{-# LANGUAGE FlexibleContexts #-} {-# LANGUAGE FlexibleInstances #-} {-# LANGUAGE NoMonomorphismRestriction #-} {-# LANGUAGE UndecidableInstances #-} {-# LANGUAGE DeriveGeneric #-} {-# LANGUAGE OverloadedStrings #-} module Language.Fixpoint.Parse ( -- * Top Level Class for Parseable Values Inputable (..) -- * Top Level Class for Parseable Values , Parser -- * Some Important keyword and parsers , reserved, reservedOp , locReserved , parens , brackets, angles, braces , semi , comma , colon , dcolon , dot , pairP , stringLiteral , locStringLiteral -- * Parsing basic entities -- fTyConP -- Type constructors , lowerIdP -- Lower-case identifiers , upperIdP -- Upper-case identifiers -- , infixIdP -- String Haskell infix Id , symbolP -- Arbitrary Symbols , locSymbolP , constantP -- (Integer) Constants , natural -- Non-negative integer , locNatural , bindP -- Binder (lowerIdP <* colon) , sortP -- Sort , mkQual -- constructing qualifiers , infixSymbolP -- parse infix symbols , locInfixSymbolP -- * Parsing recursive entities , exprP -- Expressions , predP -- Refinement Predicates , funAppP -- Function Applications , qualifierP -- Qualifiers , refaP -- Refa , refP -- (Sorted) Refinements , refDefP -- (Sorted) Refinements with default binder , refBindP -- (Sorted) Refinements with configurable sub-parsers , defineP -- function definition equations (PLE) , matchP -- measure definition equations (PLE) -- * Layout , indentedBlock , indentedLine , indentedOrExplicitBlock , explicitBlock , explicitCommaBlock , block , spaces , setLayout , popLayout -- * Raw identifiers , condIdR -- * Lexemes and lexemes with location , lexeme , located , locLexeme , locLowerIdP , locUpperIdP -- * Getting a Fresh Integer while parsing , freshIntP -- * Parsing Function , doParse' , parseTest' , parseFromFile , parseFromStdIn , remainderP -- * Utilities , isSmall , isNotReserved , initPState, PState (..) , LayoutStack(..) , Fixity(..), Assoc(..), addOperatorP, addNumTyCon -- * For testing , expr0P , dataFieldP , dataCtorP , dataDeclP ) where import Control.Monad (unless, void) import Control.Monad.Combinators.Expr import qualified Data.IntMap.Strict as IM import qualified Data.HashMap.Strict as M import qualified Data.HashSet as S import Data.List (foldl') import Data.List.NonEmpty (NonEmpty(..)) import qualified Data.Text as T import qualified Data.Text.IO as T import Data.Maybe (fromJust, fromMaybe) import Data.Void import Text.Megaparsec hiding (State, ParseError) import Text.Megaparsec.Char import qualified Text.Megaparsec.Char.Lexer as L import GHC.Generics (Generic) import qualified Data.Char as Char import Language.Fixpoint.Types.Errors import qualified Language.Fixpoint.Misc as Misc import Language.Fixpoint.Smt.Types import Language.Fixpoint.Types hiding (mapSort, fi, params, GInfo(..)) import qualified Language.Fixpoint.Types as Types (GInfo(FI)) import Text.PrettyPrint.HughesPJ (text, vcat, (<+>), Doc) import Control.Monad.State -- import Debug.Trace -- Note [Parser monad] -- -- For reference, -- -- in *parsec*, the base monad transformer is -- -- ParsecT s u m a -- -- where -- -- s is the input stream type -- u is the user state type -- m is the underlying monad -- a is the return type -- -- whereas in *megaparsec*, the base monad transformer is -- -- ParsecT e s m a -- -- where -- -- e is the custom data component for errors -- s is the input stream type -- m is the underlying monad -- a is the return type -- -- The Liquid Haskell parser tracks state in 'PState', primarily -- for operator fixities. -- -- The old Liquid Haskell parser did not use parsec's "user state" -- functionality for 'PState', but instead wrapped a state monad -- in a parsec monad. We do the same thing for megaparsec. -- -- However, user state was still used for an additional 'Integer' -- as a unique supply. We incorporate this in the 'PState'. -- -- Furthermore, we have to decide whether the state in the parser -- should be "backtracking" or not. "Backtracking" state resets when -- the parser backtracks, and thus only contains state modifications -- performed by successful parses. On the other hand, non-backtracking -- state would contain all modifications made during the parsing -- process and allow us to observe unsuccessful attempts. -- -- It turns out that: -- -- - parsec's old built-in user state is backtracking -- - using @StateT s (ParsecT ...)