Agda-2.6.0: src/full/Agda/Syntax/Common.hs

{-# LANGUAGE CPP                        #-}
{-# LANGUAGE DeriveDataTypeable         #-}
{-# LANGUAGE DeriveGeneric              #-}
{-# LANGUAGE GeneralizedNewtypeDeriving #-}
{-# LANGUAGE UndecidableInstances       #-} -- for: LensNamed name (Arg a)

{-| Some common syntactic entities are defined in this module.
-}
module Agda.Syntax.Common where

import Control.DeepSeq

import Data.ByteString.Char8 (ByteString)
import qualified Data.ByteString.Char8 as ByteString
import Data.Foldable
import Data.Hashable (Hashable(..))
import qualified Data.Strict.Maybe as Strict
import Data.Semigroup hiding (Arg)
import Data.Traversable
import Data.Data (Data)
import Data.Word
import Data.IntSet (IntSet)
import qualified Data.IntSet as IntSet

import GHC.Generics (Generic)

import Agda.Syntax.Position

import Agda.Utils.Functor
import Agda.Utils.Lens
import Agda.Utils.PartialOrd
import Agda.Utils.POMonoid
import Agda.Utils.Pretty hiding ((<>))

#include "undefined.h"
import Agda.Utils.Impossible

---------------------------------------------------------------------------
-- * Delayed
---------------------------------------------------------------------------

-- | Used to specify whether something should be delayed.
data Delayed = Delayed | NotDelayed
  deriving (Data, Show, Eq, Ord)

instance KillRange Delayed where
  killRange = id

---------------------------------------------------------------------------
-- * File
---------------------------------------------------------------------------

data FileType = AgdaFileType | MdFileType | RstFileType | TexFileType | OrgFileType
  deriving (Data, Eq, Ord, Show)

instance Pretty FileType where
  pretty = \case
    AgdaFileType -> "Agda"
    MdFileType   -> "Markdown"
    RstFileType  -> "ReStructedText"
    TexFileType  -> "LaTeX"
    OrgFileType  -> "org-mode"

---------------------------------------------------------------------------
-- * Eta-equality
---------------------------------------------------------------------------

data HasEta = NoEta | YesEta
  deriving (Data, Show, Eq, Ord)

instance HasRange HasEta where
  getRange _ = noRange

instance KillRange HasEta where
  killRange = id

instance NFData HasEta where
  rnf NoEta  = ()
  rnf YesEta = ()

---------------------------------------------------------------------------
-- * Induction
---------------------------------------------------------------------------

data Induction = Inductive | CoInductive
  deriving (Data, Eq, Ord, Show)

instance Pretty Induction where
  pretty Inductive   = "inductive"
  pretty CoInductive = "coinductive"

instance HasRange Induction where
  getRange _ = noRange

instance KillRange Induction where
  killRange = id

instance NFData Induction where
  rnf Inductive   = ()
  rnf CoInductive = ()

---------------------------------------------------------------------------
-- * Hiding
---------------------------------------------------------------------------

data Overlappable = YesOverlap | NoOverlap
  deriving (Data, Show, Eq, Ord)

data Hiding  = Hidden | Instance Overlappable | NotHidden
  deriving (Data, Show, Eq, Ord)

instance Pretty Hiding where
  pretty = \case
    Hidden     -> "hidden"
    NotHidden  -> "visible"
    Instance{} -> "instance"

-- | Just for the 'Hiding' instance. Should never combine different
--   overlapping.
instance Semigroup Overlappable where
  NoOverlap  <> NoOverlap  = NoOverlap
  YesOverlap <> YesOverlap = YesOverlap
  _          <> _          = __IMPOSSIBLE__

-- | 'Hiding' is an idempotent partial monoid, with unit 'NotHidden'.
--   'Instance' and 'NotHidden' are incompatible.
instance Semigroup Hiding where
  NotHidden  <> h           = h
  h          <> NotHidden   = h
  Hidden     <> Hidden      = Hidden
  Instance o <> Instance o' = Instance (o <> o')
  _          <> _           = __IMPOSSIBLE__

instance Monoid Overlappable where
  mempty  = NoOverlap
  mappend = (<>)

instance Monoid Hiding where
  mempty = NotHidden
  mappend = (<>)

instance KillRange Hiding where
  killRange = id

instance NFData Overlappable where
  rnf NoOverlap  = ()
  rnf YesOverlap = ()

instance NFData Hiding where
  rnf Hidden       = ()
  rnf (Instance o) = rnf o
  rnf NotHidden    = ()

-- | Decorating something with 'Hiding' information.
data WithHiding a = WithHiding
  { whHiding :: !Hiding
  , whThing  :: a
  }
  deriving (Data, Eq, Ord, Show, Functor, Foldable, Traversable)

instance Decoration WithHiding where
  traverseF f (WithHiding h a) = WithHiding h <$> f a

instance Applicative WithHiding where
  pure = WithHiding mempty
  WithHiding h f <*> WithHiding h' a = WithHiding (mappend h h') (f a)

instance HasRange a => HasRange (WithHiding a) where
  getRange = getRange . dget

instance SetRange a => SetRange (WithHiding a) where
  setRange = fmap . setRange

instance KillRange a => KillRange (WithHiding a) where
  killRange = fmap killRange

instance NFData a => NFData (WithHiding a) where
  rnf (WithHiding _ a) = rnf a

-- | A lens to access the 'Hiding' attribute in data structures.
--   Minimal implementation: @getHiding@ and one of @setHiding@ or @mapHiding@.
class LensHiding a where

  getHiding :: a -> Hiding

  setHiding :: Hiding -> a -> a
  setHiding h = mapHiding (const h)

  mapHiding :: (Hiding -> Hiding) -> a -> a
  mapHiding f a = setHiding (f $ getHiding a) a

instance LensHiding Hiding where
  getHiding = id
  setHiding = const
  mapHiding = id

instance LensHiding (WithHiding a) where
  getHiding   (WithHiding h _) = h
  setHiding h (WithHiding _ a) = WithHiding h a
  mapHiding f (WithHiding h a) = WithHiding (f h) a

-- | Monoidal composition of 'Hiding' information in some data.
mergeHiding :: LensHiding a => WithHiding a -> a
mergeHiding (WithHiding h a) = mapHiding (mappend h) a

-- | 'NotHidden' arguments are @visible@.
visible :: LensHiding a => a -> Bool
visible a = getHiding a == NotHidden

-- | 'Instance' and 'Hidden' arguments are @notVisible@.
notVisible :: LensHiding a => a -> Bool
notVisible a = getHiding a /= NotHidden

-- | 'Hidden' arguments are @hidden@.
hidden :: LensHiding a => a -> Bool
hidden a = getHiding a == Hidden

hide :: LensHiding a => a -> a
hide = setHiding Hidden

hideOrKeepInstance :: LensHiding a => a -> a
hideOrKeepInstance x =
  case getHiding x of
    Hidden     -> x
    Instance{} -> x
    NotHidden  -> setHiding Hidden x

makeInstance :: LensHiding a => a -> a
makeInstance = makeInstance' NoOverlap

makeInstance' :: LensHiding a => Overlappable -> a -> a
makeInstance' o = setHiding (Instance o)

isOverlappable :: LensHiding a => a -> Bool
isOverlappable x =
  case getHiding x of
    Instance YesOverlap -> True
    _ -> False

isInstance :: LensHiding a => a -> Bool
isInstance x =
  case getHiding x of
    Instance{} -> True
    _          -> False

