaborates to a primitive application, X arg implicit.
Of type nat * ?ex
No Printing All: p r
Set Printing Projections.: r.(p)
Printing All: r.(@p) ?ex
*)
Check p r.
Set Printing Projections.
Check p r.
Unset Printing Projections.
Set Printing All.
Check p r.
Unset Printing All.
Check p r (X:=nat).
Set Printing Projections.
Check p r (X:=nat).
Unset Printing Projections.
Set Printing All.
Check p r (X:=nat).
Unset Printing All.
(* Same elaboration, printing for p r *)
(** Explicit version of the primitive projection, under applied w.r.t implicit arguments
can be printed only using projection notation. r.(@p) *)
Check r.(@p _).
Set Printing Projections.
Check r.(@p _).
Unset Printing Projections.
Set Printing All.
Check r.(@p _).
Unset Printing All.
(** Explicit version of the primitive projection, applied to its implicit arguments
can be printed using application notation r.(p), r.(@p) in fully explicit form *)
Check r.(@p _) nat.
Set Printing Projections.
Check r.(@p _) nat.
Unset Printing Projections.
Set Printing All.
Check r.(@p _) nat.
Unset Printing All.
Parameter r' : R' nat.
Check (r'.(p')).
Set Printing Projections.
Check (r'.(p')).
Unset Printing Projections.
Set Printing All.
Check (r'.(p')).
Unset Printing All.
(* Check (r'.(p')).
Elaborates to a primitive application, X arg explicit.
Of type forall X : Set, nat * X
No Printing All: p' r'
Set Printing Projections.: r'.(p')
Printing All: r'.(@p')
*)
Check p' r'.
Set Printing Projections.
Check p' r'.
Unset Printing Projections.
Set Printing All.
Check p' r'.
Unset Printing All.
(* Same elaboration, printing for p r *)
(** Explicit version of the primitive projection, under applied w.r.t implicit arguments
can be printed only using projection notation. r.(@p) *)
Check r'.(@p' _).
Set Printing Projections.
Check r'.(@p' _).
Unset Printing Projections.
Set Printing All.
Check r'.(@p' _).
Unset Printing All.
(** Explicit version of the primitive projection, applied to its implicit arguments
can be printed only using projection notation r.(p), r.(@p) in fully explicit form *)
Check p' r' nat.
Set Printing Projections.
Check p' r' nat.
Unset Printing Projections.
Set Printing All.
Check p' r' nat.
Unset Printing All.
Check (@p' nat).
Check p'.
Set Printing All.
Check (@p' nat).
Check p'.
Unset Printing All.
Record wrap (A : Type) := { unwrap : A; unwrap2 : A }.
Definition term (x : wrap nat) := x.(unwrap).
Definition term' (x : wrap nat) := let f := (@unwrap2 nat) in f x.
Require Coq.extraction.Extraction.
Recursive Extraction term term'.
Extraction TestCompile term term'.
(*Unset Printing Primitive Projection Parameters.*)
(* Primitive projections in the presence of let-ins (was not failing in beta3)*)
Set Primitive Projections.
Record s (x:nat) (y:=S x) := {c:=x; d:x=c}.
Lemma f : 0=1.
Proof.
Fail apply d.
(*
split.
reflexivity.
Qed.
*)
|
