Agda-2.6.1.1: A dependently typed functional programming language and proof assistant
Safe HaskellNone
LanguageHaskell2010

Agda.TypeChecking.Free.Lazy

Description

Computing the free variables of a term lazily.

We implement a reduce (traversal into monoid) over internal syntax for a generic collection (monoid with singletons). This should allow a more efficient test for the presence of a particular variable.

Worst-case complexity does not change (i.e. the case when a variable does not occur), but best case-complexity does matter. For instance, see mkAbs: each time we construct a dependent function type, we check whether it is actually dependent.

The distinction between rigid and strongly rigid occurrences comes from: Jason C. Reed, PhD thesis, 2009, page 96 (see also his LFMTP 2009 paper)

The main idea is that x = t(x) is unsolvable if x occurs strongly rigidly in t. It might have a solution if the occurrence is not strongly rigid, e.g.

x = f -> suc (f (x ( y -> k))) has x = f -> suc (f (suc k))

Jason C. Reed, PhD thesis, page 106

Under coinductive constructors, occurrences are never strongly rigid. Also, function types and lambdas do not establish strong rigidity. Only inductive constructors do so. (See issue 1271).

For further reading on semirings and semimodules for variable occurrence, see e.g. Conor McBrides "I got plenty of nuttin'" (Wadlerfest 2016). There, he treats the "quantity" dimension of variable occurrences.

The semiring has an additive operation for combining occurrences of subterms, and a multiplicative operation of representing function composition. E.g. if variable x appears o in term u, but u appears in context q in term t then occurrence of variable x coming from u is accounted for as q o in t.

Consider example (λ{ x → (x,x)}) y:

  • Variable x occurs once unguarded in x.
  • It occurs twice unguarded in the aggregation x x
  • Inductive constructor , turns this into two strictly rigid occurrences.

If , is a record constructor, then we stay unguarded.

  • The function ({λ x → (x,x)}) provides a context for variable y. This context can be described as weakly rigid with quantity two.
  • The final occurrence of y is obtained as composing the context with the occurrence of y in itself (which is the unit for composition). Thus, y occurs weakly rigid with quantity two.

It is not a given that the context can be described in the same way as the variable occurrence. However, for quantity it is the case and we obtain a semiring of occurrences with 0, 1, and even ω, which is an absorptive element for addition.

Synopsis

Set of meta variables.

newtype MetaSet Source #

A set of meta variables. Forms a monoid under union.

Constructors

MetaSet 

Fields

Instances

Instances details
Eq MetaSet Source # 
Instance details

Defined in Agda.TypeChecking.Free.Lazy

Methods

(==) :: MetaSet -> MetaSet -> Bool #

(/=) :: MetaSet -> MetaSet -> Bool #

Show MetaSet Source # 
Instance details

Defined in Agda.TypeChecking.Free.Lazy

Semigroup MetaSet Source # 
Instance details

Defined in Agda.TypeChecking.Free.Lazy

Monoid MetaSet Source # 
Instance details

Defined in Agda.TypeChecking.Free.Lazy

Null MetaSet Source # 
Instance details

Defined in Agda.TypeChecking.Free.Lazy

Singleton MetaId MetaSet Source # 
Instance details

Defined in Agda.TypeChecking.Free.Lazy

foldrMetaSet :: (MetaId -> a -> a) -> a -> MetaSet -> a Source #

Flexible and rigid occurrences (semigroup)

data FlexRig' a Source #

Depending on the surrounding context of a variable, it's occurrence can be classified as flexible or rigid, with finer distinctions.

The constructors are listed in increasing order (wrt. information content).

Constructors

Flexible a

In arguments of metas. The set of metas is used by 'NonLinMatch' to generate the right blocking information. The semantics is that the status of a variable occurrence may change if one of the metas in the set gets solved. We may say the occurrence is tainted by the meta variables in the set.

WeaklyRigid

In arguments to variables and definitions.

Unguarded

In top position, or only under inductive record constructors (unit).

StronglyRigid

Under at least one and only inductive constructors.