-- | Ignores 'Overlappable'.
sameHiding :: (LensHiding a, LensHiding b) => a -> b -> Bool
sameHiding x y =
  case (getHiding x, getHiding y) of
    (Instance{}, Instance{}) -> True
    (hx, hy)                 -> hx == hy

---------------------------------------------------------------------------
-- * Modalities
---------------------------------------------------------------------------

-- | We have a tuple of modalities, which might not be fully orthogonal.
--   For instance, irrelevant stuff is also run-time irrelevant.
data Modality = Modality
  { modRelevance :: Relevance
      -- ^ Legacy irrelevance.
      --   See Pfenning, LiCS 2001; Abel/Vezzosi/Winterhalter, ICFP 2017.
  , modQuantity  :: Quantity
      -- ^ Cardinality / runtime erasure.
      --   See Conor McBride, I got plenty o' nutting, Wadlerfest 2016.
      --   See Bob Atkey, Syntax and Semantics of Quantitative Type Theory, LiCS 2018.
  } deriving (Data, Eq, Ord, Show, Generic)

defaultModality :: Modality
defaultModality = Modality defaultRelevance defaultQuantity

-- | Pointwise composition.
instance Semigroup Modality where
  Modality r q <> Modality r' q' = Modality (r <> r') (q <> q')

-- | Pointwise unit.
instance Monoid Modality where
  mempty = Modality mempty mempty
  mappend = (<>)

-- | Dominance ordering.
instance PartialOrd Modality where
  comparable (Modality r q) (Modality r' q') = comparable (r, q) (r', q')

instance POSemigroup Modality where
instance POMonoid Modality where

instance LeftClosedPOMonoid Modality where
  inverseCompose = inverseComposeModality

-- | @m `moreUsableModality` m'@ means that an @m@ can be used
--   where ever an @m'@ is required.

moreUsableModality :: Modality -> Modality -> Bool
moreUsableModality m m' = related m POLE m'

usableModality :: LensModality a => a -> Bool
usableModality a = usableRelevance m && usableQuantity m
  where m = getModality a

composeModality :: Modality -> Modality -> Modality
composeModality = (<>)

-- | Compose with modality flag from the left.
--   This function is e.g. used to update the modality information
--   on pattern variables @a@ after a match against something of modality @q@.
applyModality :: LensModality a => Modality -> a -> a
applyModality m = mapModality (m `composeModality`)

-- | @inverseComposeModality r x@ returns the least modality @y@
--   such that forall @x@, @y@ we have
--   @x \`moreUsableModality\` (r \`composeModality\` y)@
--   iff
--   @(r \`inverseComposeModality\` x) \`moreUsableModality\` y@ (Galois connection).
inverseComposeModality :: Modality -> Modality -> Modality
inverseComposeModality (Modality r q) (Modality r' q') =
  Modality (r `inverseComposeRelevance` r')
           (q `inverseComposeQuantity`  q')

-- | Left division by a 'Modality'.
--   Used e.g. to modify context when going into a @m@ argument.
inverseApplyModality :: LensModality a => Modality -> a -> a
inverseApplyModality m = mapModality (m `inverseComposeModality`)


-- boilerplate instances

instance KillRange Modality where
  killRange = id

instance NFData Modality where

-- Lens stuff

lModRelevance :: Lens' Relevance Modality
lModRelevance f m = f (modRelevance m) <&> \ r -> m { modRelevance = r }

lModQuantity :: Lens' Quantity Modality
lModQuantity f m = f (modQuantity m) <&> \ q -> m { modQuantity = q }

class LensModality a where

  getModality :: a -> Modality

  setModality :: Modality -> a -> a
  setModality = mapModality . const

  mapModality :: (Modality -> Modality) -> a -> a
  mapModality f a = setModality (f $ getModality a) a

instance LensModality Modality where
  getModality = id
  setModality = const
  mapModality = id

instance LensRelevance Modality where
  getRelevance = modRelevance
  setRelevance h m = m { modRelevance = h }
  mapRelevance f m = m { modRelevance = f (modRelevance m) }

instance LensQuantity Modality where
  getQuantity = modQuantity
  setQuantity h m = m { modQuantity = h }
  mapQuantity f m = m { modQuantity = f (modQuantity m) }

-- default accessors for Relevance

getRelevanceMod :: LensModality a => LensGet Relevance a
getRelevanceMod = getRelevance . getModality

setRelevanceMod :: LensModality a => LensSet Relevance a
setRelevanceMod = mapModality . setRelevance

mapRelevanceMod :: LensModality a => LensMap Relevance a
mapRelevanceMod = mapModality . mapRelevance

-- default accessors for Quantity

getQuantityMod :: LensModality a => LensGet Quantity a
getQuantityMod = getQuantity . getModality

setQuantityMod :: LensModality a => LensSet Quantity a
setQuantityMod = mapModality . setQuantity

mapQuantityMod :: LensModality a => LensMap Quantity a
mapQuantityMod = mapModality . mapQuantity

---------------------------------------------------------------------------
-- * Quantities
---------------------------------------------------------------------------

-- | Quantity for linearity.
--
--   A quantity is a set of natural numbers, indicating possible semantic
--   uses of a variable.  A singleton set @{n}@ requires that the
--   corresponding variable is used exactly @n@ times.
--
data Quantity
  = Quantity0  -- ^ Zero uses @{0}@, erased at runtime.
  | Quantity1  -- ^ Linear use @{1}@ (could be updated destructively).
    -- Mostly TODO (needs postponable constraints between quantities to compute uses).
  | Quantityω  -- ^ Unrestricted use @ℕ@.
  deriving (Data, Show, Generic, Eq, Enum, Bounded, Ord)
    -- @Ord@ instance in case @Quantity@ is used in keys for maps etc.

defaultQuantity :: Quantity
defaultQuantity = Quantityω

-- | Composition of quantities (multiplication).
--
-- 'Quantity0' is dominant.
-- 'Quantity1' is neutral.
--
instance Semigroup Quantity where
  Quantity1 <> q = q
  q <> Quantity1 = q
  Quantity0 <> _ = Quantity0
  _ <> Quantity0 = Quantity0
  Quantityω <> _ = Quantityω
  -- _ <> Quantityω = Quantityω  -- redundant

-- | In the absense of finite quantities besides 0, ω is the unit.
--   Otherwise, 1 is the unit.
instance Monoid Quantity where
  mempty  = Quantity1
  mappend = (<>)

-- | Note that the order is @ω ≤ 0,1@, more options is smaller.
instance PartialOrd Quantity where
  comparable = curry $ \case
    (q, q') | q == q' -> POEQ
    -- ω is least
    (Quantityω, _)    -> POLT
    (_, Quantityω)    -> POGT
    -- others are uncomparable
    _ -> POAny

instance POSemigroup Quantity where
instance POMonoid Quantity where

instance LeftClosedPOMonoid Quantity where
  inverseCompose = inverseComposeQuantity

-- | @m `moreUsableQuantity` m'@ means that an @m@ can be used
--   where ever an @m'@ is required.

moreQuantity :: Quantity -> Quantity -> Bool
moreQuantity m m' = related m POLE m'

-- | A thing of quantity 0 is unusable, all others are usable.

usableQuantity :: LensQuantity a => a -> Bool
usableQuantity a = getQuantity a /= Quantity0

composeQuantity :: Quantity -> Quantity -> Quantity
composeQuantity = (<>)

