Parser.idr

module Text.Parser

%default total

-- TODO: Add some primitives for helping with error messages.
-- e.g. perhaps set a string to state what we're currently trying to 
-- parse, or to say what the next expected token is in words

||| Description of a language's grammar. The `tok` parameter is the type
||| of tokens, and the `consumes` flag is True if the language is guaranteed
||| to be non-empty - that is, successfully parsing the language is guaranteed
||| to consume some input.
export
data Grammar : (tok : Type) -> (consumes : Bool) -> Type -> Type where
     Empty : (val : ty) -> Grammar tok False ty
     Terminal : (tok -> Maybe a) -> Grammar tok True a
     NextIs : (tok -> Bool) -> Grammar tok False tok
     EOF : Grammar tok False ()

     Fail : String -> Grammar tok c ty
     Commit : Grammar tok False ()

     SeqEat : Grammar tok True a -> Inf (a -> Grammar tok c2 b) ->
              Grammar tok True b
     SeqEmpty : {c1, c2 : Bool} ->
                Grammar tok c1 a -> (a -> Grammar tok c2 b) ->
                Grammar tok (c1 || c2) b
     Alt : {c1, c2 : Bool} ->
           Grammar tok c1 ty -> Grammar tok c2 ty -> 
           Grammar tok (c1 && c2) ty

public export
inf : Bool -> Type -> Type
inf True t = Inf t
inf False t = t
  
||| Sequence two grammars. If either consumes some input, the sequence is
||| guaranteed to consume some input. If the first one consumes input, the
||| second is allowed to be recursive (because it means some input has been
||| consumed and therefore the input is smaller)
export %inline
(>>=) : {c1 : Bool} ->
        Grammar tok c1 a -> inf c1 (a -> Grammar tok c2 b) ->
        Grammar tok (c1 || c2) b
(>>=) {c1 = False} = SeqEmpty
(>>=) {c1 = True} = SeqEat
    
||| Give two alternative grammars. If both consume, the combination is
||| guaranteed to consume.
export
(<|>) : Grammar tok c1 ty -> Grammar tok c2 ty -> 
        Grammar tok (c1 && c2) ty
(<|>) = Alt

export
pure : (val : ty) -> Grammar tok False ty
pure = Empty

||| Check whether the next token satisfies a predicate
export
nextIs : (tok -> Bool) -> Grammar tok False tok
nextIs = NextIs

||| Look at the next token in the input
export
peek : Grammar tok False tok
peek = nextIs (const True)

||| Succeeds if running the predicate on the next token returns Just x,
||| returning x. Otherwise fails.
export
terminal : (tok -> Maybe a) -> Grammar tok True a
terminal = Terminal

||| Always fail with a message
export
fail : String -> Grammar tok c ty
fail = Fail

||| Succeed if the input is empty
export
eof : Grammar tok False ()
eof = EOF

||| Commit to an alternative; if the current branch of an alternative 
||| fails to parse, no more branches will be tried
export
commit : Grammar tok False ()
commit = Commit

data ParseResult : List tok -> (consumes : Bool) -> Type -> Type where
     Failure : {xs : List tok} -> 
               (committed : Bool) ->
               (err : String) -> (rest : List tok) -> ParseResult xs c ty
     EmptyRes : (committed : Bool) ->
                (val : ty) -> (more : List tok) -> ParseResult more False ty
     NonEmptyRes : (committed : Bool) ->
                   (val : ty) -> (more : List tok) ->
                   ParseResult (x :: xs ++ more) c ty 

weakenRes : {whatever, c : Bool} -> {xs : List tok} ->
            ParseResult xs c ty -> ParseResult xs (whatever && c) ty
weakenRes (Failure com msg ts) = Failure com msg ts
weakenRes {whatever=True} (EmptyRes com val xs) = EmptyRes com val xs
weakenRes {whatever=False} (EmptyRes com val xs) = EmptyRes com val xs
weakenRes (NonEmptyRes com val more) = NonEmptyRes com val more

shorter : (more : List tok) -> .(ys : List tok) -> 
          LTE (S (length more)) (S (length (ys ++ more)))
shorter more [] = lteRefl
shorter more (x :: xs) = LTESucc (lteSuccLeft (shorter more xs))

doParse : {c : Bool} ->
          (commit : Bool) -> (xs : List tok) -> (act : Grammar tok c ty) -> 
          ParseResult xs c ty
doParse com xs act with (sizeAccessible xs)
  doParse com xs (Empty val) | sml = EmptyRes com val xs
  doParse com [] (Fail str) | sml = Failure com str []
  doParse com (x :: xs) (Fail str) | sml = Failure com str (x :: xs)
  doParse com xs Commit | sml = EmptyRes True () xs