Instances

Instances details
Functor FlexRig' Source # 
Instance details

Defined in Agda.TypeChecking.Free.Lazy

Methods

fmap :: (a -> b) -> FlexRig' a -> FlexRig' b #

(<$) :: a -> FlexRig' b -> FlexRig' a #

Foldable FlexRig' Source # 
Instance details

Defined in Agda.TypeChecking.Free.Lazy

Methods

fold :: Monoid m => FlexRig' m -> m #

foldMap :: Monoid m => (a -> m) -> FlexRig' a -> m #

foldMap' :: Monoid m => (a -> m) -> FlexRig' a -> m #

foldr :: (a -> b -> b) -> b -> FlexRig' a -> b #

foldr' :: (a -> b -> b) -> b -> FlexRig' a -> b #

foldl :: (b -> a -> b) -> b -> FlexRig' a -> b #

foldl' :: (b -> a -> b) -> b -> FlexRig' a -> b #

foldr1 :: (a -> a -> a) -> FlexRig' a -> a #

foldl1 :: (a -> a -> a) -> FlexRig' a -> a #

toList :: FlexRig' a -> [a] #

null :: FlexRig' a -> Bool #

length :: FlexRig' a -> Int #

elem :: Eq a => a -> FlexRig' a -> Bool #

maximum :: Ord a => FlexRig' a -> a #

minimum :: Ord a => FlexRig' a -> a #

sum :: Num a => FlexRig' a -> a #

product :: Num a => FlexRig' a -> a #

LensFlexRig a (FlexRig' a) Source # 
Instance details

Defined in Agda.TypeChecking.Free.Lazy

Eq a => Eq (FlexRig' a) Source # 
Instance details

Defined in Agda.TypeChecking.Free.Lazy

Methods

(==) :: FlexRig' a -> FlexRig' a -> Bool #

(/=) :: FlexRig' a -> FlexRig' a -> Bool #

Show a => Show (FlexRig' a) Source # 
Instance details

Defined in Agda.TypeChecking.Free.Lazy

Methods

showsPrec :: Int -> FlexRig' a -> ShowS #

show :: FlexRig' a -> String #

showList :: [FlexRig' a] -> ShowS #

Singleton (Variable, FlexRig' ()) FlexRigMap Source # 
Instance details

Defined in Agda.TypeChecking.Free.Lazy

class LensFlexRig a o | o -> a where Source #

Instances

Instances details
LensFlexRig a (VarOcc' a) Source #

Access to varFlexRig in VarOcc.

Instance details

Defined in Agda.TypeChecking.Free.Lazy

LensFlexRig a (FlexRig' a) Source # 
Instance details

Defined in Agda.TypeChecking.Free.Lazy

LensFlexRig a (FreeEnv' a b c) Source # 
Instance details

Defined in Agda.TypeChecking.Free.Lazy

Methods

lensFlexRig :: Lens' (FlexRig' a) (FreeEnv' a b c) Source #

addFlexRig :: Semigroup a => FlexRig' a -> FlexRig' a -> FlexRig' a Source #

FlexRig aggregation (additive operation of the semiring). For combining occurrences of the same variable in subterms. This is a refinement of the max operation for FlexRig which would work if Flexible did not have the MetaSet as an argument. Now, to aggregate two Flexible occurrences, we union the involved MetaSets.

composeFlexRig :: Semigroup a => FlexRig' a -> FlexRig' a -> FlexRig' a Source #

FlexRig composition (multiplicative operation of the semiring). For accumulating the context of a variable.

Flexible is dominant. Once we are under a meta, we are flexible regardless what else comes. We taint all variable occurrences under a meta by this meta.

WeaklyRigid is next in strength. Destroys strong rigidity.

StronglyRigid is still dominant over Unguarded.

Unguarded is the unit. It is the top (identity) context.

Multi-dimensional feature vector for variable occurrence (semigroup)

data VarOcc' a Source #

Occurrence of free variables is classified by several dimensions. Currently, we have FlexRig and Modality.

Constructors

VarOcc 

Instances

Instances details
LensFlexRig a (VarOcc' a) Source #

Access to varFlexRig in VarOcc.

Instance details

Defined in Agda.TypeChecking.Free.Lazy

Eq a => Eq (VarOcc' a) Source #

Equality up to origin.

