Agda.TypeChecking.Free

Computing the free variables of a term.

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).

If you need the occurrence information for all free variables, you can use freeVars which has amoungst others this instance freeVars :: Term -> VarMap From VarMap, specific information can be extracted, e.g., relevantVars :: VarMap -> VarSet relevantVars = filterVarMap isRelevant

To just check the status of a single free variable, there are more efficient methods, e.g., freeIn :: Nat -> Term -> Bool

Tailored optimized variable checks can be implemented as semimodules to VarOcc', see, for example, VarCounts or SingleFlexRig.

Documentation

newtype VarCounts

Constructors

VarCounts

Fields

• varCounts :: IntMap Int

Instances

Monoid VarCounts

Defined in Agda.TypeChecking.Free

Methods

mempty :: VarCounts

mappend :: VarCounts -> VarCounts -> VarCounts

mconcat :: [VarCounts] -> VarCounts

Semigroup VarCounts

Defined in Agda.TypeChecking.Free

Methods

(<>) :: VarCounts -> VarCounts -> VarCounts

sconcat :: NonEmpty VarCounts -> VarCounts

stimes :: Integral b => b -> VarCounts -> VarCounts

IsVarSet () VarCounts

Defined in Agda.TypeChecking.Free

Methods

withVarOcc :: VarOcc' () -> VarCounts -> VarCounts

Singleton Variable VarCounts

Defined in Agda.TypeChecking.Free

Methods

singleton :: Variable -> VarCounts

class Free t

Gather free variables in a collection.

Instances

Free Clause

Defined in Agda.TypeChecking.Free.Lazy

Methods

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

Free EqualityView

Defined in Agda.TypeChecking.Free.Lazy

Methods

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

Free Level

Defined in Agda.TypeChecking.Free.Lazy

Methods

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

Free Sort

Defined in Agda.TypeChecking.Free.Lazy

Methods

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

Free Term

Defined in Agda.TypeChecking.Free.Lazy

Methods

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

Free Candidate

Defined in Agda.TypeChecking.Monad.Base

Methods

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

Free CompareAs

Defined in Agda.TypeChecking.Monad.Base

Methods

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

Free Constraint

Defined in Agda.TypeChecking.Monad.Base

Methods

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

Free DisplayForm

Defined in Agda.TypeChecking.Monad.Base

Methods

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

Free DisplayTerm

Defined in Agda.TypeChecking.Monad.Base

Methods

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

Free NLPSort

Defined in Agda.TypeChecking.Rewriting.NonLinPattern

Methods

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

Free NLPType

Defined in Agda.TypeChecking.Rewriting.NonLinPattern

Methods

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

Free NLPat

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

Defined in Agda.TypeChecking.Rewriting.NonLinPattern

Methods

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

Free t => Free (Arg t)

Defined in Agda.TypeChecking.Free.Lazy

Methods

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

Free t => Free (WithHiding t)

Defined in Agda.TypeChecking.Free.Lazy

Methods

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

Free t => Free (Abs t)

Defined in Agda.TypeChecking.Free.Lazy

Methods

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

Free t => Free (Dom t)

Defined in Agda.TypeChecking.Free.Lazy

Methods

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

Free t => Free (PlusLevel' t)

Defined in Agda.TypeChecking.Free.Lazy

Methods

freeVars' :: IsVarSet a c => PlusLevel' t -> FreeM a c

Free t => Free (Tele t)

Defined in Agda.TypeChecking.Free.Lazy

Methods

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

Free t => Free (Type' t)

Defined in Agda.TypeChecking.Free.Lazy

Methods

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

Free t => Free (Elim' t)

Defined in Agda.TypeChecking.Free.Lazy

Methods

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

Free t => Free (SingleLevel' t)

Defined in Agda.TypeChecking.Level

Methods

freeVars' :: IsVarSet a c => SingleLevel' t -> FreeM a c

Free t => Free (Maybe t)

Defined in Agda.TypeChecking.Free.Lazy

Methods

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

Free t => Free [t]

Defined in Agda.TypeChecking.Free.Lazy

Methods

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

Free t => Free (Named nm t)

Defined in Agda.TypeChecking.Free.Lazy

Methods

freeVars' :: IsVarSet a c => Named nm t -> FreeM a c

(Free t, Free u) => Free (t, u)

Defined in Agda.TypeChecking.Free.Lazy

Methods

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

(Free t, Free u, Free v) => Free (t, u, v)

Defined in Agda.TypeChecking.Free.Lazy

Methods

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

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

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

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

IsVarSet () VarCounts

Defined in Agda.TypeChecking.Free

Methods

withVarOcc :: VarOcc' () -> VarCounts -> VarCounts

IsVarSet () FlexRigMap

Compose everything with the varFlexRig part of the VarOcc'.

