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00a054f1
Commit
00a054f1
authored
Feb 25, 2016
by
Robbert Krebbers
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Simplify f_equiv a bit.
parent
8a1a8f00
Pipeline
#166
passed with stage
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prelude/tactics.v
prelude/tactics.v
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prelude/tactics.v
View file @
00a054f1
...
...
@@ 233,7 +233,7 @@ Ltac setoid_subst :=
If it cannot solve an equality, it will leave that to the user. *)
Ltac
f_equiv
:
=
(* Deal with "pointwise_relation" *)
try
lazymatch
goal
with
repeat
lazymatch
goal
with


pointwise_relation
_
_
_
_
=>
intros
?
end
;
(* Normalize away equalities. *)
...
...
@@ 249,13 +249,9 @@ Ltac f_equiv :=
destruct
x
;
f_equiv
(* First assume that the arguments need the same relation as the result *)


?R
(
?f
?x
)
(
?f
_
)
=>
let
H
:
=
fresh
"Proper"
in
assert
(
Proper
(
R
==>
R
)
f
)
as
H
by
(
eapply
_
)
;
apply
H
;
clear
H
;
f_equiv
apply
(
_
:
Proper
(
R
==>
R
)
f
)
;
f_equiv


?R
(
?f
?x
?y
)
(
?f
_
_
)
=>
let
H
:
=
fresh
"Proper"
in
assert
(
Proper
(
R
==>
R
==>
R
)
f
)
as
H
by
(
eapply
_
)
;
apply
H
;
clear
H
;
f_equiv
apply
(
_
:
Proper
(
R
==>
R
==>
R
)
f
)
;
f_equiv
(* Next, try to infer the relation. Unfortunately, there is an instance
of Proper for (eq ==> _), which will always be matched. *)
(* TODO: Can we exclude that instance? *)
...
...
@@ 263,17 +259,9 @@ Ltac f_equiv :=
query for "pointwise_relation"'s. But that leads to a combinatorial
explosion about which arguments are and which are not the same. *)


?R
(
?f
?x
)
(
?f
_
)
=>
let
R1
:
=
fresh
"R"
in
let
H
:
=
fresh
"HProp"
in
let
T
:
=
type
of
x
in
evar
(
R1
:
relation
T
)
;
assert
(
Proper
(
R1
==>
R
)
f
)
as
H
by
(
subst
R1
;
eapply
_
)
;
subst
R1
;
apply
H
;
clear
H
;
f_equiv
apply
(
_
:
Proper
(
_
==>
R
)
f
)
;
f_equiv


?R
(
?f
?x
?y
)
(
?f
_
_
)
=>
let
R1
:
=
fresh
"R"
in
let
R2
:
=
fresh
"R"
in
let
H
:
=
fresh
"HProp"
in
let
T1
:
=
type
of
x
in
evar
(
R1
:
relation
T1
)
;
let
T2
:
=
type
of
y
in
evar
(
R2
:
relation
T2
)
;
assert
(
Proper
(
R1
==>
R2
==>
R
)
f
)
as
H
by
(
subst
R1
R2
;
eapply
_
)
;
subst
R1
R2
;
apply
H
;
clear
H
;
f_equiv
apply
(
_
:
Proper
(
_
==>
_
==>
R
)
f
)
;
f_equiv
(* In case the function symbol differs, but the arguments are the same,
maybe we have a pointwise_relation in our context. *)

H
:
pointwise_relation
_
?R
?f
?g

?R
(
?f
?x
)
(
?g
?x
)
=>
...
...
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