module Quox.Parser.Parser

import public Quox.Parser.Lexer
import public Quox.Parser.Syntax

import Data.Fin
import Data.Vect
import public Text.Parser

%default total


public export
0 Grammar : Bool -> Type -> Type
Grammar = Core.Grammar () Token
%hide Core.Grammar


export
res : (str : String) -> (0 _ : IsReserved str) => Grammar True ()
res str = terminal "expecting \"\{str}\"" $ guard . (== Reserved str)

export
resC : (str : String) -> (0 _ : IsReserved str) => Grammar True ()
resC str = do res str; commit


parameters {default True commit : Bool}
  private
  maybeCommit : Grammar False ()
  maybeCommit = when commit Core.commit

  export
  betweenR : {c : Bool} -> (op, cl : String) ->
             (0 _ : IsReserved op) => (0 _ : IsReserved cl) =>
             Grammar c a -> Grammar True a
  betweenR o c p = res o *> maybeCommit *> p <* res c <* maybeCommit

  export
  parens, bracks, braces : {c : Bool} -> Grammar c a -> Grammar True a
  parens = betweenR "(" ")"
  bracks = betweenR "[" "]"
  braces = betweenR "{" "}"


export
commaSep : {c : Bool} -> Grammar c a -> Grammar False (List a)
commaSep = sepEndBy (res ",")
  -- don't commit because of the possible terminating ","

export
semiSep : {c : Bool} -> Grammar c a -> Grammar False (List a)
semiSep = sepEndBy (res ";")

export
commaSep1 : {c : Bool} -> Grammar c a -> Grammar c (List1 a)
commaSep1 = sepEndBy1 (res ",")

export
darr : Grammar True ()
darr = resC "⇒"


export
name : Grammar True PName
name = terminal "expecting name" $
  \case Name i => Just i; _ => Nothing

export
mods : Grammar True Mods
mods = name <&> \n => n.mods :< n.base

export
baseName : Grammar True String
baseName = terminal "expecting unqualified name" $
  \case Name i => guard (null i.mods) $> i.base
        _      => Nothing

export
nat : Grammar True Nat
nat = terminal "expecting natural number" $
  \case Nat n => pure n; _ => Nothing

export
string : Grammar True String
string = terminal "expecting string literal" $
  \case Str s => pure s; _ => Nothing

export
tag : Grammar True String
tag = terminal "expecting tag constructor" $
  \case Tag t => pure t; _ => Nothing

export
bareTag : Grammar True String
bareTag = string <|> [|toDotsP name|]

export
universe : Grammar True PUniverse
universe = terminal "expecting type universe" $
  \case TYPE u => Just u; _ => Nothing

export
bname : Grammar True BName
bname = Nothing <$ res "_"
    <|> [|Just baseName|]

export
dimConst : Grammar True DimConst
dimConst = terminal "expecting 0 or 1" $
  \case Nat 0 => Just Zero; Nat 1 => Just One; _ => Nothing

export
qty : Grammar True PQty
qty = terminal "expecting quantity" $
  \case Nat 0 => Just Zero; Nat 1 => Just One; Reserved "ω" => Just Any
        _ => Nothing


public export
AllReserved : List (a, String) -> Type
AllReserved = foldr (\x, ps => (IsReserved $ snd x, ps)) ()

export
symbols : (lst : List (a, String)) -> (0 _ : AllReserved lst) =>
          Grammar True a
symbols []                 = fail "no symbols found"
symbols ((x, str) :: rest) = x <$ res str <|> symbols rest

export
symbolsC : (lst : List (a, String)) -> (0 _ : AllReserved lst) =>
           Grammar True a
symbolsC lst = symbols lst <* commit


private covering
qtys : Grammar False (List PQty)
qtys = option [] [|toList $ some qty <* res "."|]


export
dim : Grammar True PDim
dim = [|V baseName|] <|> [|K dimConst|]

private
0 PBinderHead : Nat -> Type
PBinderHead n = (Vect n PQty, BName, PTerm)

private
toVect : List a -> (n ** Vect n a)
toVect []        = (_ ** [])
toVect (x :: xs) = (_ ** x :: snd (toVect xs))

private
0 MakeBinder : Nat -> Type
MakeBinder n = (String, PBinderHead n -> PTerm -> PTerm)

private
makePi : MakeBinder 1
makePi = ("→", \([pi], x, s) => Pi pi x s)

private
makeSig : MakeBinder 0
makeSig = ("×", \([], x, s) => Sig x s)

private
makeBinder : (m ** PBinderHead m) -> (n ** MakeBinder n) -> PTerm ->
             Grammar False PTerm
makeBinder (m ** h) (n ** (str, f)) t =
  case decEq m n of
    Yes Refl => pure $ f h t
    No  _    =>
      let q = if m == 1 then "quantity" else "quantities" in
      fatalError "'\{str}' expects \{show m} \{q}, got \{show n}"

private
binderInfix : Grammar True (n ** MakeBinder n)
binderInfix = symbols [((1 ** makePi), "→"), ((0 ** makeSig), "×")]

private
lamIntro : Grammar True (BName -> PTerm -> PTerm)
lamIntro = symbolsC [(Lam, "λ"), (DLam, "δ")]

private covering
caseIntro : Grammar True PQty
caseIntro = symbols [(One, "case1"), (Any, "caseω")]
        <|> resC "case" *> qty <* resC "."

