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9589d1ba
Commit
9589d1ba
authored
Feb 25, 2016
by
Robbert Krebbers
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Make identation of solve_proper and f_equiv more consistent.
parent
00a054f1
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#167
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prelude/tactics.v
prelude/tactics.v
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prelude/tactics.v
View file @
9589d1ba
...
...
@@ 234,40 +234,39 @@ Ltac setoid_subst :=
Ltac
f_equiv
:
=
(* Deal with "pointwise_relation" *)
repeat
lazymatch
goal
with


pointwise_relation
_
_
_
_
=>
intros
?
end
;


pointwise_relation
_
_
_
_
=>
intros
?
end
;
(* Normalize away equalities. *)
subst
;
(* repeatedly apply congruence lemmas and use the equalities in the hypotheses. *)
first
[
reflexivity

assumption

symmetry
;
assumption

match
goal
with
(* We support matches on both sides, *if* they concern the same
variable.
TODO: We should support different variables, provided that we can
derive contradictions for the offdiagonal cases. *)


?R
(
match
?x
with
_
=>
_
end
)
(
match
?x
with
_
=>
_
end
)
=>
destruct
x
;
f_equiv
(* First assume that the arguments need the same relation as the result *)


?R
(
?f
?x
)
(
?f
_
)
=>
apply
(
_
:
Proper
(
R
==>
R
)
f
)
;
f_equiv


?R
(
?f
?x
?y
)
(
?f
_
_
)
=>
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? *)
(* TODO: If some of the arguments are the same, we could also
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
_
)
=>
apply
(
_
:
Proper
(
_
==>
R
)
f
)
;
f_equiv


?R
(
?f
?x
?y
)
(
?f
_
_
)
=>
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
)
=>
apply
H
;
f_equiv
end

idtac
(* Let the user solve this goal *)
].
try
match
goal
with

_
=>
first
[
reflexivity

assumption

symmetry
;
assumption
]
(* We support matches on both sides, *if* they concern the same
variable.
TODO: We should support different variables, provided that we can
derive contradictions for the offdiagonal cases. *)


?R
(
match
?x
with
_
=>
_
end
)
(
match
?x
with
_
=>
_
end
)
=>
destruct
x
;
f_equiv
(* First assume that the arguments need the same relation as the result *)


?R
(
?f
?x
)
(
?f
_
)
=>
apply
(
_
:
Proper
(
R
==>
R
)
f
)
;
f_equiv


?R
(
?f
?x
?y
)
(
?f
_
_
)
=>
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? *)
(* TODO: If some of the arguments are the same, we could also
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
_
)
=>
apply
(
_
:
Proper
(
_
==>
R
)
f
)
;
f_equiv


?R
(
?f
?x
?y
)
(
?f
_
_
)
=>
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
)
=>
apply
H
;
f_equiv
end
.
(** solve_proper solves goals of the form "Proper (R1 ==> R2)", for any
number of relations. All the actual work is done by f_equiv;
...
...
@@ 277,9 +276,9 @@ Ltac solve_proper :=
(* Introduce everything *)
intros
;
repeat
lazymatch
goal
with


Proper
_
_
=>
intros
???


(
_
==>
_
)%
signature
_
_
=>
intros
???
end
;


Proper
_
_
=>
intros
???


(
_
==>
_
)%
signature
_
_
=>
intros
???
end
;
(* Unfold the head symbol, which is the one we are proving a new property about *)
lazymatch
goal
with


?R
(
?f
_
_
_
_
_
_
_
_
)
(
?f
_
_
_
_
_
_
_
_
)
=>
unfold
f
...
...
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