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Jonas Kastberg
iris
Commits
94ced2c9
Commit
94ced2c9
authored
Feb 24, 2019
by
Dan Frumin
Browse files
Some more text about the modalities.
parent
36f10273
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theories/proofmode/modalities.v
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94ced2c9
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@@ 6,8 +6,21 @@ Import bi.
(** The `iModIntro` tactic is not tied the Iris modalities, but can be
instantiated with a variety of modalities.
In order to plug in a modality, one has to decide for both the intuitionistic and
spatial context what action should be performed upon introducing the modality:
For the purpose of MoSeL, a modality is a mapping of propositions
`M : PROP → PROP` (where `PROP` is a type of biassertions) that is
monotone and distributes over finite products. Specifically, the following
rules have to be satisfied.
P ⊢ Q emp ⊢ M emp

M P ⊢ M Q M P ∗ M Q ⊢ M (P ∗ Q)
Together those conditions allow one to introduce the modality in the
goal, while stripping away the modalities in the context.
Additionally, upon introducing a modality one can perform a number of
associated actions on the intuitionistic and spatial contexts.
Such an action can be one of the following:
 Introduction is only allowed when the context is empty.
 Introduction is only allowed when all hypotheses satisfy some predicate
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@@ 19,7 +32,19 @@ spatial context what action should be performed upon introducing the modality:
 Introduction will clear the context.
 Introduction will keep the context asif.
Formally, these actions correspond to the following inductive type: *)
Formally, these actions correspond to the inductive type [modality_action].
For each of those actions you have to prove that the transformation is valid.
To instantiate the modality you have to define: 1) a mixin `modality_mixin`,
2) a record `modality`, 3) a `FromModal` type class instance from `classes.v`.
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 BIalgebras.
For instance, the <affine> modality maps propositions of an arbitrary BIalgebra into
the subBIalgebra of affine propositions.
*)
Inductive
modality_action
(
PROP1
:
bi
)
:
bi
→
Type
:
=

MIEnvIsEmpty
{
PROP2
:
bi
}
:
modality_action
PROP1
PROP2
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