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Janno
iris-coq
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ff41b98a
Commit
ff41b98a
authored
Feb 25, 2019
by
Dan Frumin
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clarify text further
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theories/proofmode/modalities.v
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theories/proofmode/modalities.v
View file @
ff41b98a
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@@ -7,9 +7,9 @@ Import bi.
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@@ -7,9 +7,9 @@ Import bi.
instantiated with a variety of modalities.
instantiated with a variety of modalities.
For the purpose of MoSeL, a modality is a mapping of propositions
For the purpose of MoSeL, a modality is a mapping of propositions
`M : PROP1 → PROP2` (where `PROP1` and `PROP2` are BI-algebras
)
`M : PROP1 → PROP2` (where `PROP1` and `PROP2` are BI-algebras
, although usually
that is monotone and distributes over finite products.
Specifically,
it is the same algebra)
that is monotone and distributes over finite products.
the following rules have to be satisfied:
Specifically,
the following rules have to be satisfied:
P ⊢ Q emp ⊢ M emp
P ⊢ Q emp ⊢ M emp
----------
----------
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@@ -41,9 +41,12 @@ To instantiate the modality you have to define: 1) a mixin `modality_mixin`,
...
@@ -41,9 +41,12 @@ To instantiate the modality you have to define: 1) a mixin `modality_mixin`,
For examples consult `modality_id` at the end of this file, or the instances
For examples consult `modality_id` at the end of this file, or the instances
in the `modality_instances.v` file.
in the `modality_instances.v` file.
Note that in MoSeL modality can map the propositions between two different BI-algebras.
Note that in MoSeL modalities can map the propositions between two different
For instance, the <affine> modality maps propositions of an arbitrary BI-algebra into
BI-algebras. Most of the modalities in Iris operate on the same type of
the sub-BI-algebra of affine propositions.
assertions. For example, the <affine> modality can potentially maps propositions
of an arbitrary BI-algebra into the sub-BI-algebra of affine propositions, but
it is implemented as an endomapping. On the other hand, the embedding modality
⎡-⎤ is a mapping between propositions of different BI-algebras.
*)
*)
Inductive
modality_action
(
PROP1
:
bi
)
:
bi
→
Type
:
=
Inductive
modality_action
(
PROP1
:
bi
)
:
bi
→
Type
:
=
...
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