@ is backtracking -- - using @ParsecT ... (StateT s ...)@ is non-backtracking -- -- We want all our state to be backtracking. -- -- Note that this is in deviation from what the old LH parser did, -- but I think that was plainly wrong. type Parser = StateT PState (Parsec Void String) -- | The parser state. -- -- We keep track of the fixities of infix operators. -- -- We also keep track of whether empty list and singleton lists -- syntax is allowed (and how they are to be interpreted, if they -- are). -- -- We also keep track of an integer counter that can be used to -- supply unique integers during the parsing process. -- -- Finally, we keep track of the layout stack. -- data PState = PState { fixityTable :: OpTable , fixityOps :: [Fixity] , empList :: Maybe Expr , singList :: Maybe (Expr -> Expr) , supply :: !Integer , layoutStack :: LayoutStack , numTyCons :: !(S.HashSet Symbol) } -- | The layout stack tracks columns at which layout blocks -- have started. -- data LayoutStack = Empty -- ^ no layout info | Reset LayoutStack -- ^ in a block not using layout | At Pos LayoutStack -- ^ in a block at the given column | After Pos LayoutStack -- ^ past a block at the given column deriving Show -- | Pop the topmost element from the stack. popLayoutStack :: LayoutStack -> LayoutStack popLayoutStack Empty = error "unbalanced layout stack" popLayoutStack (Reset s) = s popLayoutStack (At _ s) = s popLayoutStack (After _ s) = s -- | Modify the layout stack using the given function. modifyLayoutStack :: (LayoutStack -> LayoutStack) -> Parser () modifyLayoutStack f = modify (\ s -> s { layoutStack = f (layoutStack s) }) -- | Start a new layout block at the current indentation level. setLayout :: Parser () setLayout = do i <- L.indentLevel -- traceShow ("setLayout", i) $ pure () modifyLayoutStack (At i) -- | Temporarily reset the layout information, because we enter -- a block with explicit separators. -- resetLayout :: Parser () resetLayout = do -- traceShow ("resetLayout") $ pure () modifyLayoutStack Reset -- | Remove the topmost element from the layout stack. popLayout :: Parser () popLayout = do -- traceShow ("popLayout") $ pure () modifyLayoutStack popLayoutStack -- | Consumes all whitespace, including LH comments. -- -- Should not be used directly, but primarily via 'lexeme'. -- -- The only "valid" use case for spaces is in top-level parsing -- function, to consume initial spaces. -- spaces :: Parser () spaces = L.space space1 lhLineComment lhBlockComment -- | Verify that the current indentation level is in the given -- relation to the provided reference level, otherwise fail. -- -- This is a variant of 'indentGuard' provided by megaparsec, -- only that it does not consume whitespace. -- guardIndentLevel :: Ordering -> Pos -> Parser () guardIndentLevel ord ref = do actual <- L.indentLevel -- traceShow ("guardIndentLevel", actual, ord, ref) $ pure () unless (compare actual ref == ord) (L.incorrectIndent ord ref actual) -- | Checks the current indentation level with respect to the -- current layout stack. May fail. Returns the parser to run -- after the next token. -- -- This function is intended to be used within a layout block -- to check whether the next token is valid within the current -- block. -- guardLayout :: Parser (Parser ()) guardLayout = do stack <- gets layoutStack -- traceShow ("guardLayout", stack) $ pure () case stack of At i s -> guardIndentLevel EQ i *> pure (modifyLayoutStack (const (After i (At i s)))) -- Note: above, we must really set the stack to 'After i (At i s)' explicitly. -- Otherwise, repeated calls to 'guardLayout' at the same column could push -- multiple 'After' entries on the stack. After i _ -> guardIndentLevel GT i *> pure (pure ()) _ -> pure (pure ()) -- | Checks the current indentation level with respect to the -- current layout stack. The current indentation level must -- be strictly greater than the one of the surrounding block. -- May fail. -- -- This function is intended to be used before we establish -- a new, nested, layout block, which should be indented further -- than the surrounding blocks. -- strictGuardLayout :: Parser () strictGuardLayout = do stack <- gets layoutStack -- traceShow ("strictGuardLayout", stack) $ pure () case stack of At i _ -> guardIndentLevel GT i *> pure () After i _ -> guardIndentLevel GT i *> pure () _ -> pure () -- | Indentation-aware lexeme parser. Before parsing, establishes -- whether we are in a position permitted by the layout stack. -- After the token, consume whitespace and potentially change state. -- lexeme :: Parser a -> Parser a lexeme p = do after <- guardLayout p <* spaces <* after -- | Indentation-aware located lexeme parser. -- -- This is defined in such a way that it determines the actual source range -- covered by the identifier. I.e., it consumes additional whitespace in the -- end, but that is not part of the source range reported for the identifier. -- locLexeme :: Parser a -> Parser (Located a) locLexeme p = do after <- guardLayout l1 <- getSourcePos x <- p l2 <- getSourcePos spaces <* after pure (Loc l1 l2 x) -- | Make a parser location-aware. -- -- This is at the cost of an imprecise span because we still -- consume spaces in the end first. -- located :: Parser a -> Parser (Located a) located p = do l1 <- getSourcePos x <- p l2 <- getSourcePos pure (Loc l1 l2 x) -- | Parse a block delimited by layout. -- The block must be indented more than the surrounding blocks, -- otherwise we return an empty list. -- -- Assumes that the parser for items does not accept the empty string. -- indentedBlock :: Parser a -> Parser [a] indentedBlock p = strictGuardLayout *> setLayout *> many (p <* popLayout) <* popLayout -- We have to pop after every p, because the first successful -- token moves from 'At' to 'After'. We have to pop at the end, -- because we want to remove 'At'. <|> pure [] -- We need to have a fallback with the empty list, because if the -- layout check fails, we still want to accept this as an empty block. -- | Parse a single line that may be continued via layout. indentedLine :: Parser a -> Parser a indentedLine p = setLayout *> p <* popLayout <* popLayout -- We have to pop twice, because the first successful token -- moves from 'At' to 'After', so we have to remove both. -- | Parse a block of items which can be delimited either via -- layout or via explicit delimiters as specified. -- -- Assumes that the parser for items does not accept the empty string. -- indentedOrExplicitBlock :: Parser open -> Parser close -> Parser sep -> Parser a -> Parser [a] indentedOrExplicitBlock open close sep p = explicitBlock open close sep p <|> (concat <$> indentedBlock (sepEndBy1 p sep)) -- | Parse a block of items that are delimited via explicit delimiters. -- Layout is disabled/reset for the scope of this block. -- explicitBlock :: Parser open -> Parser close -> Parser sep -> Parser a -> Parser [a] explicitBlock open close sep p = resetLayout *> open *> sepEndBy p sep <* close <* popLayout -- | Symbolic lexeme. Stands on its own. sym :: String -> Parser String sym x = lexeme (string x) -- | Located variant of 'sym'. locSym :: String -> Parser (Located String) locSym x = locLexeme (string x) semi, comma, colon, dcolon, dot :: Parser String semi = sym ";" comma = sym "," colon = sym ":" -- Note: not a reserved symbol; use with care dcolon = sym "::" -- Note: not a reserved symbol; use with care dot = sym "." -- Note: not a reserved symbol; use with care -- | Parses a block via layout or explicit braces and semicolons. -- -- Assumes that the parser for items does not accept the empty string. -- -- However, even in layouted mode, we are allowing semicolons to -- separate block contents. We also allow semicolons at the beginning, -- end, and multiple subsequent semicolons, so the resulting parser -- provides the illusion of allowing empty items. -- block :: Parser a -> Parser [a] block = indentedOrExplicitBlock (sym "{" *> many semi) (sym "}") (some semi) -- | Parses a block with explicit braces and commas as separator. -- Used for record constructors in datatypes. -- explicitCommaBlock :: Parser a -> Parser [a] explicitCommaBlock = explicitBlock (sym "{") (sym "}") comma -------------------------------------------------------------------- reservedNames :: S.HashSet String reservedNames = S.fromList [ -- reserved words used in fixpoint "SAT" , "UNSAT" , "true" , "false" , "mod" , "data" , "Bexp" -- , "True" -- , "Int" , "import" , "if", "then", "else" , "func" , "autorewrite" , "rewrite" -- reserved words used in liquid haskell , "forall" , "coerce" , "exists" , "module" , "spec" , "where" , "decrease" , "lazyvar" , "LIQUID" , "lazy" , "local" , "assert" , "assume" , "automatic-instances" , "autosize" , "axiomatize" , "bound" , "class" , "data" , "define" , "defined" , "embed" , "expression" , "import" , "include" , "infix" , "infixl" , "infixr" , "inline" , "instance" , "invariant" , "measure" , "newtype" , "predicate" , "qualif" , "reflect" , "type" , "using" , "with" , "in" ] -- TODO: This is currently unused. -- -- The only place where this is used in the original parsec code is in the -- Text.Parsec.Token.operator parser. -- _reservedOpNames :: [String] _reservedOpNames = [ "+", "-", "*", "/", "\\", ":" , "<", ">", "<=", ">=", "=", "!=" , "/=" , "mod", "and", "or" --, "is" , "&&", "||" , "~", "=>", "==>", "<=>" , "->" , ":=" , "&", "^", "<<", ">>", "--" , "?", "Bexp" , "'" , "_|_" , "|" , "<:" , "|-" , "::" , "." ] {- lexer :: Monad m => Token.GenTokenParser String u m lexer = Token.makeTokenParser languageDef -} -- | Consumes a line comment. lhLineComment :: Parser () lhLineComment = L.skipLineComment "// " -- | Consumes a block comment. lhBlockComment :: Parser () lhBlockComment = L.skipBlockComment "/* " "*/" -- | Parser that consumes a single char within an identifier (not start of identifier). identLetter :: Parser Char identLetter = alphaNumChar <|> oneOf ("_" :: String) -- | Parser that consumes a single char within an operator (not start of operator). opLetter :: Parser Char opLetter = oneOf (":!#$%&*+./<=>?@\\^|-~'" :: String) -- | Parser that consumes the given reserved word. -- -- The input token cannot be longer than the given name. -- -- NOTE: we currently don't double-check that the reserved word is in the -- list of reserved words. -- reserved :: String -> Parser () reserved x = void $ lexeme (try (string x <* notFollowedBy identLetter)) locReserved :: String -> Parser (Located String) locReserved x = locLexeme (try (string x <* notFollowedBy identLetter)) -- | Parser that consumes the given reserved operator. -- -- The input token cannot be longer than the given name. -- -- NOTE: we currently don't double-check that the reserved operator is in the -- list of reserved operators. -- reservedOp :: String -> Parser () reservedOp x = void $ lexeme (try (string x <* notFollowedBy opLetter)) -- | Parser that consumes the given symbol. -- -- The difference with 'reservedOp' is that the given symbol is seen -- as a token of its own, so the next character that follows does not -- matter. -- -- symbol :: String -> Parser String -- symbol x = -- L.symbol spaces (string