-- | Compose with quantity flag from the left.
--   This function is e.g. used to update the quantity information
--   on pattern variables @a@ after a match against something of quantity @q@.
applyQuantity :: LensQuantity a => Quantity -> a -> a
applyQuantity q = mapQuantity (q `composeQuantity`)

-- | @inverseComposeQuantity r x@ returns the least quantity @y@
--   such that forall @x@, @y@ we have
--   @x \`moreQuantity\` (r \`composeQuantity\` y)@
--   iff
--   @(r \`inverseComposeQuantity\` x) \`moreQuantity\` y@ (Galois connection).
inverseComposeQuantity :: Quantity -> Quantity -> Quantity
inverseComposeQuantity q x =
  case (q, x) of
    (Quantity1 , x)          -> x          -- going to linear arg: nothing changes
    (Quantity0 , x)          -> Quantityω  -- going to erased arg: every thing usable
    (Quantityω , Quantityω)  -> Quantityω
    (Quantityω , _)          -> Quantity0  -- linear resources are unusable as arguments to unrestricted functions

-- | Left division by a 'Quantity'.
--   Used e.g. to modify context when going into a @q@ argument.
inverseApplyQuantity :: LensQuantity a => Quantity -> a -> a
inverseApplyQuantity q = mapQuantity (q `inverseComposeQuantity`)


-- boilerplate instances

class LensQuantity a where

  getQuantity :: a -> Quantity

  setQuantity :: Quantity -> a -> a
  setQuantity = mapQuantity . const

  mapQuantity :: (Quantity -> Quantity) -> a -> a
  mapQuantity f a = setQuantity (f $ getQuantity a) a

instance LensQuantity Quantity where
  getQuantity = id
  setQuantity = const
  mapQuantity = id

instance KillRange Quantity where
  killRange = id

instance NFData Quantity where
  rnf Quantity0 = ()
  rnf Quantity1 = ()
  rnf Quantityω = ()

---------------------------------------------------------------------------
-- * Relevance
---------------------------------------------------------------------------

-- | A function argument can be relevant or irrelevant.
--   See "Agda.TypeChecking.Irrelevance".
data Relevance
  = Relevant    -- ^ The argument is (possibly) relevant at compile-time.
  | NonStrict   -- ^ The argument may never flow into evaluation position.
                --   Therefore, it is irrelevant at run-time.
                --   It is treated relevantly during equality checking.
  | Irrelevant  -- ^ The argument is irrelevant at compile- and runtime.
    deriving (Data, Show, Eq, Enum, Bounded, Generic)

allRelevances :: [Relevance]
allRelevances = [minBound..maxBound]

defaultRelevance :: Relevance
defaultRelevance = Relevant

instance KillRange Relevance where
  killRange rel = rel -- no range to kill

instance NFData Relevance where
  rnf Relevant   = ()
  rnf NonStrict  = ()
  rnf Irrelevant = ()

-- | A lens to access the 'Relevance' attribute in data structures.
--   Minimal implementation: @getRelevance@ and one of @setRelevance@ or @mapRelevance@.
class LensRelevance a where

  getRelevance :: a -> Relevance

  setRelevance :: Relevance -> a -> a
  setRelevance h = mapRelevance (const h)

  mapRelevance :: (Relevance -> Relevance) -> a -> a
  mapRelevance f a = setRelevance (f $ getRelevance a) a

instance LensRelevance Relevance where
  getRelevance = id
  setRelevance = const
  mapRelevance = id

isRelevant :: LensRelevance a => a -> Bool
isRelevant a = getRelevance a == Relevant

isIrrelevant :: LensRelevance a => a -> Bool
isIrrelevant a = getRelevance a == Irrelevant

isNonStrict :: LensRelevance a => a -> Bool
isNonStrict a = getRelevance a == NonStrict

-- | Information ordering.
-- @Relevant  \`moreRelevant\`
--  NonStrict \`moreRelevant\`
--  Irrelevant@
moreRelevant :: Relevance -> Relevance -> Bool
moreRelevant = (<=)

-- | More relevant is smaller.
instance Ord Relevance where
  compare = curry $ \case
    (r, r') | r == r' -> EQ
    -- top
    (_, Irrelevant) -> LT
    (Irrelevant, _) -> GT
    -- bottom
    (Relevant, _) -> LT
    (_, Relevant) -> GT
    -- redundant case
    (NonStrict,NonStrict) -> EQ

-- | More relevant is smaller.
instance PartialOrd Relevance where
  comparable = comparableOrd

-- | @usableRelevance rel == False@ iff we cannot use a variable of @rel@.
usableRelevance :: LensRelevance a => a -> Bool
usableRelevance a = case getRelevance a of
  Irrelevant -> False
  NonStrict  -> False
  Relevant   -> True

-- | 'Relevance' composition.
--   'Irrelevant' is dominant, 'Relevant' is neutral.
composeRelevance :: Relevance -> Relevance -> Relevance
composeRelevance r r' =
  case (r, r') of
    (Irrelevant, _) -> Irrelevant
    (_, Irrelevant) -> Irrelevant
    (NonStrict, _)  -> NonStrict
    (_, NonStrict)  -> NonStrict
    (Relevant, Relevant) -> Relevant

-- | Compose with relevance flag from the left.
--   This function is e.g. used to update the relevance information
--   on pattern variables @a@ after a match against something @rel@.
applyRelevance :: LensRelevance a => Relevance -> a -> a
applyRelevance rel = mapRelevance (rel `composeRelevance`)

-- | @inverseComposeRelevance r x@ returns the most irrelevant @y@
--   such that forall @x@, @y@ we have
--   @x \`moreRelevant\` (r \`composeRelevance\` y)@
--   iff
--   @(r \`inverseComposeRelevance\` x) \`moreRelevant\` y@ (Galois connection).
inverseComposeRelevance :: Relevance -> Relevance -> Relevance
inverseComposeRelevance r x =
  case (r, x) of
    (Relevant  , x)          -> x          -- going to relevant arg.: nothing changes
                                           -- because Relevant is comp.-neutral
    (Irrelevant, x)          -> Relevant   -- going irrelevant: every thing usable
    (NonStrict , Irrelevant) -> Irrelevant -- otherwise: irrelevant things remain unusable
    (NonStrict , _)          -> Relevant   -- but @NonStrict@s become usable

-- | Left division by a 'Relevance'.
--   Used e.g. to modify context when going into a @rel@ argument.
inverseApplyRelevance :: LensRelevance a => Relevance -> a -> a
inverseApplyRelevance rel = mapRelevance (rel `inverseComposeRelevance`)

-- | 'Relevance' forms a semigroup under composition.
instance Semigroup Relevance where
  (<>) = composeRelevance

-- | 'Relevant' is the unit.
instance Monoid Relevance where
  mempty  = Relevant
  mappend = (<>)

instance POSemigroup Relevance where
instance POMonoid Relevance where

instance LeftClosedPOMonoid Relevance where
  inverseCompose = inverseComposeRelevance

-- | Irrelevant function arguments may appear non-strictly in the codomain type.
irrToNonStrict :: Relevance -> Relevance
irrToNonStrict Irrelevant = NonStrict
irrToNonStrict rel        = rel