Instance details

Defined in Agda.TypeChecking.Free.Lazy

Methods

(==) :: VarOcc' a -> VarOcc' a -> Bool #

(/=) :: VarOcc' a -> VarOcc' a -> Bool #

Show a => Show (VarOcc' a) Source # 
Instance details

Defined in Agda.TypeChecking.Free.Lazy

Methods

showsPrec :: Int -> VarOcc' a -> ShowS #

show :: VarOcc' a -> String #

showList :: [VarOcc' a] -> ShowS #

Semigroup a => Semigroup (VarOcc' a) Source #

The default way of aggregating free variable info from subterms is by adding the variable occurrences. For instance, if we have a pair (t₁,t₂) then and t₁ has o₁ the occurrences of a variable x and t₂ has o₂ the occurrences of the same variable, then (t₁,t₂) has mappend o₁ o₂ occurrences of that variable.

From counting Quantity, we extrapolate this to FlexRig and Relevance: we care most about about StronglyRigid Relevant occurrences. E.g., if t₁ has a StronglyRigid occurrence and t₂ a Flexible occurrence, then (t₁,t₂) still has a StronglyRigid occurrence. Analogously, Relevant occurrences count most, as we wish e.g. to forbid relevant occurrences of variables that are declared to be irrelevant.

VarOcc forms a semiring, and this monoid is the addition of the semiring.

Instance details

Defined in Agda.TypeChecking.Free.Lazy

Methods

(<>) :: VarOcc' a -> VarOcc' a -> VarOcc' a #

sconcat :: NonEmpty (VarOcc' a) -> VarOcc' a #

stimes :: Integral b => b -> VarOcc' a -> VarOcc' a #

(Semigroup a, Monoid a) => Monoid (VarOcc' a) Source #

The neutral element for variable occurrence aggregation is least serious occurrence: flexible, irrelevant. This is also the absorptive element for composeVarOcc, if we ignore the MetaSet in Flexible.

Instance details

Defined in Agda.TypeChecking.Free.Lazy

Methods

mempty :: VarOcc' a #

mappend :: VarOcc' a -> VarOcc' a -> VarOcc' a #

mconcat :: [VarOcc' a] -> VarOcc' a #

LensRelevance (VarOcc' a) Source # 
Instance details

Defined in Agda.TypeChecking.Free.Lazy

LensQuantity (VarOcc' a) Source # 
Instance details

Defined in Agda.TypeChecking.Free.Lazy

LensModality (VarOcc' a) Source # 
Instance details

Defined in Agda.TypeChecking.Free.Lazy

topVarOcc :: VarOcc' a Source #

The absorptive element of variable occurrence under aggregation: strongly rigid, relevant.

composeVarOcc :: Semigroup a => VarOcc' a -> VarOcc' a -> VarOcc' a Source #

First argument is the outer occurrence (context) and second is the inner. This multiplicative operation is to modify an occurrence under a context.

Storing variable occurrences (semimodule).

class (Singleton MetaId a, Semigroup a, Monoid a, Semigroup c, Monoid c) => IsVarSet a c | c -> a where Source #

Any representation c of a set of variables need to be able to be modified by a variable occurrence. This is to ensure that free variable analysis is compositional. For instance, it should be possible to compute `fv (v [u/x])` from `fv v` and `fv u`.

In algebraic terminology, a variable set a needs to be (almost) a left semimodule to the semiring VarOcc.

Methods

withVarOcc :: VarOcc' a -> c -> c Source #

Laws * Respects monoid operations: ``` withVarOcc o mempty == mempty withVarOcc o (x <> y) == withVarOcc o x <> withVarOcc o y ``` * Respects VarOcc composition: ``` withVarOcc oneVarOcc = id withVarOcc (composeVarOcc o1 o2) = withVarOcc o1 . withVarOcc o2 ``` * Respects VarOcc aggregation: ``` withVarOcc (o1 <> o2) x = withVarOcc o1 x <> withVarOcc o2 x ``` Since the corresponding unit law may fail, ``` withVarOcc mempty x = mempty ``` it is not quite a semimodule.

Instances

Instances details
IsVarSet () All Source # 
Instance details

Defined in Agda.TypeChecking.Free

Methods

withVarOcc :: VarOcc' () -> All -> All Source #

IsVarSet () Any Source # 
Instance details

Defined in Agda.TypeChecking.Free

Methods

withVarOcc :: VarOcc' () -> Any -> Any Source #

IsVarSet () FlexRigMap Source #

Compose everything with the varFlexRig part of the VarOcc.

