{-# LANGUAGE DeriveAnyClass             #-}
{-# LANGUAGE DeriveDataTypeable         #-}
{-# LANGUAGE DeriveFoldable             #-}
{-# LANGUAGE DeriveFunctor              #-}
{-# LANGUAGE DeriveGeneric              #-}
{-# LANGUAGE DeriveTraversable          #-}
{-# LANGUAGE DerivingStrategies         #-}
{-# LANGUAGE GeneralizedNewtypeDeriving #-}
{-# LANGUAGE LambdaCase                 #-}
{-# LANGUAGE PatternSynonyms            #-}
{-# LANGUAGE TemplateHaskell            #-}
{-# LANGUAGE TypeFamilies               #-}

-- | This is a module containing types to model the ATS syntax tree. As it is
-- collapsed by the pretty printer, you may see that in some places it is
-- focused on the lexical side of things.
module Language.ATS.Types
    ( ATS (..)
    , Declaration (..)
    , Type (..)
    , Name (..)
    , Pattern (..)
    , PatternF (..)
    , Arg (..)
    , Universal (..)
    , Function (..)
    , Expression (..)
    , ExpressionF (..)
    , Implementation (..)
    , BinOp (..)
    , UnOp (..)
    , TypeF (..)
    , Existential (..)
    , LambdaType (..)
    , Addendum (..)
    , DataPropLeaf (..)
    , PreFunction (..)
    , Paired (..)
    , Leaf (..)
    , StaticExpression (..)
    , StaticExpressionF (..)
    , Fixity (..)
    , StackFunction (..)
    , Sort (..)
    , SortArg (..)
    , SortArgs
    , rewriteATS
    , rewriteDecl
    -- * Lenses
    , leaves
    , constructorUniversals
    , typeCall
    , typeCallArgs
    ) where

import           Control.DeepSeq          (NFData)
import           Control.Lens
import           Data.Functor.Foldable    (ListF (Cons), ana, cata, embed, project)
import           Data.Functor.Foldable.TH (makeBaseFunctor)
import           Data.Maybe               (isJust)
import           Data.Semigroup           (Semigroup)
import           GHC.Generics             (Generic)
import           Language.ATS.Lexer       (Addendum (..), AlexPosn)

data Fixity = RightFix AlexPosn
            | LeftFix AlexPosn
            | Pre AlexPosn
            | Post AlexPosn
            deriving (Show, Eq, Generic, NFData)

-- | Newtype wrapper containing a list of declarations
newtype ATS = ATS { unATS :: [Declaration] }
    deriving (Show, Eq, Generic)
    deriving newtype (NFData, Semigroup, Monoid)

data Leaf = Leaf { _constructorUniversals :: [Universal], name :: String, constructorArgs :: [String], maybeType :: Maybe Type }
    deriving (Show, Eq, Generic, NFData)

type SortArgs = Maybe [SortArg]

-- | Declare something in a scope (a function, value, action, etc.)
data Declaration = Func AlexPosn Function
                 | Impl [Arg] Implementation -- TODO do something better for implicit universals
                 | ProofImpl [Arg] Implementation
                 | Val Addendum (Maybe Type) Pattern Expression
                 | StaVal [Universal] String Type
                 | PrVal Pattern Expression
                 | Var (Maybe Type) Pattern (Maybe Expression) (Maybe Expression) -- TODO AlexPosn
                 | AndDecl (Maybe Type) Pattern Expression
                 | Include String
                 | Staload Bool (Maybe String) String
                 | Stadef String Name [Type]
                 | CBlock String
                 | TypeDef AlexPosn String SortArgs Type
                 | ViewTypeDef AlexPosn String SortArgs Type
                 | SumType { typeName :: String, typeArgs :: SortArgs, _leaves :: [Leaf] }
                 | SumViewType { typeName :: String, typeArgs :: SortArgs, _leaves :: [Leaf] }
                 | AbsType AlexPosn String SortArgs (Maybe Type)
                 | AbsViewType AlexPosn String SortArgs (Maybe Type)
                 | AbsView AlexPosn String [Arg] (Maybe Type)
                 | AbsVT0p AlexPosn String SortArgs (Maybe Type)
                 | AbsT0p AlexPosn String Type
                 | ViewDef AlexPosn String [Arg] Type
                 | OverloadOp AlexPosn BinOp Name
                 | OverloadIdent AlexPosn String Name (Maybe Int)
                 | Comment String
                 | DataProp AlexPosn String SortArgs [DataPropLeaf]
                 | Extern AlexPosn Declaration
                 | Define String
                 | SortDef AlexPosn String Sort
                 | AndD Declaration Declaration
                 | Local AlexPosn ATS ATS
                 | AbsProp AlexPosn String [Arg]
                 | Assume Name [Arg] Type
                 | TKind AlexPosn Name String
                 | SymIntr AlexPosn Name
                 | Stacst AlexPosn Name Type (Maybe Expression)
                 | PropDef AlexPosn String [Arg] Type
                 -- uses an 'Int' because you fully deserve what you get if your
                 -- fixity declarations overflow.
                 | FixityDecl Fixity (Either String Int) [String]
                 deriving (Show, Eq, Generic, NFData)