-- | Applied when working on types (unless --experimental-irrelevance).
nonStrictToRel :: Relevance -> Relevance
nonStrictToRel NonStrict = Relevant
nonStrictToRel rel       = rel

nonStrictToIrr :: Relevance -> Relevance
nonStrictToIrr NonStrict = Irrelevant
nonStrictToIrr rel       = rel

---------------------------------------------------------------------------
-- * Origin of arguments (user-written, inserted or reflected)
---------------------------------------------------------------------------

-- | Origin of arguments.
data Origin
  = UserWritten  -- ^ From the source file / user input.  (Preserve!)
  | Inserted     -- ^ E.g. inserted hidden arguments.
  | Reflected    -- ^ Produced by the reflection machinery.
  | CaseSplit    -- ^ Produced by an interactive case split.
  | Substitution -- ^ Named application produced to represent a substitution. E.g. "?0 (x = n)" instead of "?0 n"
  deriving (Data, Show, Eq, Ord)

instance KillRange Origin where
  killRange = id

instance NFData Origin where
  rnf UserWritten = ()
  rnf Inserted = ()
  rnf Reflected = ()
  rnf CaseSplit = ()
  rnf Substitution = ()

-- | Decorating something with 'Origin' information.
data WithOrigin a = WithOrigin
  { woOrigin :: !Origin
  , woThing  :: a
  }
  deriving (Data, Eq, Ord, Show, Functor, Foldable, Traversable)

instance Decoration WithOrigin where
  traverseF f (WithOrigin h a) = WithOrigin h <$> f a

instance HasRange a => HasRange (WithOrigin a) where
  getRange = getRange . dget

instance SetRange a => SetRange (WithOrigin a) where
  setRange = fmap . setRange

instance KillRange a => KillRange (WithOrigin a) where
  killRange = fmap killRange

instance NFData a => NFData (WithOrigin a) where
  rnf (WithOrigin _ a) = rnf a

-- | A lens to access the 'Origin' attribute in data structures.
--   Minimal implementation: @getOrigin@ and one of @setOrigin@ or @mapOrigin@.

class LensOrigin a where

  getOrigin :: a -> Origin

  setOrigin :: Origin -> a -> a
  setOrigin o = mapOrigin (const o)

  mapOrigin :: (Origin -> Origin) -> a -> a
  mapOrigin f a = setOrigin (f $ getOrigin a) a

instance LensOrigin Origin where
  getOrigin = id
  setOrigin = const
  mapOrigin = id

instance LensOrigin (WithOrigin a) where
  getOrigin   (WithOrigin h _) = h
  setOrigin h (WithOrigin _ a) = WithOrigin h a
  mapOrigin f (WithOrigin h a) = WithOrigin (f h) a

-----------------------------------------------------------------------------
-- * Free variable annotations
-----------------------------------------------------------------------------

data FreeVariables = UnknownFVs | KnownFVs IntSet
  deriving (Data, Eq, Ord, Show)

instance Semigroup FreeVariables where
  UnknownFVs   <> _            = UnknownFVs
  _            <> UnknownFVs   = UnknownFVs
  KnownFVs vs1 <> KnownFVs vs2 = KnownFVs (IntSet.union vs1 vs2)

instance Monoid FreeVariables where
  mempty  = KnownFVs IntSet.empty
  mappend = (<>)

instance NFData FreeVariables where
  rnf UnknownFVs    = ()
  rnf (KnownFVs fv) = rnf fv

unknownFreeVariables :: FreeVariables
unknownFreeVariables = UnknownFVs

noFreeVariables :: FreeVariables
noFreeVariables = mempty

oneFreeVariable :: Int -> FreeVariables
oneFreeVariable = KnownFVs . IntSet.singleton

freeVariablesFromList :: [Int] -> FreeVariables
freeVariablesFromList = mconcat . map oneFreeVariable

-- | A lens to access the 'FreeVariables' attribute in data structures.
--   Minimal implementation: @getFreeVariables@ and one of @setFreeVariables@ or @mapFreeVariables@.
class LensFreeVariables a where

  getFreeVariables :: a -> FreeVariables

  setFreeVariables :: FreeVariables -> a -> a
  setFreeVariables o = mapFreeVariables (const o)

  mapFreeVariables :: (FreeVariables -> FreeVariables) -> a -> a
  mapFreeVariables f a = setFreeVariables (f $ getFreeVariables a) a

instance LensFreeVariables FreeVariables where
  getFreeVariables = id
  setFreeVariables = const
  mapFreeVariables = id

hasNoFreeVariables :: LensFreeVariables a => a -> Bool
hasNoFreeVariables x =
  case getFreeVariables x of
    UnknownFVs  -> False
    KnownFVs fv -> IntSet.null fv

---------------------------------------------------------------------------
-- * Argument decoration
---------------------------------------------------------------------------

-- | A function argument can be hidden and/or irrelevant.

data ArgInfo = ArgInfo
  { argInfoHiding        :: Hiding
  , argInfoModality      :: Modality
  , argInfoOrigin        :: Origin
  , argInfoFreeVariables :: FreeVariables
  } deriving (Data, Eq, Ord, Show)

instance KillRange ArgInfo where
  killRange i = i -- There are no ranges in ArgInfo's

class LensArgInfo a where
  getArgInfo :: a -> ArgInfo
  setArgInfo :: ArgInfo -> a -> a
  setArgInfo ai = mapArgInfo (const ai)
  mapArgInfo :: (ArgInfo -> ArgInfo) -> a -> a
  mapArgInfo f a = setArgInfo (f $ getArgInfo a) a

instance LensArgInfo ArgInfo where
  getArgInfo = id
  setArgInfo = const
  mapArgInfo = id

instance NFData ArgInfo where
  rnf (ArgInfo a b c d) = rnf a `seq` rnf b `seq` rnf c `seq` rnf d

instance LensHiding ArgInfo where
  getHiding = argInfoHiding
  setHiding h ai = ai { argInfoHiding = h }
  mapHiding f ai = ai { argInfoHiding = f (argInfoHiding ai) }

instance LensModality ArgInfo where
  getModality = argInfoModality
  setModality m ai = ai { argInfoModality = m }
  mapModality f ai = ai { argInfoModality = f (argInfoModality ai) }

instance LensOrigin ArgInfo where
  getOrigin = argInfoOrigin
  setOrigin o ai = ai { argInfoOrigin = o }
  mapOrigin f ai = ai { argInfoOrigin = f (argInfoOrigin ai) }

instance LensFreeVariables ArgInfo where
  getFreeVariables = argInfoFreeVariables
  setFreeVariables o ai = ai { argInfoFreeVariables = o }
  mapFreeVariables f ai = ai { argInfoFreeVariables = f (argInfoFreeVariables ai) }

-- inherited instances

instance LensRelevance ArgInfo where
  getRelevance = getRelevanceMod
  setRelevance = setRelevanceMod
  mapRelevance = mapRelevanceMod

instance LensQuantity ArgInfo where
  getQuantity = getQuantityMod
  setQuantity = setQuantityMod
  mapQuantity = mapQuantityMod

defaultArgInfo :: ArgInfo
defaultArgInfo =  ArgInfo
  { argInfoHiding        = NotHidden
  , argInfoModality      = defaultModality
  , argInfoOrigin        = UserWritten
  , argInfoFreeVariables = UnknownFVs
  }