Instance details

Defined in Agda.TypeChecking.Free.Lazy

IsVarSet () VarCounts Source # 
Instance details

Defined in Agda.TypeChecking.Free

IsVarSet () AllowedVar Source # 
Instance details

Defined in Agda.TypeChecking.MetaVars.Occurs

IsVarSet () [Int] Source # 
Instance details

Defined in Agda.TypeChecking.Free

Methods

withVarOcc :: VarOcc' () -> [Int] -> [Int] Source #

(Singleton MetaId a, Semigroup a, Monoid a) => IsVarSet a (VarMap' a) Source # 
Instance details

Defined in Agda.TypeChecking.Free.Lazy

Methods

withVarOcc :: VarOcc' a -> VarMap' a -> VarMap' a Source #

type TheVarMap' a = IntMap (VarOcc' a) Source #

Representation of a variable set as map from de Bruijn indices to VarOcc.

newtype VarMap' a Source #

Constructors

VarMap 

Fields

Instances

Instances details
Singleton Variable (VarMap' a) Source #

A "set"-style Singleton instance with default/initial variable occurrence.

Instance details

Defined in Agda.TypeChecking.Free.Lazy

(Singleton MetaId a, Semigroup a, Monoid a) => IsVarSet a (VarMap' a) Source # 
Instance details

Defined in Agda.TypeChecking.Free.Lazy

Methods

withVarOcc :: VarOcc' a -> VarMap' a -> VarMap' a Source #

Eq a => Eq (VarMap' a) Source # 
Instance details

Defined in Agda.TypeChecking.Free.Lazy

Methods

(==) :: VarMap' a -> VarMap' a -> Bool #

(/=) :: VarMap' a -> VarMap' a -> Bool #

Show a => Show (VarMap' a) Source # 
Instance details

Defined in Agda.TypeChecking.Free.Lazy

Methods

showsPrec :: Int -> VarMap' a -> ShowS #

show :: VarMap' a -> String #

showList :: [VarMap' a] -> ShowS #

Semigroup a => Semigroup (VarMap' a) Source #

Proper monoid instance for VarMap rather than inheriting the broken one from IntMap. We combine two occurrences of a variable using mappend.

Instance details

Defined in Agda.TypeChecking.Free.Lazy

Methods

(<>) :: VarMap' a -> VarMap' a -> VarMap' a #

sconcat :: NonEmpty (VarMap' a) -> VarMap' a #

stimes :: Integral b => b -> VarMap' a -> VarMap' a #

Semigroup a => Monoid (VarMap' a) Source # 
Instance details

Defined in Agda.TypeChecking.Free.Lazy

Methods

mempty :: VarMap' a #

mappend :: VarMap' a -> VarMap' a -> VarMap' a #

mconcat :: [VarMap' a] -> VarMap' a #

Simple flexible/rigid variable collection.

type TheFlexRigMap = IntMap (FlexRig' ()) Source #

Keep track of FlexRig for every variable, but forget the involved meta vars.

Environment for collecting free variables.

data IgnoreSorts Source #

Where should we skip sorts in free variable analysis?

Constructors

IgnoreNot

Do not skip.

IgnoreInAnnotations

Skip when annotation to a type.

IgnoreAll

Skip unconditionally.

Instances

Instances details
Eq IgnoreSorts Source # 
Instance details

Defined in Agda.TypeChecking.Free.Lazy

Show IgnoreSorts Source # 
Instance details

Defined in Agda.TypeChecking.Free.Lazy

data FreeEnv' a b c Source #

The current context.