data DataPropLeaf = DataPropLeaf [Universal] Expression (Maybe Expression)
                  deriving (Show, Eq, Generic, NFData)

-- | A type for parsed ATS types
data Type = Tuple AlexPosn [Type]
          | Named Name
          | Ex Existential Type
          | ForA Universal Type
          | Dependent { _typeCall :: Name, _typeCallArgs :: [Type] }
          | Unconsumed Type -- !a
          | AsProof Type (Maybe Type) -- a >> b
          | FromVT Type -- For a viewtype VT, we can prove there exist a view V and type T such that `VT` is equivalent to `(V | T)` - that T is `VT?!`
          | MaybeVal Type -- This is just `a?` or the like
          | At AlexPosn (Maybe Type) Type
          | ProofType AlexPosn [Type] Type -- Aka (prf | val)
          | ConcreteType StaticExpression
          | RefType Type
          | ViewType AlexPosn Type
          | FunctionType String Type Type
          | NoneType AlexPosn
          | ImplicitType AlexPosn
          | ViewLiteral Addendum
          | AnonymousRecord AlexPosn [(String, Type)]
          | ParenType AlexPosn Type
          deriving (Show, Eq, Generic, NFData)

-- | A type for the various lambda arrows (@=>@, @=\<cloref1>@, etc.)
data LambdaType = Plain AlexPosn
                | Full AlexPosn String
                | Spear AlexPosn
                deriving (Show, Eq, Generic, NFData)

-- | A name can be qualified (@$UN.unsafefn@) or not
data Name = Unqualified String
          | Qualified AlexPosn String String -- TODO String Name
          | SpecialName AlexPosn String
          | Functorial String String
          | Unnamed AlexPosn
          | FieldName AlexPosn String String
          deriving (Show, Eq, Generic, NFData)

-- | A data type for patterns.
data Pattern = Wildcard AlexPosn
             | PName Name [Pattern]
             | PSum String Pattern
             | PLiteral Expression
             | Guarded AlexPosn Expression Pattern
             | Free Pattern
             | Proof AlexPosn [Pattern] [Pattern]
             | TuplePattern [Pattern]
             | AtPattern AlexPosn Pattern
             | UniversalPattern AlexPosn String [Universal] Pattern
             | ExistentialPattern Existential Pattern
             deriving (Show, Eq, Generic, NFData)

data Paired a b = Both a b
                | First a
                | Second b
                deriving (Show, Eq, Generic, NFData)

data SortArg = SortArg String Sort
             | Anonymous Sort
    deriving (Show, Eq, Generic, NFData)

-- | An argument to a function.
data Arg = Arg (Paired String Type)
         | PrfArg Arg Arg
         | NoArgs
    deriving (Show, Eq, Generic, NFData)

-- | A datatype for sorts.
data Sort = NamedSort String
          | T0p Addendum -- ^ t@ype
          | Vt0p Addendum -- ^ vt@ype
          | Addr
          | View AlexPosn Addendum -- ^ view
          deriving (Show, Eq, Generic, NFData)