-- Accessing through ArgInfo

-- default accessors for Hiding

getHidingArgInfo :: LensArgInfo a => LensGet Hiding a
getHidingArgInfo = getHiding . getArgInfo

setHidingArgInfo :: LensArgInfo a => LensSet Hiding a
setHidingArgInfo = mapArgInfo . setHiding

mapHidingArgInfo :: LensArgInfo a => LensMap Hiding a
mapHidingArgInfo = mapArgInfo . mapHiding

-- default accessors for Modality

getModalityArgInfo :: LensArgInfo a => LensGet Modality a
getModalityArgInfo = getModality . getArgInfo

setModalityArgInfo :: LensArgInfo a => LensSet Modality a
setModalityArgInfo = mapArgInfo . setModality

mapModalityArgInfo :: LensArgInfo a => LensMap Modality a
mapModalityArgInfo = mapArgInfo . mapModality

-- default accessors for Origin

getOriginArgInfo :: LensArgInfo a => LensGet Origin a
getOriginArgInfo = getOrigin . getArgInfo

setOriginArgInfo :: LensArgInfo a => LensSet Origin a
setOriginArgInfo = mapArgInfo . setOrigin

mapOriginArgInfo :: LensArgInfo a => LensMap Origin a
mapOriginArgInfo = mapArgInfo . mapOrigin

-- default accessors for FreeVariables

getFreeVariablesArgInfo :: LensArgInfo a => LensGet FreeVariables a
getFreeVariablesArgInfo = getFreeVariables . getArgInfo

setFreeVariablesArgInfo :: LensArgInfo a => LensSet FreeVariables a
setFreeVariablesArgInfo = mapArgInfo . setFreeVariables

mapFreeVariablesArgInfo :: LensArgInfo a => LensMap FreeVariables a
mapFreeVariablesArgInfo = mapArgInfo . mapFreeVariables


---------------------------------------------------------------------------
-- * Arguments
---------------------------------------------------------------------------

data Arg e  = Arg
  { argInfo :: ArgInfo
  , unArg :: e
  } deriving (Data, Ord, Show, Functor, Foldable, Traversable)

instance Decoration Arg where
  traverseF f (Arg ai a) = Arg ai <$> f a

instance HasRange a => HasRange (Arg a) where
    getRange = getRange . unArg

instance SetRange a => SetRange (Arg a) where
  setRange r = fmap $ setRange r

instance KillRange a => KillRange (Arg a) where
  killRange (Arg info a) = killRange2 Arg info a

-- | Ignores 'Quantity', 'Relevance', 'Origin', and 'FreeVariables'.
--   Ignores content of argument if 'Irrelevant'.
--
instance Eq a => Eq (Arg a) where
  Arg (ArgInfo h1 m1 _ _) x1 == Arg (ArgInfo h2 m2 _ _) x2 =
    h1 == h2 && (isIrrelevant m1 || isIrrelevant m2 || x1 == x2)
    -- Andreas, 2017-10-04, issue #2775, ignore irrelevant arguments during with-abstraction.
    -- This is a hack, we should not use '(==)' in with-abstraction
    -- and more generally not use it on Syntax.
    -- Andrea: except for caching.

-- instance Show a => Show (Arg a) where
--     show (Arg (ArgInfo h (Modality r q) o fv) a) = showFVs fv $ showQ q $ showR r $ showO o $ showH h $ show a
--       where
--         showH Hidden       s = "{" ++ s ++ "}"
--         showH NotHidden    s = "(" ++ s ++ ")"
--         showH (Instance o) s = showOv o ++ "{{" ++ s ++ "}}"
--           where showOv YesOverlap = "overlap "
--                 showOv NoOverlap  = ""
--         showR r s = case r of
--           Irrelevant   -> "." ++ s
--           NonStrict    -> "?" ++ s
--           Relevant     -> "r" ++ s -- Andreas: I want to see it explicitly
--         showQ q s = case q of
--           Quantity0   -> "0" ++ s
--           Quantity1   -> "1" ++ s
--           Quantityω   -> "ω" ++ s
--         showO o s = case o of
--           UserWritten -> "u" ++ s
--           Inserted    -> "i" ++ s
--           Reflected   -> "g" ++ s -- generated by reflection
--           CaseSplit   -> "c" ++ s -- generated by case split
--           Substitution -> "s" ++ s
--         showFVs UnknownFVs    s = s
--         showFVs (KnownFVs fv) s = "fv" ++ show (IntSet.toList fv) ++ s

-- -- defined in Concrete.Pretty
-- instance Pretty a => Pretty (Arg a) where
--     pretty (Arg (ArgInfo h (Modality r q) o fv) a) = prettyFVs fv $ prettyQ q $ prettyR r $ prettyO o $ prettyH h $ pretty a
--       where
--         prettyH Hidden       s = "{" <> s <> "}"
--         prettyH NotHidden    s = "(" <> s <> ")"
--         prettyH (Instance o) s = prettyOv o <> "{{" <> s <> "}}"
--           where prettyOv YesOverlap = "overlap "
--                 prettyOv NoOverlap  = ""
--         prettyR r s = case r of
--           Irrelevant   -> "." <> s
--           NonStrict    -> "?" <> s
--           Relevant     -> "r" <> s -- Andreas: I want to see it explicitly
--         prettyQ q s = case q of
--           Quantity0   -> "0" <> s
--           Quantity1   -> "1" <> s
--           Quantityω   -> "ω" <> s
--         prettyO o s = case o of
--           UserWritten -> "u" <> s
--           Inserted    -> "i" <> s
--           Reflected   -> "g" <> s -- generated by reflection
--           CaseSplit   -> "c" <> s -- generated by case split
--           Substitution -> "s" <> s
--         prettyFVs UnknownFVs    s = s
--         prettyFVs (KnownFVs fv) s = "fv" <> pretty (IntSet.toList fv) <> s

instance NFData e => NFData (Arg e) where
  rnf (Arg a b) = rnf a `seq` rnf b

instance LensArgInfo (Arg a) where
  getArgInfo        = argInfo
  setArgInfo ai arg = arg { argInfo = ai }
  mapArgInfo f arg  = arg { argInfo = f $ argInfo arg }

-- The other lenses are defined through LensArgInfo

instance LensHiding (Arg e) where
  getHiding = getHidingArgInfo
  setHiding = setHidingArgInfo
  mapHiding = mapHidingArgInfo

instance LensModality (Arg e) where
  getModality = getModalityArgInfo
  setModality = setModalityArgInfo
  mapModality = mapModalityArgInfo

instance LensOrigin (Arg e) where
  getOrigin = getOriginArgInfo
  setOrigin = setOriginArgInfo
  mapOrigin = mapOriginArgInfo

instance LensFreeVariables (Arg e) where
  getFreeVariables = getFreeVariablesArgInfo
  setFreeVariables = setFreeVariablesArgInfo
  mapFreeVariables = mapFreeVariablesArgInfo

-- Since we have LensModality, we get relevance and quantity by default

instance LensRelevance (Arg e) where
  getRelevance = getRelevanceMod
  setRelevance = setRelevanceMod
  mapRelevance = mapRelevanceMod

instance LensQuantity (Arg e) where
  getQuantity = getQuantityMod
  setQuantity = setQuantityMod
  mapQuantity = mapQuantityMod

defaultArg :: a -> Arg a
defaultArg = Arg defaultArgInfo

-- | @xs \`withArgsFrom\` args@ translates @xs@ into a list of 'Arg's,
-- using the elements in @args@ to fill in the non-'unArg' fields.
--
-- Precondition: The two lists should have equal length.

