| Safe Haskell | None |
|---|---|
| Language | Haskell2010 |
Agda.TypeChecking.Irrelevance
Description
Compile-time irrelevance.
In type theory with compile-time irrelevance à la Pfenning (LiCS 2001),
variables in the context are annotated with relevance attributes.
@
Γ = r₁x₁:A₁, ..., rⱼxⱼ:Aⱼ
To handle irrelevant projections, we also record the current relevance
attribute in the judgement. For instance, this attribute is equal to
to Irrelevant if we are in an irrelevant position, like an
irrelevant argument.
Γ ⊢r t : A
Only relevant variables can be used:
@
(Relevant x : A) ∈ Γ
--------------------
Γ ⊢r x : A
@
Irrelevant global declarations can only be used if r = Irrelevant@.
When we enter a r'-relevant function argument, we compose the r with r'
and (left-)divide the attributes in the context by r'.
@
Γ ⊢r t : (r' x : A) → B r' Γ ⊢(r'·r) u : A
---------------------------------------------------------
Γ ⊢r t u : B[u/x]
No surprises for abstraction:
@
Γ, (r' x : A) ⊢r : B ----------------------------- Γ ⊢r λxt : (r' x : A) → B @@
This is different for runtime irrelevance (erasure) which is `flat',
meaning that once one is in an irrelevant context, all new assumptions will
be usable, since they are turned relevant once entering the context.
See Conor McBride (WadlerFest 2016), for a type system in this spirit:
We use such a rule for runtime-irrelevance:
@
Γ, (q q') x : A ⊢q t : B
------------------------------
Γ ⊢q λxt : (q' x : A) → B
@
Conor's system is however set up differently, with a very different variable rule:
@@
(q x : A) ∈ Γ -------------- Γ ⊢q x : A
Γ, (q·p) x : A ⊢q t : B ----------------------------- Γ ⊢q λxt : (p x : A) → B
Γ ⊢q t : (p x : A) → B Γ' ⊢qp u : A ------------------------------------------------- Γ + Γ' ⊢q t u : B[u/x] @@
Synopsis
- hideAndRelParams :: Dom a -> Dom a
- workOnTypes :: (MonadTCEnv m, HasOptions m, MonadDebug m) => m a -> m a
- workOnTypes' :: MonadTCEnv m => Bool -> m a -> m a
- applyRelevanceToContext :: (MonadTCEnv tcm, LensRelevance r) => r -> tcm a -> tcm a
- applyRelevanceToContextOnly :: MonadTCEnv tcm => Relevance -> tcm a -> tcm a
- applyRelevanceToJudgementOnly :: MonadTCEnv tcm => Relevance -> tcm a -> tcm a
- applyRelevanceToContextFunBody :: (MonadTCM tcm, LensRelevance r) => r -> tcm a -> tcm a
- applyQuantityToContext :: (MonadTCEnv tcm, LensQuantity q) => q -> tcm a -> tcm a
- applyQuantityToContextOnly :: MonadTCEnv tcm => Quantity -> tcm a -> tcm a
- applyQuantityToJudgementOnly :: MonadTCEnv tcm => Quantity -> tcm a -> tcm a
- applyCohesionToContext :: (MonadTCEnv tcm, LensCohesion m) => m -> tcm a -> tcm a
- applyCohesionToContextOnly :: MonadTCEnv tcm => Cohesion -> tcm a -> tcm a
- splittableCohesion :: (HasOptions m, LensCohesion a) => a -> m Bool
- applyModalityToContext :: (MonadTCEnv tcm, LensModality m) => m -> tcm a -> tcm a
- applyModalityToContextOnly :: MonadTCEnv tcm => Modality -> tcm a -> tcm a
- applyModalityToJudgementOnly :: MonadTCEnv tcm => Modality -> tcm a -> tcm a
- applyModalityToContextFunBody :: (MonadTCM tcm, LensModality r) => r -> tcm a -> tcm a
- wakeIrrelevantVars :: MonadTCEnv tcm => tcm a -> tcm a
- class UsableRelevance a where
- class UsableModality a where
- isPropM :: (LensSort a, PrettyTCM a, MonadReduce m, MonadDebug m) => a -> m Bool
- isIrrelevantOrPropM :: (LensRelevance a, LensSort a, PrettyTCM a, MonadReduce m, MonadDebug m) => a -> m Bool
Operations on Dom.