-- FIXME a type for sorts?
-- | Wrapper for universal quantifiers (refinement types)
data Universal = Universal { bound :: [String], typeU :: Maybe Sort, prop :: Maybe StaticExpression } -- TODO NonEmpty type?
    deriving (Show, Eq, Generic, NFData)

-- | Wrapper for existential quantifiers/types
data Existential = Existential { boundE :: [String], isOpen :: Bool, typeE :: Maybe Sort, propE :: Maybe StaticExpression }
    deriving (Show, Eq, Generic, NFData)

-- | @~@ is used to negate numbers in ATS
data UnOp = Negate
    deriving (Show, Eq, Generic, NFData)

-- | Binary operators on expressions
data BinOp = Add
           | Mult
           | Div
           | Sub
           | GreaterThan
           | GreaterThanEq
           | LessThan
           | LessThanEq
           | Equal
           | NotEqual
           | LogicalAnd
           | LogicalOr
           | StaticEq
           | Mod
           | NotEq
           deriving (Show, Eq, Generic, NFData)

-- FIXME add position information?
data StaticExpression = StaticVal Name
                      | StaticBinary BinOp StaticExpression StaticExpression
                      | StaticInt Int
                      | SPrecede StaticExpression StaticExpression
                      | StaticBool Bool
                      | StaticVoid AlexPosn
                      | Sif { scond :: StaticExpression, wwhenTrue :: StaticExpression, selseExpr :: StaticExpression } -- Static if (for proofs)
                      | SCall Name [StaticExpression]
                      | SUnary UnOp StaticExpression
                      | SLet AlexPosn [Declaration] (Maybe StaticExpression)
                      deriving (Show, Eq, Generic, NFData)

-- | A (possibly effectful) expression.
data Expression = Let AlexPosn ATS (Maybe Expression)
                | VoidLiteral -- The '()' literal representing inaction.
                    AlexPosn
                -- function call: <a>, then {n}
                | Call Name [[Type]] [Type] (Maybe [Expression]) [Expression]
                | NamedVal Name
                | ListLiteral AlexPosn String Type [Expression]
                | If { cond     :: Expression -- ^ Expression evaluating to a boolean value
                     , whenTrue :: Expression -- ^ Expression to be returned when true
                     , elseExpr :: Maybe Expression -- ^ Expression to be returned when false
                     }
                | BoolLit Bool
                | TimeLit String
                | FloatLit Float
                | IntLit Int
                | UnderscoreLit AlexPosn
                | Lambda AlexPosn LambdaType Pattern Expression
                | LinearLambda AlexPosn LambdaType Pattern Expression
                | Index AlexPosn Name Expression
                | Access AlexPosn Expression Name
                | StringLit String
                | CharLit Char
                | AtExpr Expression Expression
                | AddrAt AlexPosn Expression
                | ViewAt AlexPosn Expression
                | Binary BinOp Expression Expression
                | Unary UnOp Expression
                | IfCase { posE   :: AlexPosn
                         , ifArms :: [(Expression, LambdaType, Expression)]
                         }
                | Case { posE :: AlexPosn
                       , kind :: Addendum
                       , val  :: Expression
                       , arms :: [(Pattern, LambdaType, Expression)] -- ^ Each @(Pattern, Expression)@ pair corresponds to a branch of the 'case' statement
                       }
                | RecordValue AlexPosn [(String, Expression)] (Maybe Type)
                | Precede Expression Expression
                | PlainMutate { old :: Expression
                              , new :: Expression
                              }
                | FieldMutate { posE  :: AlexPosn
                              , old   :: Expression -- ^ Record to modify
                              , field :: String -- ^ Field being modified
                              , new   :: Expression -- ^ New value of the field
                              }
                | Mutate Expression Expression
                | Deref AlexPosn Expression
                | ProofExpr AlexPosn Expression Expression
                | TypeSignature Expression Type
                | WhereExp Expression [Declaration]
                | TupleEx AlexPosn [Expression] -- TODO support boxed tuples
                | While AlexPosn Expression Expression
                | Actions ATS
                | Begin AlexPosn Expression
                | BinList { _op :: BinOp, _exprs :: [Expression] }
                | PrecedeList { _exprs :: [Expression] }
                | FixAt String StackFunction
                | LambdaAt StackFunction
                | ParenExpr AlexPosn Expression
                | CommentExpr String Expression
                deriving (Show, Eq, Generic, NFData)