x) parens, brackets, angles, braces :: Parser a -> Parser a parens = between (sym "(") (sym ")") brackets = between (sym "[") (sym "]") angles = between (sym "<") (sym ">") braces = between (sym "{") (sym "}") locParens :: Parser a -> Parser (Located a) locParens p = (\ (Loc l1 _ _) a (Loc _ l2 _) -> Loc l1 l2 a) <$> locSym "(" <*> p <*> locSym ")" -- | Parses a string literal as a lexeme. This is based on megaparsec's -- 'charLiteral' parser, which claims to handle all the single-character -- escapes defined by the Haskell grammar. -- stringLiteral :: Parser String stringLiteral = lexeme stringR "string literal" locStringLiteral :: Parser (Located String) locStringLiteral = locLexeme stringR "string literal" stringR :: Parser String stringR = char '\"' *> manyTill L.charLiteral (char '\"') -- | Consumes a float literal lexeme. double :: Parser Double double = lexeme L.float "float literal" -- identifier :: Parser String -- identifier = Token.identifier lexer -- | Consumes a natural number literal lexeme, which can be -- in decimal, octal and hexadecimal representation. -- -- This does not parse negative integers. Unary minus is available -- as an operator in the expression language. -- natural :: Parser Integer natural = lexeme naturalR "nat literal" locNatural :: Parser (Located Integer) locNatural = locLexeme naturalR "nat literal" naturalR :: Parser Integer naturalR = try (char '0' *> char' 'x') *> L.hexadecimal <|> try (char '0' *> char' 'o') *> L.octal <|> L.decimal -- | Raw (non-whitespace) parser for an identifier adhering to certain conditions. -- -- The arguments are as follows, in order: -- -- * the parser for the initial character, -- * a predicate indicating which subsequent characters are ok, -- * a check for the entire identifier to be applied in the end, -- * an error message to display if the final check fails. -- condIdR :: Parser Char -> (Char -> Bool) -> (String -> Bool) -> String -> Parser Symbol condIdR initial okChars condition msg = do s <- (:) <$> initial <*> takeWhileP Nothing okChars if condition s then pure (symbol s) else fail (msg <> " " <> show s) -- TODO: The use of the following parsers is unsystematic. -- | Raw parser for an identifier starting with an uppercase letter. -- -- See Note [symChars]. -- upperIdR :: Parser Symbol upperIdR = condIdR upperChar (`S.member` symChars) (const True) "unexpected" -- | Raw parser for an identifier starting with a lowercase letter. -- -- See Note [symChars]. -- lowerIdR :: Parser Symbol lowerIdR = condIdR (lowerChar <|> char '_') (`S.member` symChars) isNotReserved "unexpected reserved word" -- | Raw parser for an identifier starting with any letter. -- -- See Note [symChars]. -- symbolR :: Parser Symbol symbolR = condIdR (letterChar <|> char '_') (`S.member` symChars) isNotReserved "unexpected reserved word" isNotReserved :: String -> Bool isNotReserved s = not (s `S.member` reservedNames) -- | Predicate version to check if the characer is a valid initial -- character for 'lowerIdR'. -- -- TODO: What is this needed for? -- isSmall :: Char -> Bool isSmall c = Char.isLower c || c == '_' -- Note [symChars]. -- -- The parser 'symChars' is very permissive. In particular, we allow -- dots (for qualified names), and characters such as @$@ to be able -- to refer to identifiers as they occur in e.g. GHC Core. ---------------------------------------------------------------- ------------------------- Expressions -------------------------- ---------------------------------------------------------------- -- | Lexeme version of 'upperIdR'. -- upperIdP :: Parser Symbol upperIdP = lexeme upperIdR "upperIdP" -- | Lexeme version of 'lowerIdR'. -- lowerIdP :: Parser Symbol lowerIdP = lexeme lowerIdR "lowerIdP" -- | Unconstrained identifier, lower- or uppercase. -- -- Must not be a reserved word. -- -- Lexeme version of 'symbolR'. -- symbolP :: Parser Symbol symbolP = lexeme