Defined in Agda.TypeChecking.Free.Lazy

Methods

withVarOcc :: VarOcc' () -> FlexRigMap -> FlexRigMap

IsVarSet () AllowedVar

Defined in Agda.TypeChecking.MetaVars.Occurs

Methods

withVarOcc :: VarOcc' () -> AllowedVar -> AllowedVar

IsVarSet () All

Defined in Agda.TypeChecking.Free

Methods

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

IsVarSet () Any

Defined in Agda.TypeChecking.Free

Methods

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

IsVarSet () [Int]

Defined in Agda.TypeChecking.Free

Methods

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

(Singleton MetaId a, Semigroup a, Monoid a) => IsVarSet a (VarMap' a)

Defined in Agda.TypeChecking.Free.Lazy

Methods

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

data IgnoreSorts

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

Show IgnoreSorts

Defined in Agda.TypeChecking.Free.Lazy

Methods

showsPrec :: Int -> IgnoreSorts -> ShowS

show :: IgnoreSorts -> String

showList :: [IgnoreSorts] -> ShowS

Eq IgnoreSorts

Defined in Agda.TypeChecking.Free.Lazy

Methods

(==) :: IgnoreSorts -> IgnoreSorts -> Bool

(/=) :: IgnoreSorts -> IgnoreSorts -> Bool

freeVars :: (IsVarSet a c, Singleton Variable c, Free t) => t -> c

Collect all free variables together with information about their occurrence.

Doesn't go inside solved metas, but collects the variables from a metavariable application X ts as flexibleVars.

freeVars' :: (Free t, IsVarSet a c) => t -> FreeM a c

filterVarMap :: (VarOcc -> Bool) -> VarMap -> VarSet

filterVarMapToList :: (VarOcc -> Bool) -> VarMap -> [Variable]

runFree :: (IsVarSet a c, Free t) => SingleVar c -> IgnoreSorts -> t -> c

Compute free variables.

rigidVars :: VarMap -> VarSet

Rigid variables: either strongly rigid, unguarded, or weakly rigid.

stronglyRigidVars :: VarMap -> VarSet

Variables under only and at least one inductive constructor(s).

unguardedVars :: VarMap -> VarSet

Variables at top or only under inductive record constructors λs and Πs. The purpose of recording these separately is that they can still become strongly rigid if put under a constructor whereas weakly rigid ones stay weakly rigid.

allVars :: VarMap -> VarSet

flexibleVars :: VarMap -> IntMap MetaSet

Variables occuring in arguments of metas. These are only potentially free, depending how the meta variable is instantiated. The set contains the id's of the meta variables that this variable is an argument to.

allFreeVars :: Free t => t -> VarSet

Collect all free variables.

allRelevantVars :: Free t => t -> VarSet

Collect all relevant free variables, excluding the "unused" ones.

allRelevantVarsIgnoring :: Free t => IgnoreSorts -> t -> VarSet

Collect all relevant free variables, possibly ignoring sorts.

freeVarsIgnore :: (IsVarSet a c, Singleton Variable c, Free t) => IgnoreSorts -> t -> c

freeIn :: Free a => Nat -> a -> Bool

freeInIgnoringSorts :: Free a => Nat -> a -> Bool

isBinderUsed :: Free a => Abs a -> Bool

Is the variable bound by the abstraction actually used?

relevantIn :: Free t => Nat -> t -> Bool

relevantInIgnoringSortAnn :: Free t => Nat -> t -> Bool

data FlexRig' a

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

Foldable FlexRig'

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

Functor FlexRig'

Defined in Agda.TypeChecking.Free.Lazy

Methods

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

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

LensFlexRig a (FlexRig' a)

Defined in Agda.TypeChecking.Free.Lazy

Methods

lensFlexRig :: Lens' (FlexRig' a) (FlexRig' a)

Show a => Show (FlexRig' a)

Defined in Agda.TypeChecking.Free.Lazy

Methods

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

show :: FlexRig' a -> String

showList :: [FlexRig' a] -> ShowS

Eq a => Eq (FlexRig' a)

Defined in Agda.TypeChecking.Free.Lazy

Methods

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

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

Singleton (Variable, FlexRig' ()) FlexRigMap

Defined in Agda.TypeChecking.Free.Lazy

Methods

singleton :: (Variable, FlexRig' ()) -> FlexRigMap

type FlexRig = FlexRig' MetaSet

class LensFlexRig a o | o -> a where

Methods

lensFlexRig :: Lens' (FlexRig' a) o

Instances

LensFlexRig a (FlexRig' a)

Defined in Agda.TypeChecking.Free.Lazy

Methods

lensFlexRig :: Lens' (FlexRig' a) (FlexRig' a)

LensFlexRig a (VarOcc' a)

Access to varFlexRig in VarOcc'.