Constructors

FreeEnv 

Fields

Instances

Instances details
LensFlexRig a (FreeEnv' a b c) Source # 
Instance details

Defined in Agda.TypeChecking.Free.Lazy

Methods

lensFlexRig :: Lens' (FlexRig' a) (FreeEnv' a b c) Source #

LensRelevance (FreeEnv' a b c) Source # 
Instance details

Defined in Agda.TypeChecking.Free.Lazy

LensQuantity (FreeEnv' a b c) Source # 
Instance details

Defined in Agda.TypeChecking.Free.Lazy

LensModality (FreeEnv' a b c) Source # 
Instance details

Defined in Agda.TypeChecking.Free.Lazy

(Applicative m, Semigroup c) => Semigroup (FreeT a b m c) Source # 
Instance details

Defined in Agda.TypeChecking.Free.Lazy

Methods

(<>) :: FreeT a b m c -> FreeT a b m c -> FreeT a b m c #

sconcat :: NonEmpty (FreeT a b m c) -> FreeT a b m c #

stimes :: Integral b0 => b0 -> FreeT a b m c -> FreeT a b m c #

(Functor m, Applicative m, Monad m, Semigroup c, Monoid c) => Monoid (FreeT a b m c) Source # 
Instance details

Defined in Agda.TypeChecking.Free.Lazy

Methods

mempty :: FreeT a b m c #

mappend :: FreeT a b m c -> FreeT a b m c -> FreeT a b m c #

mconcat :: [FreeT a b m c] -> FreeT a b m c #

type SingleVar c = Variable -> c Source #

feIgnoreSorts :: FreeEnv' a IgnoreSorts c -> IgnoreSorts Source #

Ignore free variables in sorts.

initFreeEnv :: Monoid c => b -> SingleVar c -> FreeEnv' a b c Source #

The initial context.

type FreeT a b m c = ReaderT (FreeEnv' a b c) m c Source #

runFreeM :: IsVarSet a c => SingleVar c -> IgnoreSorts -> FreeM a c -> c Source #

Run function for FreeM.

variable :: (Monad m, IsVarSet a c) => Int -> FreeT a b m c Source #

Base case: a variable.

subVar :: Int -> Maybe Variable -> Maybe Variable Source #

Subtract, but return Nothing if result is negative.

underBinder :: MonadReader (FreeEnv' a b c) m => m z -> m z Source #

Going under a binder.

underBinder' :: MonadReader (FreeEnv' a b c) m => Nat -> m z -> m z Source #

Going under n binders.

underModality :: (MonadReader r m, LensModality r, LensModality o) => o -> m z -> m z Source #

Changing the Modality.

underRelevance :: (MonadReader r m, LensRelevance r, LensRelevance o) => o -> m z -> m z Source #

Changing the Relevance.

underFlexRig :: (MonadReader r m, LensFlexRig a r, Semigroup a, LensFlexRig a o) => o -> m z -> m z Source #

Changing the FlexRig context.

underConstructor :: (MonadReader r m, LensFlexRig a r, Semigroup a) => ConHead -> m z -> m z Source #

What happens to the variables occurring under a constructor?

Recursively collecting free variables.

class Free t where Source #

Gather free variables in a collection.

Minimal complete definition

Nothing

Methods

freeVars' :: IsVarSet a c => t -> FreeM a c Source #

default freeVars' :: (t ~ f b, Foldable f, Free b) => IsVarSet a c => t -> FreeM a c Source #

