Commit 9b44e889 authored by Robbert Krebbers's avatar Robbert Krebbers
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Merge branch 'modalities-doc' into 'master'

[documentation] Some more text about the modalities.

See merge request !220
parents 36f10273 ff41b98a
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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 : 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
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
......@@ -19,7 +32,22 @@ spatial context what action should be performed upon introducing the modality:
- Introduction will clear the context.
- Introduction will keep the context as-if.
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 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 :=
| MIEnvIsEmpty {PROP2 : bi} : modality_action PROP1 PROP2
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