Set Primitive Projections.
Record mix := { a : nat ; b : a = a ; c : nat ; d : a = c ; e : nat ; f : nat }.
Ltac strip_args T ctor :=
lazymatch type of ctor with
| context[T]
=> match eval cbv beta in ctor with
| ?ctor _ => strip_args T ctor
| _ => ctor
end
end.
Ltac get_ctor T :=
let full_ctor := constr:(ltac:(let x := fresh in intro x; econstructor; apply
x) : T -> T) in
let ctor := constr:(fun x : T => ltac:(let v := strip_args T (full_ctor x) in
exact v)) in
lazymatch ctor with
| fun _ => ?ctor => ctor
end.
Ltac uncurry_domain f :=
lazymatch type of f with
| forall (a : ?A) (b : @ ?B a), _
=> uncurry_domain (fun ab : { a : A & B a } => f (projT1 ab) (projT2 ab))
| _ => eval cbv beta in f
end.
Ltac get_of_sigma T :=
let ctor := get_ctor T in
uncurry_domain ctor.
Ltac repeat_existT :=
lazymatch goal with
| [ |- sigT _ ] => simple refine (existT _ _ _); [ repeat_existT | shelve ]
| _ => shelve
end.
Ltac prove_to_of_sigma_goal of_sigma :=
let v := fresh "v" in
simple refine (exist _ _ (fun v => _ : id _ (of_sigma v) = v));
try unfold of_sigma;
[ intro v; destruct v; repeat_existT
| cbv beta;
repeat match goal with
| [ |- context[projT2 ?k] ]
=> let x := fresh "x" in
is_var k;
destruct k as [k x]; cbn [projT1 projT2]
end;
unfold id; reflexivity ].
Ltac prove_to_of_sigma of_sigma :=
constr:(
ltac:(prove_to_of_sigma_goal of_sigma)
: { to_sigma : _ | forall v, id to_sigma (of_sigma v) = v }).
Ltac get_to_sigma_gen of_sigma :=
let v := prove_to_of_sigma of_sigma in
eval hnf in (proj1_sig v).
Ltac get_to_sigma T :=
let of_sigma := get_of_sigma T in
get_to_sigma_gen of_sigma.
Definition to_sigma := ltac:(let v := get_to_sigma mix in exact v).
(* Error:
In nested Ltac calls to "get_to_sigma", "get_to_sigma_gen",
"prove_to_of_sigma",
"(_ : {to_sigma : _ | forall v, id to_sigma (of_sigma v) = v})" (with
of_sigma:=fun
ab : {_
: {_
: {ab : {_ : {a : nat & a = a} & nat} &
projT1 (projT1 ab) = projT2 ab} & nat} & nat} =>
{|
a := projT1 (projT1 (projT1 (projT1 (projT1 ab))));
b := projT2 (projT1 (projT1 (projT1 (projT1 ab))));
c := projT2 (projT1 (projT1 (projT1 ab)));
d := projT2 (projT1 (projT1 ab));
e := projT2 (projT1 ab);
f := projT2 ab |}) and "prove_to_of_sigma_goal", last call failed.
Anomaly "Uncaught exception Not_found." Please report at
http://coq.inria.fr/bugs/.
frame @ file "toplevel/coqtop.ml", line 640, characters 6-22
frame @ file "list.ml", line 73, characters 12-15
frame @ file "toplevel/vernac.ml", line 344, characters 2-13
frame @ file "toplevel/vernac.ml", line 308, characters 14-75
raise @ file "lib/exninfo.ml", line 63, characters 8-15
frame @ file "lib/flags.ml", line 141, characters 19-40
raise @ file "lib/exninfo.ml", line 63, characters 8-15
frame @ file "lib/flags.ml", line 11, characters 15-18
raise @ file "lib/exninfo.ml", line 63, characters 8-15
frame @ file "toplevel/vernac.ml", line 167, characters 6-16
frame @ file "toplevel/vernac.ml", line 151, characters 26-39
frame @ file "stm/stm.ml", line 2365, characters 2-35
raise @ file "lib/exninfo.ml", line 63, characters 8-15
frame @ file "stm/stm.ml", line 2355, characters 4-48
frame @ file "stm/stm.ml", line 2321, characters 4-100
raise @ file "lib/exninfo.ml", line 63, characters 8-15
frame @ file "stm/stm.ml", line 832, characters 6-10
frame @ file "stm/stm.ml", line 2206, characters 10-32
raise @ file "lib/exninfo.ml", line 63, characters 8-15
frame @ file "stm/stm.ml", line 975, characters 8-81
raise @ file "lib/exninfo.ml", line 63, characters 8-15
frame @ file "vernac/vernacentries.ml", line 2216, characters 10-389
frame @ file "lib/flags.ml", line 141, characters 19-40
raise @ file "lib/exninfo.ml", line 63, characters 8-15
frame @ file "lib/flags.ml", line 11, characters 15-18
frame @ file "vernac/command.ml", line 150, characters 4-56
frame @ file "interp/constrintern.ml", line 2046, characters 2-73
frame @ file "pretyping/pretyping.ml", line 1194, characters 19-77
frame @ file "pretyping/pretyping.ml", line 1155, characters 8-72
frame @ file "pretyping/pretyping.ml", line 628, characters 23-65
frame @ file "plugins/ltac/tacinterp.ml", line 2095, characters 21-61
frame @ file "proofs/pfedit.ml", line 178, characters 6-22
raise @ file "lib/exninfo.ml", line 63, characters 8-15
frame @ file "proofs/pfedit.ml", line 174, characters 8-36
frame @ file "proofs/proof.ml", line 351, characters 4-30
raise @ file "lib/exninfo.ml", line 63, characters 8-15
frame @ file "engine/proofview.ml", line 1222, characters 8-12
frame @ file "plugins/ltac/tacinterp.ml", line 2020, characters 19-36
frame @ file "plugins/ltac/tacinterp.ml", line 618, characters 4-70
raise @ file "lib/exninfo.ml", line 63, characters 8-15
frame @ file "plugins/ltac/tacinterp.ml", line 214, characters 6-9
frame @ file "pretyping/pretyping.ml", line 1198, characters 19-62
frame @ file "pretyping/pretyping.ml", line 1155, characters 8-72
raise @ unknown
frame @ file "pretyping/pretyping.ml", line 628, characters 23-65
frame @ file "plugins/ltac/tacinterp.ml", line 2095, characters 21-61
frame @ file "proofs/pfedit.ml", line 178, characters 6-22
raise @ file "lib/exninfo.ml", line 63, characters 8-15
frame @ file "proofs/pfedit.ml", line 174, characters 8-36
frame @ file "proofs/proof.ml", line 351, characters 4-30
raise @ file "lib/exninfo.ml", line 63, characters 8-15
*)
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