  doParse com [] (Terminal f) | sml = Failure com "End of input" []
  doParse com (x :: xs) (Terminal f) | sml 
        = maybe
             (Failure com "Unrecognised token" (x :: xs))
             (\a => NonEmptyRes com {xs=[]} a xs)
             (f x)
  doParse com [] EOF | sml = EmptyRes com () []
  doParse com (x :: xs) EOF | sml 
        = Failure com "Expected end of input" (x :: xs)
  doParse com [] (NextIs f) | sml = Failure com "End of input" []
  doParse com (x :: xs) (NextIs f) | sml 
        = if f x 
             then EmptyRes com x (x :: xs)
             else Failure com "Unrecognised token" (x :: xs)
  doParse com xs (Alt x y) | sml with (doParse False xs x | sml)
    doParse com xs (Alt x y) | sml | Failure com' msg ts
          = if com' -- If the alternative had committed, don't try the
                    -- other branch (and reset commit flag)
               then Failure com msg ts
               else weakenRes (doParse False xs y | sml)
    -- Successfully parsed the first option, so use the outer commit flag
    doParse com xs (Alt x y) | sml | (EmptyRes _ val xs) 
          = EmptyRes com val xs
    doParse com (z :: (ys ++ more)) (Alt x y) | sml | (NonEmptyRes _ val more) 
          = NonEmptyRes com val more
  doParse com xs (SeqEmpty act next) | (Access morerec)
          = case doParse com xs act | Access morerec of
                 Failure com msg ts => Failure com msg ts
                 EmptyRes com val xs => 
                       case doParse com xs (next val) | (Access morerec) of
                            Failure com' msg ts => Failure com' msg ts
                            EmptyRes com' val xs => EmptyRes com' val xs
                            NonEmptyRes com' val more => NonEmptyRes com' val more
                 NonEmptyRes {x} {xs=ys} com val more => 
                       case (doParse com more (next val) | morerec _ (shorter more ys)) of
                            Failure com' msg ts => Failure com' msg ts
                            EmptyRes com' val _ => NonEmptyRes com' val more
                            NonEmptyRes {x=x1} {xs=xs1} com' val more' =>
                                 rewrite appendAssociative (x :: ys) (x1 :: xs1) more' in
                                         NonEmptyRes com' val more'
  doParse com xs (SeqEat act next) | sml with (doParse com xs act | sml)
    doParse com xs (SeqEat act next) | sml | Failure com' msg ts 
         = Failure com' msg ts
    doParse com (x :: (ys ++ more)) (SeqEat act next) | (Access morerec) | (NonEmptyRes com' val more) 
         = case doParse com' more (next val) | morerec _ (shorter more ys) of
                Failure com' msg ts => Failure com' msg ts
                EmptyRes com' val _ => NonEmptyRes com' val more
                NonEmptyRes {x=x1} {xs=xs1} com' val more' => 
                     rewrite appendAssociative (x :: ys) (x1 :: xs1) more' in
                             NonEmptyRes com' val more'
  -- This next line is not strictly necessary, but it stops the coverage
  -- checker taking a really long time and eating lots of memory...
  doParse _ _ _ | sml = Failure True "Help the coverage checker!" []

public export
data ParseError tok = Error String (List tok)

||| Parse a list of tokens according to the given grammar. If successful,
||| returns a pair of the parse result and the unparsed tokens (the remaining
||| input).
export
parse : (xs : List tok) -> (act : Grammar tok c ty) -> 
        Either (ParseError tok) (ty, List tok)
parse xs act
    = case doParse False xs act of
           Failure _ msg ts => Left (Error msg ts)
           EmptyRes _ val rest => pure (val, rest)
           NonEmptyRes _ val rest => pure (val, rest)

||| Parse one or more things
export
some : Grammar tok True a -> 
       Grammar tok True (List a)
some p = do x <- p
            (do xs <- some p
                pure (x :: xs)) <|> pure [x]

||| Parse zero or more things (may match the empty input)
export
many : Grammar tok True a -> 
       Grammar tok False (List a)
many p = some p
     <|> pure []

||| Parse one or more things, separated by another thing
export
sepBy1 : Grammar tok True () -> Grammar tok True a -> 
         Grammar tok True (List a)
sepBy1 sep p = do x <- p
                  (do sep
                      xs <- sepBy1 sep p
                      pure (x :: xs)) <|> pure [x]

||| Parse zero or more things, separated by another thing. May
||| match the empty input.
export
sepBy : Grammar tok True () -> Grammar tok True a -> 
        Grammar tok False (List a)
sepBy sep p = sepBy1 sep p <|> pure []

||| Optionally parse a thing, with a default value if the grammar doesn't
||| match. May match the empty input.
export
optional : Grammar tok True a -> (ifNothing : a) ->
           Grammar tok False a
optional p def = p <|> pure def