private
optNameBinder : Grammar False BName
optNameBinder = [|join $ optional $ bname <* darr|]

mutual
  export covering
  term : Grammar True PTerm
  term = lamTerm <|> caseTerm <|> bindTerm <|> annTerm

  private covering
  lamTerm : Grammar True PTerm
  lamTerm = flip . foldr <$> lamIntro <*> some bname <* darr <*> term

  private covering
  caseTerm : Grammar True PTerm
  caseTerm =
    [|Case caseIntro term
           (resC "return" *> optBinderTerm)
           (resC "of"     *> caseBody)|]

  private covering
  caseBody : Grammar True PCaseBody
  caseBody = braces $
        [|CasePair (pairPat <* darr) (term <* optSemi)|]
    <|> [|CaseEnum $ semiSep [|MkPair tag (darr *> term)|]|]
  where
    optSemi = optional $ res ";"
    pairPat = parens [|MkPair bname (resC "," *> bname)|]

  private covering
  bindTerm : Grammar True PTerm
  bindTerm = join [|makeBinder binderHead binderInfix term|]

  private covering
  annTerm : Grammar True PTerm
  annTerm = [|annotate infixEqTerm (optional $ resC "∷" *> term)|]
  where annotate s a = maybe s (s :#) a

  private covering
  infixEqTerm : Grammar True PTerm
  infixEqTerm = do
    l <- infixTimesTerm
    rty <- optional [|MkPair (resC "≡" *> term) (resC ":" *> infixTimesTerm)|]
    pure $ maybe l (\rty => Eq (Nothing, snd rty) l (fst rty)) rty

  private covering
  infixTimesTerm : Grammar True PTerm
  infixTimesTerm = foldr1 (Sig Nothing) <$> sepBy1 (resC "×") appTerm

  private covering
  appTerm : Grammar True PTerm
  appTerm = resC "★"  *> [|TYPE nat|]
        <|> resC "Eq" *> [|Eq (bracks optBinderTerm) aTerm aTerm|]
        <|> [|apply aTerm (many appArg)|]
  where
    data PArg = TermArg PTerm | DimArg PDim

    appArg : Grammar True PArg
    appArg = [|DimArg $ resC "@" *> dim|] <|> [|TermArg aTerm|]

    apply : PTerm -> List PArg -> PTerm
    apply = foldl apply1 where
      apply1 : PTerm -> PArg -> PTerm
      apply1 f (TermArg x) = f :@ x
      apply1 f (DimArg  p) = f :% p

  private covering
  aTerm : Grammar True PTerm
  aTerm = [|Enum $ braces $ commaSep bareTag|]
      <|> [|TYPE universe|]
      <|> [|V name|]
      <|> [|Tag tag|]
      <|> foldr1 Pair <$> parens (commaSep1 term)

  private covering
  binderHead : Grammar True (n ** PBinderHead n)
  binderHead = parens {commit = False} $ do
    qs   <- [|toVect qtys|]
    name <- bname
    ty   <- resC ":" *> term
    pure (qs.fst ** (qs.snd, name, ty))

  private covering
  optBinderTerm : Grammar True (BName, PTerm)
  optBinderTerm = [|MkPair optNameBinder term|]


export covering
defIntro : Grammar True PQty
defIntro = symbols [(Zero, "def0"), (Any, "defω")]
       <|> resC "def" *> option Any (qty <* resC ".")

export covering
definition : Grammar True PDefinition
definition =
  [|MkPDef defIntro name (optional (resC ":" *> term)) (resC "=" *> term)|]

export
load : Grammar True String
load = resC "load" *> string

mutual
  export covering
  namespace_ : Grammar True PNamespace
  namespace_ =
    [|MkPNamespace (resC "namespace" *> mods) (braces $ many decl)|]

  export covering
  decl : Grammar True PDecl
  decl = [|PDef definition|]
     <|> [|PNs  namespace_|]

export covering
topLevel : Grammar True PTopLevel
topLevel = [|PLoad load|]
       <|> [|PD    decl|]

export covering
input : Grammar False (List PTopLevel)
input = skipSemis *> many (topLevel <* skipSemis)
  where skipSemis = ignore $ many $ resC ";"


public export
data Error =
    LexError   Lexer.Error
  | ParseError (List1 (ParsingError Token))
%hide Lexer.Error

export
lexParseWith : {c : Bool} -> Grammar c a -> String -> Either Error a
lexParseWith grm input = do
  toks <- mapFst LexError $ lex input
  bimap ParseError fst $ parse (grm <* eof) toks

export covering %inline
lexParseInput : String -> Either Error (List PTopLevel)
lexParseInput = lexParseWith input

export covering %inline
lexParseTerm : String -> Either Error PTerm
lexParseTerm = lexParseWith term