hideAndRelParams :: Dom a -> Dom a Source #
Prepare parts of a parameter telescope for abstraction in constructors and projections.
Operations on Context.
workOnTypes :: (MonadTCEnv m, HasOptions m, MonadDebug m) => m a -> m a Source #
Modify the context whenever going from the l.h.s. (term side) of the typing judgement to the r.h.s. (type side).
workOnTypes' :: MonadTCEnv m => Bool -> m a -> m a Source #
Internal workhorse, expects value of --experimental-irrelevance flag as argument.
applyRelevanceToContext :: (MonadTCEnv tcm, LensRelevance r) => r -> tcm a -> tcm a Source #
(Conditionally) wake up irrelevant variables and make them relevant. For instance, in an irrelevant function argument otherwise irrelevant variables may be used, so they are awoken before type checking the argument.
Also allow the use of irrelevant definitions.
applyRelevanceToContextOnly :: MonadTCEnv tcm => Relevance -> tcm a -> tcm a Source #
(Conditionally) wake up irrelevant variables and make them relevant. For instance, in an irrelevant function argument otherwise irrelevant variables may be used, so they are awoken before type checking the argument.
Precondition: Relevance /= Relevant
applyRelevanceToJudgementOnly :: MonadTCEnv tcm => Relevance -> tcm a -> tcm a Source #
Apply relevance rel the the relevance annotation of the (typing/equality)
judgement. This is part of the work done when going into a rel-context.
Precondition: Relevance /= Relevant
applyRelevanceToContextFunBody :: (MonadTCM tcm, LensRelevance r) => r -> tcm a -> tcm a Source #
Like applyRelevanceToContext, but only act on context if
--irrelevant-projections.
See issue #2170.
applyQuantityToContext :: (MonadTCEnv tcm, LensQuantity q) => q -> tcm a -> tcm a Source #
(Conditionally) wake up erased variables and make them unrestricted. For instance, in an erased function argument otherwise erased variables may be used, so they are awoken before type checking the argument.
Also allow the use of erased definitions.
applyQuantityToContextOnly :: MonadTCEnv tcm => Quantity -> tcm a -> tcm a Source #
(Conditionally) wake up erased variables and make them unrestricted. For instance, in an erased function argument otherwise erased variables may be used, so they are awoken before type checking the argument.
Precondition: Quantity /= Quantity1
applyQuantityToJudgementOnly :: MonadTCEnv tcm => Quantity -> tcm a -> tcm a Source #
Apply quantity q the the quantity annotation of the (typing/equality)
judgement. This is part of the work done when going into a q-context.
Precondition: Quantity /= Quantity1
applyCohesionToContext :: (MonadTCEnv tcm, LensCohesion m) => m -> tcm a -> tcm a Source #
Apply inverse composition with the given cohesion to the typing context.
applyCohesionToContextOnly :: MonadTCEnv tcm => Cohesion -> tcm a -> tcm a Source #
splittableCohesion :: (HasOptions m, LensCohesion a) => a -> m Bool Source #
Can we split on arguments of the given cohesion?
applyModalityToContext :: (MonadTCEnv tcm, LensModality m) => m -> tcm a -> tcm a Source #
(Conditionally) wake up irrelevant variables and make them relevant. For instance, in an irrelevant function argument otherwise irrelevant variables may be used, so they are awoken before type checking the argument.