withArgsFrom :: [a] -> [Arg b] -> [Arg a]
xs `withArgsFrom` args =
  zipWith (\x arg -> fmap (const x) arg) xs args

withNamedArgsFrom :: [a] -> [NamedArg b] -> [NamedArg a]
xs `withNamedArgsFrom` args =
  zipWith (\x -> fmap (x <$)) xs args

---------------------------------------------------------------------------
-- * Names
---------------------------------------------------------------------------

class Eq a => Underscore a where
  underscore   :: a
  isUnderscore :: a -> Bool
  isUnderscore = (== underscore)

instance Underscore String where
  underscore = "_"

instance Underscore ByteString where
  underscore = ByteString.pack underscore

instance Underscore Doc where
  underscore = text underscore

---------------------------------------------------------------------------
-- * Function type domain
---------------------------------------------------------------------------

-- | Similar to 'Arg', but we need to distinguish
--   an irrelevance annotation in a function domain
--   (the domain itself is not irrelevant!)
--   from an irrelevant argument.
--
--   @Dom@ is used in 'Pi' of internal syntax, in 'Context' and 'Telescope'.
--   'Arg' is used for actual arguments ('Var', 'Con', 'Def' etc.)
--   and in 'Abstract' syntax and other situations.
--
--   [ cubical ] When @domFinite = True@ for the domain of a 'Pi'
--   type, the elements should be compared by tabulating the domain type.
--   Only supported in case the domain type is primIsOne, to obtain
--   the correct equality for partial elements.
data Dom e = Dom
  { domInfo   :: ArgInfo
  , domFinite :: !Bool
  , domName   :: Maybe RString
  , unDom     :: e
  } deriving (Data, Ord, Show, Functor, Foldable, Traversable)

instance Decoration Dom where
  traverseF f (Dom ai b x a) = Dom ai b x <$> f a

instance HasRange a => HasRange (Dom a) where
  getRange = getRange . unDom

instance KillRange a => KillRange (Dom a) where
  killRange (Dom info b x a) = killRange4 Dom info b x a

-- | Ignores 'Origin' and 'FreeVariables'.
instance Eq a => Eq (Dom a) where
  Dom (ArgInfo h1 m1 _ _) b1 s1 x1 == Dom (ArgInfo h2 m2 _ _) b2 s2 x2 =
    (h1, m1, b1, s1, x1) == (h2, m2, b2, s2, x2)

-- instance Show a => Show (Dom a) where
--   show = show . argFromDom

instance LensArgInfo (Dom e) where
  getArgInfo        = domInfo
  setArgInfo ai dom = dom { domInfo = ai }
  mapArgInfo f  dom = dom { domInfo = f $ domInfo dom }

-- The other lenses are defined through LensArgInfo

instance LensHiding (Dom e) where
  getHiding = getHidingArgInfo
  setHiding = setHidingArgInfo
  mapHiding = mapHidingArgInfo

instance LensModality (Dom e) where
  getModality = getModalityArgInfo
  setModality = setModalityArgInfo
  mapModality = mapModalityArgInfo

instance LensOrigin (Dom e) where
  getOrigin = getOriginArgInfo
  setOrigin = setOriginArgInfo
  mapOrigin = mapOriginArgInfo

instance LensFreeVariables (Dom e) where
  getFreeVariables = getFreeVariablesArgInfo
  setFreeVariables = setFreeVariablesArgInfo
  mapFreeVariables = mapFreeVariablesArgInfo

-- Since we have LensModality, we get relevance and quantity by default

instance LensRelevance (Dom e) where
  getRelevance = getRelevanceMod
  setRelevance = setRelevanceMod
  mapRelevance = mapRelevanceMod

instance LensQuantity (Dom e) where
  getQuantity = getQuantityMod
  setQuantity = setQuantityMod
  mapQuantity = mapQuantityMod

argFromDom :: Dom a -> Arg a
argFromDom (Dom i _ _ a) = Arg i a

namedArgFromDom :: Dom a -> NamedArg a
namedArgFromDom (Dom i _ s a) = Arg i $ Named s a

domFromArg :: Arg a -> Dom a
domFromArg (Arg i a) = Dom i False Nothing a

domFromNamedArg :: NamedArg a -> Dom a
domFromNamedArg (Arg i a) = Dom i False (nameOf a) (namedThing a)

defaultDom :: a -> Dom a
defaultDom = defaultArgDom defaultArgInfo

defaultArgDom :: ArgInfo -> a -> Dom a
defaultArgDom info x = Dom info False Nothing x

defaultNamedArgDom :: ArgInfo -> String -> a -> Dom a
defaultNamedArgDom info s = Dom info False (Just $ unranged s)

---------------------------------------------------------------------------
-- * Named arguments
---------------------------------------------------------------------------

-- | Something potentially carrying a name.
data Named name a =
    Named { nameOf     :: Maybe name
          , namedThing :: a
          }
    deriving (Eq, Ord, Show, Data, Functor, Foldable, Traversable)

-- | Standard naming.
type Named_ = Named RString

unnamed :: a -> Named name a
unnamed = Named Nothing

named :: name -> a -> Named name a
named = Named . Just

-- | Accessor/editor for the 'nameOf' component.
class LensNamed name a | a -> name where
  lensNamed :: Lens' (Maybe name) a

instance LensNamed name (Named name a) where
  lensNamed f (Named mn a) = f mn <&> \ mn' -> Named mn' a

getNameOf :: LensNamed name a => a -> Maybe name
getNameOf a = a ^. lensNamed

setNameOf :: LensNamed name a => Maybe name -> a -> a
setNameOf = set lensNamed

mapNameOf :: LensNamed name a => (Maybe name -> Maybe name) -> a -> a
mapNameOf = over lensNamed

-- Lenses lift through decorations:
-- instance (Decoration f, LensNamed name a) => LensNamed name (f a) where

instance LensNamed name a => LensNamed name (Arg a) where
  lensNamed = traverseF . lensNamed

-- Standard instances for 'Named':

instance Decoration (Named name) where
  traverseF f (Named n a) = Named n <$> f a

instance HasRange a => HasRange (Named name a) where
    getRange = getRange . namedThing

instance SetRange a => SetRange (Named name a) where
  setRange r = fmap $ setRange r

instance (KillRange name, KillRange a) => KillRange (Named name a) where
  killRange (Named n a) = Named (killRange n) (killRange a)

-- instance Show a => Show (Named_ a) where
--     show (Named Nothing a)  = show a
--     show (Named (Just n) a) = rawNameToString (rangedThing n) ++ " = " ++ show a

-- -- Defined in Concrete.Pretty
-- instance Pretty a => Pretty (Named_ a) where
--     pretty (Named Nothing a)  = pretty a
--     pretty (Named (Just n) a) = text (rawNameToString (rangedThing n)) <+> "=" <+> pretty a

instance (NFData name, NFData a) => NFData (Named name a) where
  rnf (Named a b) = rnf a `seq` rnf b

-- | Only 'Hidden' arguments can have names.
type NamedArg a = Arg (Named_ a)

-- | Get the content of a 'NamedArg'.
namedArg :: NamedArg a -> a
namedArg = namedThing . unArg

defaultNamedArg :: a -> NamedArg a
defaultNamedArg = unnamedArg defaultArgInfo

unnamedArg :: ArgInfo -> a -> NamedArg a
unnamedArg info = Arg info . unnamed

-- | The functor instance for 'NamedArg' would be ambiguous,
--   so we give it another name here.
updateNamedArg :: (a -> b) -> NamedArg a -> NamedArg b
updateNamedArg = fmap . fmap