-- | An 'implement' declaration
data Implementation = Implement { pos            :: AlexPosn
                                , preUniversalsI :: [Universal]
                                , implicits      :: [[Type]] -- ^ Implicit arguments
                                , universalsI    :: [Universal] -- ^ Universal quantifiers
                                , nameI          :: Name -- ^ Name of the template being implemented
                                , iArgs          :: [Arg] -- ^ Arguments
                                , iExpression    :: Either StaticExpression Expression -- ^ Expression (or static expression) holding the function body.
                                }
    deriving (Show, Eq, Generic, NFData)

-- | A function declaration accounting for all keywords ATS uses to
-- define them.
data Function = Fun PreFunction
              | Fn PreFunction
              | Fnx PreFunction
              | And PreFunction
              | PrFun PreFunction
              | PrFn PreFunction
              | Praxi PreFunction
              | CastFn PreFunction
              deriving (Show, Eq, Generic, NFData)

data StackFunction = StackF { stSig        :: String
                            , stArgs       :: [Arg]
                            , stReturnType :: Type
                            , stExpression :: Expression
                            }
                            deriving (Show, Eq, Generic, NFData)

data PreFunction = PreF { fname         :: Name -- ^ Function name
                        , sig           :: String -- ^ e.g. <> or \<!wrt>
                        , preUniversals :: [Universal] -- ^ Universal quantifiers making a function generic
                        , universals    :: [Universal] -- ^ Universal quantifiers/refinement type
                        , args          :: [Arg] -- ^ Actual function arguments
                        , returnType    :: Maybe Type -- ^ Return type
                        , termetric     :: Maybe StaticExpression -- ^ Optional termination metric
                        , expression    :: Maybe Expression -- ^ Expression holding the actual function body (not present in static templates)
                        }
                        deriving (Show, Eq, Generic, NFData)

makeBaseFunctor ''Pattern
makeBaseFunctor ''Expression
makeBaseFunctor ''StaticExpression
makeBaseFunctor ''Type
makeLenses ''Leaf
makeLenses ''Declaration
makeLenses ''Type

rewriteDecl :: Declaration -> Declaration
rewriteDecl x@SumViewType{} = g x
    where g = over (leaves.mapped.constructorUniversals) h
          h :: [Universal] -> [Universal]
          h = ana c where
            c (y:y':ys)
                | typeU y == typeU y' && isJust (typeU y) =
                    Cons (Universal (bound y ++ bound y') (typeU y) (StaticBinary LogicalAnd <$> prop y <*> prop y')) ys
            c y = project y
rewriteDecl x = x

-- precedence: rewrite n + 2 * x to n + (2 * x)
-- TODO: rewrite multiple universals when it's the right context?
rewriteATS :: Expression -> Expression
rewriteATS = cata a where
    a (CallF n ts ts' me [ParenExpr _ e@NamedVal{}]) = Call n ts ts' me [e]
    a (CallF n ts ts' me [ParenExpr _ e@Call{}])     = Call n ts ts' me [e]
    a (PrecedeF e e'@PrecedeList{})                  = PrecedeList (e : _exprs e')
    a (PrecedeF e e')                                = PrecedeList [e, e']
    a (BinaryF Mult (Binary Add e e') e'')           = Binary Add e (Binary Mult e' e'')
    a (BinaryF Add e (BinList Add es))               = BinList Add (e : es)
    a (BinaryF Add e e')                             = BinList Add [e, e']
    a (ParenExprF _ e@Precede{})                     = e
    a (ParenExprF _ e@PrecedeList{})                 = e
    a x                                              = embed x