Also allow the use of irrelevant definitions.
applyModalityToContextOnly :: MonadTCEnv tcm => Modality -> tcm a -> tcm a Source #
(Conditionally) wake up irrelevant variables and make them relevant. For instance, in an irrelevant function argument otherwise irrelevant variables may be used, so they are awoken before type checking the argument.
Precondition: Modality /= Relevant
applyModalityToJudgementOnly :: MonadTCEnv tcm => Modality -> tcm a -> tcm a Source #
Apply modality m the the modality annotation of the (typing/equality)
judgement. This is part of the work done when going into a m-context.
Precondition: Modality /= Relevant
applyModalityToContextFunBody :: (MonadTCM tcm, LensModality r) => r -> tcm a -> tcm a Source #
Like applyModalityToContext, but only act on context (for Relevance) if
--irrelevant-projections.
See issue #2170.
wakeIrrelevantVars :: MonadTCEnv tcm => tcm a -> tcm a Source #
Wake up irrelevant variables and make them relevant. This is used
when type checking terms in a hole, in which case you want to be able to
(for instance) infer the type of an irrelevant variable. In the course
of type checking an irrelevant function argument applyRelevanceToContext
is used instead, which also sets the context relevance to Irrelevant.
This is not the right thing to do when type checking interactively in a
hole since it also marks all metas created during type checking as
irrelevant (issue #2568).
class UsableRelevance a where Source #
Check whether something can be used in a position of the given relevance.
This is a substitute for double-checking that only makes sure relevances are correct. See issue #2640.
Used in unifier ( unifyStep Solution{}).
At the moment, this implements McBride-style irrelevance, where Pfenning-style would be the most accurate thing. However, these two notions only differ how they handle bound variables in a term. Here, we are only concerned in the free variables, used meta-variables, and used (irrelevant) definitions.
Instances
| UsableRelevance LevelAtom Source # | |
| UsableRelevance PlusLevel Source # | |
| UsableRelevance Level Source # | |
| UsableRelevance Sort Source # | |
| UsableRelevance Term Source # | |
| UsableRelevance a => UsableRelevance [a] Source # | |
| UsableRelevance a => UsableRelevance (Arg a) Source # | |
| UsableRelevance a => UsableRelevance (Type' a) Source # | |
| (Subst t a, UsableRelevance a) => UsableRelevance (Abs a) Source # | |
| UsableRelevance a => UsableRelevance (Elim' a) Source # | |
| UsableRelevance a => UsableRelevance (Dom a) Source # | |
| (UsableRelevance a, UsableRelevance b) => UsableRelevance (a, b) Source # | |
class UsableModality a where Source #
Check whether something can be used in a position of the given modality.
This is a substitute for double-checking that only makes sure modalities are correct. See issue #2640.
Used in unifier ( unifyStep Solution{}).
This uses McBride-style modality checking. It does not differ from Pfenning-style if we are only interested in the modality of the free variables, used meta-variables, and used definitions.
Instances
| UsableModality Level Source # | |
| UsableModality Sort Source # | |
| UsableModality Term Source # | |
| UsableModality a => UsableModality [a] Source # | |
| UsableModality a => UsableModality (Arg a) Source # | |
| UsableRelevance a => UsableModality (Type' a) Source # | |
| (Subst t a, UsableModality a) => UsableModality (Abs a) Source # | |
| UsableModality a => UsableModality (Elim' a) Source # | |
| UsableModality a => UsableModality (Dom a) Source # | |
| (UsableModality a, UsableModality b) => UsableModality (a, b) Source # | |
Propositions
isPropM :: (LensSort a, PrettyTCM a, MonadReduce m, MonadDebug m) => a -> m Bool Source #
Is a type a proposition? (Needs reduction.)
isIrrelevantOrPropM :: (LensRelevance a, LensSort a, PrettyTCM a, MonadReduce m, MonadDebug m) => a -> m Bool Source #