-- | @setNamedArg a b = updateNamedArg (const b) a@
setNamedArg :: NamedArg a -> b -> NamedArg b
setNamedArg a b = (b <$) <$> a

---------------------------------------------------------------------------
-- * Range decoration.
---------------------------------------------------------------------------

-- | Thing with range info.
data Ranged a = Ranged
  { rangeOf     :: Range
  , rangedThing :: a
  }
  deriving (Data, Show, Functor, Foldable, Traversable)

-- | Thing with no range info.
unranged :: a -> Ranged a
unranged = Ranged noRange

instance Pretty a => Pretty (Ranged a) where
  pretty = pretty . rangedThing

-- instance Show a => Show (Ranged a) where
--   show = show . rangedThing

instance Eq a => Eq (Ranged a) where
  Ranged _ x == Ranged _ y = x == y

instance Ord a => Ord (Ranged a) where
  compare (Ranged _ x) (Ranged _ y) = compare x y

instance HasRange (Ranged a) where
  getRange = rangeOf

instance KillRange (Ranged a) where
  killRange (Ranged _ x) = Ranged noRange x

instance Decoration Ranged where
  traverseF f (Ranged r x) = Ranged r <$> f x

-- | Ranges are not forced.

instance NFData a => NFData (Ranged a) where
  rnf (Ranged _ a) = rnf a

---------------------------------------------------------------------------
-- * Raw names (before parsing into name parts).
---------------------------------------------------------------------------

-- | A @RawName@ is some sort of string.
type RawName = String

rawNameToString :: RawName -> String
rawNameToString = id

stringToRawName :: String -> RawName
stringToRawName = id

-- | String with range info.
type RString = Ranged RawName

---------------------------------------------------------------------------
-- * Further constructor and projection info
---------------------------------------------------------------------------

-- | Where does the 'ConP' or 'Con' come from?
data ConOrigin
  = ConOSystem  -- ^ Inserted by system or expanded from an implicit pattern.
  | ConOCon     -- ^ User wrote a constructor (pattern).
  | ConORec     -- ^ User wrote a record (pattern).
  | ConOSplit   -- ^ Generated by interactive case splitting.
  deriving (Data, Show, Eq, Ord, Enum, Bounded)

instance KillRange ConOrigin where
  killRange = id

-- | Prefer user-written over system-inserted.
bestConInfo :: ConOrigin -> ConOrigin -> ConOrigin
bestConInfo ConOSystem o = o
bestConInfo o _ = o

-- | Where does a projection come from?
data ProjOrigin
  = ProjPrefix    -- ^ User wrote a prefix projection.
  | ProjPostfix   -- ^ User wrote a postfix projection.
  | ProjSystem    -- ^ Projection was generated by the system.
  deriving (Data, Show, Eq, Ord, Enum, Bounded)

instance KillRange ProjOrigin where
  killRange = id

data DataOrRecord = IsData | IsRecord
  deriving (Data, Eq, Ord, Show)

---------------------------------------------------------------------------
-- * Infixity, access, abstract, etc.
---------------------------------------------------------------------------

-- | Functions can be defined in both infix and prefix style. See
--   'Agda.Syntax.Concrete.LHS'.
data IsInfix = InfixDef | PrefixDef
    deriving (Data, Show, Eq, Ord)

-- | Access modifier.
data Access
  = PrivateAccess Origin
      -- ^ Store the 'Origin' of the private block that lead to this qualifier.
      --   This is needed for more faithful printing of declarations.
  | PublicAccess
  | OnlyQualified  -- ^ Visible from outside, but not exported when opening the module
                             --   Used for qualified constructors.
    deriving (Data, Show, Eq, Ord)

instance Pretty Access where
  pretty = text . \case
    PrivateAccess _ -> "private"
    PublicAccess    -> "public"
    OnlyQualified   -> "only-qualified"

instance NFData Access where
  rnf _ = ()

instance HasRange Access where
  getRange _ = noRange

instance KillRange Access where
  killRange = id

-- | Abstract or concrete
data IsAbstract = AbstractDef | ConcreteDef
    deriving (Data, Show, Eq, Ord)

instance KillRange IsAbstract where
  killRange = id

-- | Is this definition eligible for instance search?
data IsInstance = InstanceDef | NotInstanceDef
    deriving (Data, Show, Eq, Ord)

instance KillRange IsInstance where
  killRange = id

instance HasRange IsInstance where
  getRange _ = noRange

instance NFData IsInstance where
  rnf InstanceDef    = ()
  rnf NotInstanceDef = ()

-- | Is this a macro definition?
data IsMacro = MacroDef | NotMacroDef
  deriving (Data, Show, Eq, Ord)

instance KillRange IsMacro where killRange = id
instance HasRange  IsMacro where getRange _ = noRange

type Nat    = Int
type Arity  = Nat

---------------------------------------------------------------------------
-- * NameId
---------------------------------------------------------------------------

-- | The unique identifier of a name. Second argument is the top-level module
--   identifier.
data NameId = NameId {-# UNPACK #-} !Word64 {-# UNPACK #-} !Word64
    deriving (Eq, Ord, Data, Generic, Show)

instance KillRange NameId where
  killRange = id

instance Pretty NameId where
  pretty (NameId n m) = text $ show n ++ "@" ++ show m

instance Enum NameId where
  succ (NameId n m)     = NameId (n + 1) m
  pred (NameId n m)     = NameId (n - 1) m
  toEnum n              = __IMPOSSIBLE__  -- should not be used
  fromEnum (NameId n _) = fromIntegral n

instance NFData NameId where
  rnf (NameId _ _) = ()

instance Hashable NameId where
  {-# INLINE hashWithSalt #-}
  hashWithSalt salt (NameId n m) = hashWithSalt salt (n, m)

---------------------------------------------------------------------------
-- * Meta variables
---------------------------------------------------------------------------

-- | A meta variable identifier is just a natural number.
--
newtype MetaId = MetaId { metaId :: Nat }
    deriving (Eq, Ord, Num, Real, Enum, Integral, Data)

instance Pretty MetaId where
  pretty (MetaId n) = text $ "_" ++ show n

-- | Show non-record version of this newtype.
instance Show MetaId where
  showsPrec p (MetaId n) = showParen (p > 0) $
    showString "MetaId " . shows n

instance NFData MetaId where
  rnf (MetaId x) = rnf x

newtype Constr a = Constr a

------------------------------------------------------------------------
-- * Placeholders (used to parse sections)
------------------------------------------------------------------------

-- | The position of a name part or underscore in a name.

data PositionInName
  = Beginning
    -- ^ The following underscore is at the beginning of the name:
    -- @_foo@.
  | Middle
    -- ^ The following underscore is in the middle of the name:
    -- @foo_bar@.
  | End
    -- ^ The following underscore is at the end of the name: @foo_@.
  deriving (Show, Eq, Ord, Data)

-- | Placeholders are used to represent the underscores in a section.

data MaybePlaceholder e
  = Placeholder !PositionInName
  | NoPlaceholder !(Strict.Maybe PositionInName) e
    -- ^ The second argument is used only (but not always) for name
    -- parts other than underscores.
  deriving (Data, Eq, Ord, Functor, Foldable, Traversable, Show)

