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George Pirlea
Iris
Commits
ff41b98a
Commit
ff41b98a
authored
Feb 25, 2019
by
Dan Frumin
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theories/proofmode/modalities.v
theories/proofmode/modalities.v
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theories/proofmode/modalities.v
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ff41b98a
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@@ -7,9 +7,9 @@ Import bi.
instantiated with a variety of modalities.
For the purpose of MoSeL, a modality is a mapping of propositions
`M : PROP1 → PROP2` (where `PROP1` and `PROP2` are BI-algebras
)
that is monotone and distributes over finite products. Specifically,
the following rules have to be satisfied:
`M : PROP1 → PROP2` (where `PROP1` and `PROP2` are BI-algebras
, although usually
it is the same algebra) that is monotone and distributes over finite products.
Specifically,
the following rules have to be satisfied:
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`,
For examples consult `modality_id` at the end of this file, or the instances
in the `modality_instances.v` file.
Note that in MoSeL modality can map the propositions between two different BI-algebras.
For instance, the <affine> modality maps propositions of an arbitrary BI-algebra into
the sub-BI-algebra of affine propositions.
Note that in MoSeL modalities can map the propositions between two different
BI-algebras. Most of the modalities in Iris operate on the same type of
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
:
=
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