Instances

Instances details
Free EqualityView Source # 
Instance details

Defined in Agda.TypeChecking.Free.Lazy

Methods

freeVars' :: IsVarSet a c => EqualityView -> FreeM a c Source #

Free Clause Source # 
Instance details

Defined in Agda.TypeChecking.Free.Lazy

Methods

freeVars' :: IsVarSet a c => Clause -> FreeM a c Source #

Free LevelAtom Source # 
Instance details

Defined in Agda.TypeChecking.Free.Lazy

Methods

freeVars' :: IsVarSet a c => LevelAtom -> FreeM a c Source #

Free PlusLevel Source # 
Instance details

Defined in Agda.TypeChecking.Free.Lazy

Methods

freeVars' :: IsVarSet a c => PlusLevel -> FreeM a c Source #

Free Level Source # 
Instance details

Defined in Agda.TypeChecking.Free.Lazy

Methods

freeVars' :: IsVarSet a c => Level -> FreeM a c Source #

Free Sort Source # 
Instance details

Defined in Agda.TypeChecking.Free.Lazy

Methods

freeVars' :: IsVarSet a c => Sort -> FreeM a c Source #

Free Term Source # 
Instance details

Defined in Agda.TypeChecking.Free.Lazy

Methods

freeVars' :: IsVarSet a c => Term -> FreeM a c Source #

Free Candidate Source # 
Instance details

Defined in Agda.TypeChecking.Monad.Base

Methods

freeVars' :: IsVarSet a c => Candidate -> FreeM a c Source #

Free NLPSort Source # 
Instance details

Defined in Agda.TypeChecking.Rewriting.NonLinPattern

Methods

freeVars' :: IsVarSet a c => NLPSort -> FreeM a c Source #

Free NLPType Source # 
Instance details

Defined in Agda.TypeChecking.Rewriting.NonLinPattern

Methods

freeVars' :: IsVarSet a c => NLPType -> FreeM a c Source #

Free NLPat Source #

Only computes free variables that are not bound (see nlPatVars), i.e., those in a PTerm.

Instance details

Defined in Agda.TypeChecking.Rewriting.NonLinPattern

Methods

freeVars' :: IsVarSet a c => NLPat -> FreeM a c Source #

Free DisplayTerm Source # 
Instance details

Defined in Agda.TypeChecking.Monad.Base

Methods

freeVars' :: IsVarSet a c => DisplayTerm -> FreeM a c Source #

Free DisplayForm Source # 
Instance details

Defined in Agda.TypeChecking.Monad.Base

Methods

freeVars' :: IsVarSet a c => DisplayForm -> FreeM a c Source #

Free CompareAs Source # 
Instance details

Defined in Agda.TypeChecking.Monad.Base

Methods

freeVars' :: IsVarSet a c => CompareAs -> FreeM a c Source #

Free Constraint Source # 
Instance details

Defined in Agda.TypeChecking.Monad.Base

Methods

freeVars' :: IsVarSet a c => Constraint -> FreeM a c Source #

Free SingleLevel Source # 
Instance details

Defined in Agda.TypeChecking.Level

Methods

freeVars' :: IsVarSet a c => SingleLevel -> FreeM a c Source #

Free t => Free [t] Source # 
Instance details

Defined in Agda.TypeChecking.Free.Lazy

Methods

freeVars' :: IsVarSet a c => [t] -> FreeM a c Source #

Free t => Free (Maybe t) Source # 
Instance details

Defined in Agda.TypeChecking.Free.Lazy

Methods

freeVars' :: IsVarSet a c => Maybe t -> FreeM a c Source #

Free t => Free (Arg t) Source # 
Instance details

Defined in Agda.TypeChecking.Free.Lazy

Methods

freeVars' :: IsVarSet a c => Arg t -> FreeM a c Source #

Free t => Free (WithHiding t) Source # 
Instance details

Defined in Agda.TypeChecking.Free.Lazy

Methods

freeVars' :: IsVarSet a c => WithHiding t -> FreeM a c Source #

Free t => Free (Tele t) Source # 
Instance details

Defined in Agda.TypeChecking.Free.Lazy

Methods

freeVars' :: IsVarSet a c => Tele t -> FreeM a c Source #

Free t => Free (Type' t) Source # 
Instance details

Defined in Agda.TypeChecking.Free.Lazy

Methods

freeVars' :: IsVarSet a c => Type' t -> FreeM a c Source #

Free t => Free (Abs t) Source # 
Instance details

Defined in Agda.TypeChecking.Free.Lazy

Methods

freeVars' :: IsVarSet a c => Abs t -> FreeM a c Source #

Free t => Free (Elim' t) Source # 
Instance details

Defined in Agda.TypeChecking.Free.Lazy

Methods

freeVars' :: IsVarSet a c => Elim' t -> FreeM a c Source #

Free t => Free (Dom t) Source # 
Instance details

Defined in Agda.TypeChecking.Free.Lazy

Methods

freeVars' :: IsVarSet a c => Dom t -> FreeM a c Source #

(Free t, Free u) => Free (t, u) Source # 
Instance details

Defined in Agda.TypeChecking.Free.Lazy

Methods

freeVars' :: IsVarSet a c => (t, u) -> FreeM a c Source #

(Free t, Free u, Free v) => Free (t, u, v) Source # 
Instance details

Defined in Agda.TypeChecking.Free.Lazy

Methods

freeVars' :: IsVarSet a c => (t, u, v) -> FreeM a c Source #

Orphan instances

Singleton MetaId () Source # 
Instance details

Methods

singleton :: MetaId -> () Source #