-- | An abbreviation: @noPlaceholder = 'NoPlaceholder'
-- 'Strict.Nothing'@.

noPlaceholder :: e -> MaybePlaceholder e
noPlaceholder = NoPlaceholder Strict.Nothing

instance HasRange a => HasRange (MaybePlaceholder a) where
  getRange Placeholder{}       = noRange
  getRange (NoPlaceholder _ e) = getRange e

instance KillRange a => KillRange (MaybePlaceholder a) where
  killRange p@Placeholder{}     = p
  killRange (NoPlaceholder p e) = killRange1 (NoPlaceholder p) e

instance NFData a => NFData (MaybePlaceholder a) where
  rnf (Placeholder _)     = ()
  rnf (NoPlaceholder _ a) = rnf a

---------------------------------------------------------------------------
-- * Interaction meta variables
---------------------------------------------------------------------------

newtype InteractionId = InteractionId { interactionId :: Nat }
    deriving ( Eq
             , Ord
             , Show
             , Num
             , Integral
             , Real
             , Enum
             , Data
             )

instance Pretty InteractionId where
    pretty (InteractionId i) = text $ "?" ++ show i

instance KillRange InteractionId where killRange = id

-----------------------------------------------------------------------------
-- * Import directive
-----------------------------------------------------------------------------

-- | The things you are allowed to say when you shuffle names between name
--   spaces (i.e. in @import@, @namespace@, or @open@ declarations).
data ImportDirective' n m = ImportDirective
  { importDirRange :: Range
  , using          :: Using' n m
  , hiding         :: [ImportedName' n m]
  , impRenaming    :: [Renaming' n m]
  , publicOpen     :: Bool -- ^ Only for @open@. Exports the opened names from the current module.
  }
  deriving (Data, Eq)

data Using' n m = UseEverything | Using [ImportedName' n m]
  deriving (Data, Eq)

instance Semigroup (Using' n m) where
  UseEverything <> u             = u
  u             <> UseEverything = u
  Using xs      <> Using ys      = Using (xs ++ ys)

instance Monoid (Using' n m) where
  mempty  = UseEverything
  mappend = (<>)

-- | Default is directive is @private@ (use everything, but do not export).
defaultImportDir :: ImportDirective' n m
defaultImportDir = ImportDirective noRange UseEverything [] [] False

isDefaultImportDir :: ImportDirective' n m -> Bool
isDefaultImportDir (ImportDirective _ UseEverything [] [] False) = True
isDefaultImportDir _                                             = False

-- | An imported name can be a module or a defined name.
data ImportedName' n m
  = ImportedModule  m  -- ^ Imported module name of type @m@.
  | ImportedName    n  -- ^ Imported name of type @n@.
  deriving (Data, Eq, Ord, Show)

setImportedName :: ImportedName' a a -> a -> ImportedName' a a
setImportedName (ImportedName   x) y = ImportedName   y
setImportedName (ImportedModule x) y = ImportedModule y

-- -- Defined in Concrete.Pretty
-- instance (Pretty n, Pretty m) => Pretty (ImportedName' n m) where
--   pretty (ImportedModule x) = "module" <+> pretty x
--   pretty (ImportedName   x) = pretty x

-- instance (Show n, Show m) => Show (ImportedName' n m) where
--   show (ImportedModule x) = "module " ++ show x
--   show (ImportedName   x) = show x

data Renaming' n m = Renaming
  { renFrom    :: ImportedName' n m
    -- ^ Rename from this name.
  , renTo      :: ImportedName' n m
    -- ^ To this one.  Must be same kind as 'renFrom'.
  , renToRange :: Range
    -- ^ The range of the \"to\" keyword.  Retained for highlighting purposes.
  }
  deriving (Data, Eq)

-- ** HasRange instances

instance (HasRange a, HasRange b) => HasRange (ImportDirective' a b) where
  getRange = importDirRange

instance (HasRange a, HasRange b) => HasRange (Using' a b) where
  getRange (Using  xs) = getRange xs
  getRange UseEverything = noRange

instance (HasRange a, HasRange b) => HasRange (Renaming' a b) where
  getRange r = getRange (renFrom r, renTo r)

instance (HasRange a, HasRange b) => HasRange (ImportedName' a b) where
  getRange (ImportedName   x) = getRange x
  getRange (ImportedModule x) = getRange x

-- ** KillRange instances

instance (KillRange a, KillRange b) => KillRange (ImportDirective' a b) where
  killRange (ImportDirective _ u h r p) =
    killRange3 (\u h r -> ImportDirective noRange u h r p) u h r

instance (KillRange a, KillRange b) => KillRange (Using' a b) where
  killRange (Using  i) = killRange1 Using  i
  killRange UseEverything = UseEverything

instance (KillRange a, KillRange b) => KillRange (Renaming' a b) where
  killRange (Renaming i n _) = killRange2 (\i n -> Renaming i n noRange) i n

instance (KillRange a, KillRange b) => KillRange (ImportedName' a b) where
  killRange (ImportedModule n) = killRange1 ImportedModule n
  killRange (ImportedName   n) = killRange1 ImportedName   n

-- ** NFData instances

-- | Ranges are not forced.

instance (NFData a, NFData b) => NFData (ImportDirective' a b) where
  rnf (ImportDirective _ a b c _) = rnf a `seq` rnf b `seq` rnf c

instance (NFData a, NFData b) => NFData (Using' a b) where
  rnf UseEverything = ()
  rnf (Using a)     = rnf a

-- | Ranges are not forced.

instance (NFData a, NFData b) => NFData (Renaming' a b) where
  rnf (Renaming a b _) = rnf a `seq` rnf b

instance (NFData a, NFData b) => NFData (ImportedName' a b) where
  rnf (ImportedModule a) = rnf a
  rnf (ImportedName a)   = rnf a

-----------------------------------------------------------------------------
-- * Termination
-----------------------------------------------------------------------------

-- | Termination check? (Default = TerminationCheck).
data TerminationCheck m
  = TerminationCheck
    -- ^ Run the termination checker.
  | NoTerminationCheck
    -- ^ Skip termination checking (unsafe).
  | NonTerminating
    -- ^ Treat as non-terminating.
  | Terminating
    -- ^ Treat as terminating (unsafe).  Same effect as 'NoTerminationCheck'.
  | TerminationMeasure Range m
    -- ^ Skip termination checking but use measure instead.
    deriving (Data, Show, Eq, Functor)

instance KillRange m => KillRange (TerminationCheck m) where
  killRange (TerminationMeasure _ m) = TerminationMeasure noRange (killRange m)
  killRange t                        = t

instance NFData a => NFData (TerminationCheck a) where
  rnf TerminationCheck         = ()
  rnf NoTerminationCheck       = ()
  rnf NonTerminating           = ()
  rnf Terminating              = ()
  rnf (TerminationMeasure _ a) = rnf a

-----------------------------------------------------------------------------
-- * Positivity
-----------------------------------------------------------------------------

-- | Positivity check? (Default = True).
type PositivityCheck = Bool

-----------------------------------------------------------------------------
-- * Universe checking
-----------------------------------------------------------------------------

-- | Universe check? (Default is yes).
data UniverseCheck = YesUniverseCheck | NoUniverseCheck
  deriving (Eq, Ord, Show, Bounded, Enum, Data)

instance KillRange UniverseCheck where
  killRange = id