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Rice Wine
Iris
Commits
0505dc66
Commit
0505dc66
authored
Feb 08, 2018
by
Robbert Krebbers
Browse files
Typeclass based conditional `TCIf P Q R` that does not backtrack on `P`.
parent
680e10eb
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theories/proofmode/class_instances.v
theories/proofmode/class_instances.v
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theories/proofmode/class_instances.v
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0505dc66
...
...
@@ 5,6 +5,21 @@ From iris.base_logic Require Import big_op tactics.
Set
Default
Proof
Using
"Type"
.
Import
uPred
.
(* FIXME: Move to stdpp *)
(* A conditional at the type class level. Note that [TCIf P Q R] is not the same
as [TCOr (TCAnd P Q) R]: the latter will backtrack to [R] if it fails to
establish [R], i.e. does not have the behavior of a conditional. Furthermore,
note that [TCOr (TCAnd P Q) (TCAnd (TCNot P) R)] would not work; we generally
would not be able to proof the negation of [P]. *)
Inductive
TCIf
(
P
Q
R
:
Prop
)
:
=

TCIf_true
:
P
→
Q
→
TCIf
P
Q
R

TCIf_false
:
R
→
TCIf
P
Q
R
.
Existing
Class
TCIf
.
Hint
Extern
0
(
TCIf
_
_
_
)
=>
first
[
apply
TCIf_true
;
[
apply
_
]

apply
TCIf_false
]
:
typeclass_instances
.
Section
classes
.
Context
{
M
:
ucmraT
}.
Implicit
Types
P
Q
R
:
uPred
M
.
...
...
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