Defined in Agda.TypeChecking.Free.Lazy

Methods

lensFlexRig :: Lens' (FlexRig' a) (VarOcc' a)

LensFlexRig a (FreeEnv' a b c)

Defined in Agda.TypeChecking.Free.Lazy

Methods

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

isFlexible :: LensFlexRig a o => o -> Bool

isUnguarded :: LensFlexRig a o => o -> Bool

isStronglyRigid :: LensFlexRig a o => o -> Bool

isWeaklyRigid :: LensFlexRig a o => o -> Bool

data VarOcc' a

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

Constructors

VarOcc

Fields

• varFlexRig :: FlexRig' a
• varModality :: Modality

Instances

LensFlexRig a (VarOcc' a)

Access to varFlexRig in VarOcc'.

Defined in Agda.TypeChecking.Free.Lazy

Methods

lensFlexRig :: Lens' (FlexRig' a) (VarOcc' a)

LensModality (VarOcc' a)

Defined in Agda.TypeChecking.Free.Lazy

Methods

getModality :: VarOcc' a -> Modality

setModality :: Modality -> VarOcc' a -> VarOcc' a

mapModality :: (Modality -> Modality) -> VarOcc' a -> VarOcc' a

LensQuantity (VarOcc' a)

Defined in Agda.TypeChecking.Free.Lazy

Methods

getQuantity :: VarOcc' a -> Quantity

setQuantity :: Quantity -> VarOcc' a -> VarOcc' a

mapQuantity :: (Quantity -> Quantity) -> VarOcc' a -> VarOcc' a

LensRelevance (VarOcc' a)

Defined in Agda.TypeChecking.Free.Lazy

Methods

getRelevance :: VarOcc' a -> Relevance

setRelevance :: Relevance -> VarOcc' a -> VarOcc' a

mapRelevance :: (Relevance -> Relevance) -> VarOcc' a -> VarOcc' a

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

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.

Defined in Agda.TypeChecking.Free.Lazy

Methods

mempty :: VarOcc' a

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

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

Semigroup a => Semigroup (VarOcc' a)

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.

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

Show a => Show (VarOcc' a)

Defined in Agda.TypeChecking.Free.Lazy

Methods

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

show :: VarOcc' a -> String

showList :: [VarOcc' a] -> ShowS

Eq a => Eq (VarOcc' a)

Equality up to origin.

Defined in Agda.TypeChecking.Free.Lazy

Methods

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

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

type VarOcc = VarOcc' MetaSet

varOccurrenceIn :: Free a => Nat -> a -> Maybe VarOcc

Get the full occurrence information of a free variable.

flexRigOccurrenceIn :: Free a => Nat -> a -> Maybe FlexRig

Get the full occurrence information of a free variable.

closed :: Free t => t -> Bool

Is the term entirely closed (no free variables)?

data MetaSet

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

Instances

Null MetaSet

Defined in Agda.TypeChecking.Free.Lazy

Methods

empty :: MetaSet

null :: MetaSet -> Bool

Monoid MetaSet

Defined in Agda.TypeChecking.Free.Lazy

Methods

mempty :: MetaSet

mappend :: MetaSet -> MetaSet -> MetaSet

mconcat :: [MetaSet] -> MetaSet

Semigroup MetaSet

Defined in Agda.TypeChecking.Free.Lazy

Methods

(<>) :: MetaSet -> MetaSet -> MetaSet

sconcat :: NonEmpty MetaSet -> MetaSet

stimes :: Integral b => b -> MetaSet -> MetaSet

Show MetaSet

Defined in Agda.TypeChecking.Free.Lazy

Methods

showsPrec :: Int -> MetaSet -> ShowS

show :: MetaSet -> String

showList :: [MetaSet] -> ShowS

Eq MetaSet

Defined in Agda.TypeChecking.Free.Lazy

Methods

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

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

Singleton MetaId MetaSet

Defined in Agda.TypeChecking.Free.Lazy

Methods

singleton :: MetaId -> MetaSet

insertMetaSet :: MetaId -> MetaSet -> MetaSet

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

metaSetToBlocker :: MetaSet -> Blocker

Orphan instances

IsVarSet () All

Methods

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

IsVarSet () Any

Methods

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

IsVarSet () [Int]

Methods

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