module Agda.TypeChecking.Free
( FreeVars(..)
, Free
, freeVars
, allVars
, relevantVars
, rigidVars
, freeIn, isBinderUsed
, freeInIgnoringSorts
, relevantIn
, Occurrence(..)
, occurrence
) where
import qualified Agda.Utils.VarSet as Set
import Agda.Utils.VarSet (VarSet)
import Agda.Syntax.Common
import Agda.Syntax.Internal
#include "../undefined.h"
import Agda.Utils.Impossible
data FreeVars = FV
{ stronglyRigidVars :: VarSet
, weaklyRigidVars :: VarSet
, flexibleVars :: VarSet
, irrelevantVars :: VarSet
}
rigidVars :: FreeVars -> VarSet
rigidVars fv = Set.union (stronglyRigidVars fv) (weaklyRigidVars fv)
allVars :: FreeVars -> VarSet
allVars fv = Set.unions [rigidVars fv, flexibleVars fv, irrelevantVars fv]
relevantVars :: FreeVars -> VarSet
relevantVars fv = Set.unions [rigidVars fv, flexibleVars fv]
data Occurrence
= NoOccurrence
| StronglyRigid
| WeaklyRigid
| Flexible
deriving (Eq,Show)
occurrence :: Nat -> FreeVars -> Occurrence
occurrence x fv
| x `Set.member` stronglyRigidVars fv = StronglyRigid
| x `Set.member` weaklyRigidVars fv = WeaklyRigid
| x `Set.member` flexibleVars fv = Flexible
| otherwise = NoOccurrence
flexible :: FreeVars -> FreeVars
flexible fv =
fv { stronglyRigidVars = Set.empty
, weaklyRigidVars = Set.empty
, flexibleVars = relevantVars fv
}
weakly :: FreeVars -> FreeVars
weakly fv = fv
{ stronglyRigidVars = Set.empty
, weaklyRigidVars = rigidVars fv
}
irrelevantly :: FreeVars -> FreeVars
irrelevantly fv = empty { irrelevantVars = allVars fv }
union :: FreeVars -> FreeVars -> FreeVars
union (FV sv1 rv1 fv1 iv1) (FV sv2 rv2 fv2 iv2) =
FV (Set.union sv1 sv2) (Set.union rv1 rv2) (Set.union fv1 fv2) (Set.union iv1 iv2)
unions :: [FreeVars] -> FreeVars
unions = foldr union empty
empty :: FreeVars
empty = FV Set.empty Set.empty Set.empty Set.empty
delete :: Nat -> FreeVars -> FreeVars
delete n (FV sv rv fv iv) = FV (Set.delete n sv) (Set.delete n rv) (Set.delete n fv) (Set.delete n iv)
subtractFV :: Nat -> FreeVars -> FreeVars
subtractFV n (FV sv rv fv iv) = FV (Set.subtract n sv) (Set.subtract n rv) (Set.subtract n fv) (Set.subtract n iv)
singleton :: Nat -> FreeVars
singleton x = FV { stronglyRigidVars = Set.singleton x
, weaklyRigidVars = Set.empty
, flexibleVars = Set.empty
, irrelevantVars = Set.empty
}
class Free a where
freeVars' :: FreeConf -> a -> FreeVars
data FreeConf = FreeConf
{ fcIgnoreSorts :: Bool
}
freeVars :: Free a => a -> FreeVars
freeVars = freeVars' FreeConf{ fcIgnoreSorts = False }
instance Free Term where
freeVars' conf t = case t of
Var n ts -> singleton n `union` weakly (freeVars' conf ts)
Lam _ t -> freeVars' conf t
Lit _ -> empty
Def _ ts -> weakly $ freeVars' conf ts
Con _ ts -> freeVars' conf ts
Pi a b -> freeVars' conf (a,b)
Sort s -> freeVars' conf s
Level l -> freeVars' conf l
MetaV _ ts -> flexible $ freeVars' conf ts
DontCare mt -> irrelevantly $ freeVars' conf mt
instance Free Type where
freeVars' conf (El s t) = freeVars' conf (s, t)
instance Free Sort where
freeVars' conf s
| fcIgnoreSorts conf = empty
| otherwise = case s of
Type a -> freeVars' conf a
Prop -> empty
Inf -> empty
DLub s1 s2 -> weakly $ freeVars' conf (s1, s2)
instance Free Level where
freeVars' conf (Max as) = freeVars' conf as
instance Free PlusLevel where
freeVars' conf ClosedLevel{} = empty
freeVars' conf (Plus _ l) = freeVars' conf l
instance Free LevelAtom where
freeVars' conf l = case l of
MetaLevel _ vs -> flexible $ freeVars' conf vs
NeutralLevel v -> freeVars' conf v
BlockedLevel _ v -> freeVars' conf v
UnreducedLevel v -> freeVars' conf v
instance Free a => Free [a] where
freeVars' conf = unions . map (freeVars' conf)
instance Free a => Free (Maybe a) where
freeVars' conf = maybe empty (freeVars' conf)
instance (Free a, Free b) => Free (a,b) where
freeVars' conf (x,y) = freeVars' conf x `union` freeVars' conf y
instance Free a => Free (Arg a) where
freeVars' conf = freeVars' conf . unArg
instance Free a => Free (Abs a) where
freeVars' conf (Abs _ b) = subtractFV 1 $ delete 0 $ freeVars' conf b
freeVars' conf (NoAbs _ b) = freeVars' conf b
instance Free a => Free (Tele a) where
freeVars' conf EmptyTel = empty
freeVars' conf (ExtendTel a tel) = freeVars' conf (a, tel)
instance Free ClauseBody where
freeVars' conf (Body t) = freeVars' conf t
freeVars' conf (Bind b) = freeVars' conf b
freeVars' conf NoBody = empty
freeIn :: Free a => Nat -> a -> Bool
freeIn v t = v `Set.member` allVars (freeVars t)
freeInIgnoringSorts :: Free a => Nat -> a -> Bool
freeInIgnoringSorts v t =
v `Set.member` allVars (freeVars' FreeConf{ fcIgnoreSorts = True } t)
relevantIn :: Free a => Nat -> a -> Bool
relevantIn v t = v `Set.member` relevantVars (freeVars' FreeConf{ fcIgnoreSorts = True } t)
isBinderUsed :: Free a => Abs a -> Bool
isBinderUsed NoAbs{} = False
isBinderUsed (Abs _ x) = 0 `freeIn` x