symbolR "identifier" -- The following are located versions of the lexeme identifier parsers. locSymbolP, locLowerIdP, locUpperIdP :: Parser LocSymbol locLowerIdP = locLexeme lowerIdR locUpperIdP = locLexeme upperIdR locSymbolP = locLexeme symbolR -- | Parser for literal numeric constants: floats or integers without sign. constantP :: Parser Constant constantP = try (R <$> double) -- float literal <|> I <$> natural -- nat literal -- | Parser for literal string contants. symconstP :: Parser SymConst symconstP = SL . T.pack <$> stringLiteral -- | Parser for "atomic" expressions. -- -- This parser is reused by Liquid Haskell. -- expr0P :: Parser Expr expr0P = trueP -- constant "true" <|> falseP -- constant "false" <|> fastIfP EIte exprP -- "if-then-else", starts with "if" <|> coerceP exprP -- coercion, starts with "coerce" <|> (ESym <$> symconstP) -- string literal, starts with double-quote <|> (ECon <$> constantP) -- numeric literal, starts with a digit <|> (reservedOp "_|_" >> return EBot) -- constant bottom, equivalent to "false" <|> lamP -- lambda abstraction, starts with backslash <|> try tupleP -- tuple expressions, starts with "(" <|> try (parens exprP) -- parenthesised expression, starts with "(" <|> try (parens exprCastP) -- explicit type annotation, starts with "(", TODO: should be an operator rather than require parentheses? <|> EVar <$> symbolP -- identifier, starts with any letter or underscore <|> try (brackets (pure ()) >> emptyListP) -- empty list, start with "[" <|> try (brackets exprP >>= singletonListP) -- singleton list, starts with "[" -- -- Note: -- -- In the parsers above, it is important that *all* parsers starting with "(" -- are prefixed with "try". This is because expr0P itself is chained with -- additional parsers in funAppP ... emptyListP :: Parser Expr emptyListP = do e <- gets empList case e of Nothing -> fail "No parsing support for empty lists" Just s -> return s singletonListP :: Expr -> Parser Expr singletonListP e = do f <- gets singList case f of Nothing -> fail "No parsing support for singleton lists" Just s -> return $ s e -- | Parser for an explicitly type-annotated expression. exprCastP :: Parser Expr exprCastP = do e <- exprP _ <- try dcolon <|> colon -- allow : or :: *and* allow following symbols ECst e <$> sortP fastIfP :: (Expr -> a -> a -> a) -> Parser a -> Parser a fastIfP f bodyP = do reserved "if" p <- predP reserved "then" b1 <- bodyP reserved "else" f p b1 <$> bodyP coerceP :: Parser Expr -> Parser Expr coerceP p = do reserved "coerce" (s, t) <- parens (pairP sortP (reservedOp "~") sortP) ECoerc s t <$> p {- qmIfP f bodyP = parens $ do p <- predP reserved "?" b1 <- bodyP colon b2 <- bodyP return $ f p b1 b2 -} -- | Parser for atomic expressions plus function applications. -- -- Base parser used in 'exprP' which adds in other operators. -- expr1P :: Parser Expr expr1P = try funAppP <|> expr0P -- | Expressions exprP :: Parser Expr exprP = do table <- gets fixityTable makeExprParser expr1P (flattenOpTable table) data Assoc = AssocNone | AssocLeft | AssocRight data Fixity = FInfix {fpred :: Maybe Int, fname :: String, fop2 :: Maybe (Expr -> Expr -> Expr), fassoc :: Assoc} | FPrefix {fpred :: Maybe Int, fname :: String, fop1 :: Maybe (Expr -> Expr)} | FPostfix {fpred :: Maybe Int, fname :: String, fop1 :: Maybe (Expr -> Expr)} -- | An OpTable stores operators by their fixity. -- -- Fixity levels range from 9 (highest) to 0 (lowest). type OpTable = IM.IntMap [Operator Parser Expr] -- [[Operator Parser Expr]] -- | Transform an operator table to the form expected by 'makeExprParser', -- which wants operators sorted by decreasing priority. -- flattenOpTable :: OpTable -> [[Operator Parser Expr]] flattenOpTable = (snd <$>) <$> IM.toDescList -- | Add an operator to the parsing state. addOperatorP :: Fixity -> Parser () addOperatorP op = modify $ \s -> s{ fixityTable = addOperator op (fixityTable s) , fixityOps = op:fixityOps s } -- | Add a new numeric FTyCon (symbol) to the parsing state. addNumTyCon :: Symbol -> Parser () addNumTyCon tc = modify $ \s -> s{ numTyCons = S.insert tc (numTyCons s) } -- | Parses any of the known infix operators. infixSymbolP :: Parser Symbol infixSymbolP = do ops <- gets infixOps choice (reserved' <$> ops) where infixOps st = [s | FInfix _ s _ _ <- fixityOps st] reserved' x = reserved x >> return (symbol x) -- | Located version of 'infixSymbolP'. locInfixSymbolP :: Parser (Located Symbol) locInfixSymbolP = do ops <- gets infixOps choice (reserved' <$> ops) where infixOps st = [s | FInfix _ s _ _ <- fixityOps st] reserved' x = locReserved x >>= \ (Loc l1 l2 _) -> return (Loc l1 l2 (symbol x)) -- | Helper function that turns an associativity into the right constructor for 'Operator'. mkInfix :: Assoc -> parser (expr -> expr -> expr) -> Operator parser expr mkInfix AssocLeft = InfixL mkInfix AssocRight = InfixR mkInfix AssocNone = InfixN -- | Add the given operator to the operator table. addOperator :: Fixity -> OpTable -> OpTable addOperator (FInfix p x f assoc) ops = insertOperator (makePrec p) (mkInfix assoc (reservedOp x >> return (makeInfixFun x f))) ops addOperator (FPrefix p x f) ops = insertOperator (makePrec p) (Prefix (reservedOp x >> return (makePrefixFun x f))) ops addOperator (FPostfix p x f) ops = insertOperator (makePrec p) (Postfix (reservedOp x >> return (makePrefixFun x f))) ops -- | Helper function for computing the priority of an operator. -- -- If no explicit priority is given, a priority of 9 is assumed. -- makePrec :: Maybe Int -> Int makePrec = fromMaybe 9 makeInfixFun :: String -> Maybe (Expr -> Expr -> Expr) -> Expr -> Expr -> Expr makeInfixFun x = fromMaybe (\e1 e2 -> EApp (EApp (EVar $ symbol x) e1) e2) makePrefixFun :: String -> Maybe (Expr -> Expr) -> Expr -> Expr makePrefixFun x = fromMaybe (EApp (EVar $ symbol x)) -- | Add an operator at the given priority to the operator table. insertOperator :: Int -> Operator Parser Expr -> OpTable -> OpTable insertOperator i op = IM.alter (Just . (op :) . fromMaybe []) i -- | The initial (empty) operator table. initOpTable :: OpTable initOpTable = IM.empty -- | Built-in operator table, parameterised over the composition function. bops :: Maybe Expr -> OpTable bops cmpFun = foldl' (flip addOperator) initOpTable builtinOps where -- Built-in Haskell operators, see https://www.haskell.org/onlinereport/decls.html#fixity builtinOps :: [Fixity] builtinOps = [ FPrefix (Just 9) "-" (Just ENeg) , FInfix (Just 7) "*" (Just $ EBin Times) AssocLeft , FInfix (Just 7) "/" (Just $ EBin Div) AssocLeft , FInfix (Just 6) "-" (Just $ EBin Minus) AssocLeft , FInfix (Just 6) "+" (Just $ EBin Plus) AssocLeft , FInfix (Just 5) "mod" (Just $ EBin Mod) AssocLeft -- Haskell gives mod 7 , FInfix (Just 9) "." applyCompose AssocRight ] applyCompose :: Maybe (Expr -> Expr -> Expr) applyCompose = (\f x y -> f `eApps` [x,y]) <$> cmpFun -- | Parser for function applications. -- -- Andres, TODO: Why is this so complicated? -- funAppP :: Parser Expr funAppP = litP <|> exprFunP <|> simpleAppP where exprFunP = mkEApp <$> funSymbolP <*> funRhsP funRhsP = some expr0P <|> parens innerP innerP = brackets (sepBy exprP semi) -- TODO:AZ the parens here should be superfluous, but it hits an infinite loop if removed simpleAppP = EApp <$> parens exprP <*> parens exprP funSymbolP = locSymbolP -- | Parser for tuple expressions (two or more components). tupleP :: Parser Expr tupleP = do Loc l1 l2 (first, rest) <- locParens ((,) <$> exprP <* comma <*> sepBy1 exprP comma) -- at least two components necessary let cons = symbol $ "(" ++ replicate (length rest) ',' ++ ")" -- stored in prefix form return $ mkEApp (Loc l1 l2 cons) (first : rest) -- | Parser for literals of all sorts. litP :: Parser Expr litP = do reserved "lit" l <- stringLiteral ECon . L (T.pack l) <$> sortP -- | Parser for lambda abstractions. lamP :: Parser Expr lamP = do reservedOp "\\" x <- symbolP _ <- colon -- TODO: this should probably be reservedOp instead t <- sortP reservedOp "->" ELam (x, t) <$> exprP varSortP :: Parser Sort varSortP = FVar <$> parens intP -- | Parser for function sorts without the "func" keyword. funcSortP :: Parser Sort funcSortP = parens $ mkFFunc <$> intP <* comma <*> sortsP sortsP :: Parser [Sort] sortsP = try (brackets (sepBy sortP semi)) <|> brackets (sepBy sortP comma) -- | Parser for sorts (types). sortP :: Parser Sort sortP = sortP' (many sortArgP) sortArgP :: Parser Sort sortArgP = sortP' (return []) {- sortFunP :: Parser Sort sortFunP = try (string "@" >> varSortP) <|> (fTyconSort <$> fTyConP) -} -- | Parser for sorts, parameterised over the parser for arguments. -- -- TODO, Andres: document the parameter better. -- sortP' :: Parser [Sort] -> Parser Sort sortP' appArgsP = parens sortP -- parenthesised sort, starts with "(" <|> (reserved "func" >> funcSortP) -- function sort, starts with "func" <|> (fAppTC listFTyCon . pure <$> brackets sortP) <|> (fAppTC <$> fTyConP <*> appArgsP) <|> (fApp <$> tvarP <*> appArgsP) tvarP :: Parser Sort tvarP = (string "@" >> varSortP) <|> (FObj . symbol <$> lowerIdP) fTyConP :: Parser FTycon fTyConP = (reserved "int" >> return intFTyCon) <|> (reserved "Integer" >> return intFTyCon) <|> (reserved "Int" >> return intFTyCon) -- <|> (reserved "int" >> return intFTyCon) -- TODO:AZ duplicate? <|> (reserved "real" >> return realFTyCon) <|> (reserved "bool" >> return boolFTyCon) <|> (reserved "num" >> return numFTyCon) <|> (reserved "Str" >> return strFTyCon) <|> (mkFTycon =<< locUpperIdP) mkFTycon :: LocSymbol -> Parser FTycon mkFTycon locSymbol = do nums <- gets numTyCons return (symbolNumInfoFTyCon locSymbol (val locSymbol `S.member` nums) False) -------------------------------------------------------------------------------- -- | Predicates ---------------------------------------------------------------- -------------------------------------------------------------------------------- -- | Parser for "atomic" predicates. -- -- This parser is reused by Liquid Haskell. -- pred0P :: Parser Expr pred0P = trueP -- constant "true" <|> falseP -- constant "false" <|> (reservedOp "??" >> makeUniquePGrad) <|> kvarPredP <|> fastIfP pIte predP -- "if-then-else", starts with "if" <|> try predrP -- binary relation, starts with anything that an expr can start with <|> parens predP -- parenthesised predicate, starts with "(" <|> (reservedOp "?" *> exprP) <|> try funAppP <|> EVar <$> symbolP -- identifier, starts with any letter or underscore <|> (reservedOp "&&" >> pGAnds <$> predsP) -- built-in prefix and <|> (reservedOp "||" >> POr <$> predsP) -- built-in prefix or makeUniquePGrad :: Parser Expr makeUniquePGrad = do uniquePos <- getSourcePos return $ PGrad (KV $ symbol $ show uniquePos) mempty (srcGradInfo uniquePos) mempty -- qmP = reserved "?" <|> reserved "Bexp" -- | Parser for the reserved constant "true". trueP :: Parser Expr trueP = reserved "true" >> return PTrue -- | Parser for the reserved constant "false". falseP :: Parser Expr falseP = reserved "false" >> return PFalse kvarPredP :: Parser Expr kvarPredP = PKVar <$> kvarP <*> substP kvarP :: Parser KVar kvarP = KV <$> lexeme (char '$' *> symbolR) substP :: Parser Subst substP = mkSubst <$> many (brackets $ pairP symbolP aP exprP) where aP = reservedOp ":=" -- | Parses a semicolon-separated bracketed list of predicates. -- -- Used as the argument of the prefix-versions of conjunction and -- disjunction. -- predsP :: Parser [Expr] predsP = brackets $ sepBy predP semi -- | Parses a predicate. -- -- Unlike for expressions, there is a built-in operator list. -- predP :: Parser Expr predP = makeExprParser pred0P lops where lops = [ [Prefix (reservedOp "~" >> return PNot)] , [Prefix (reserved "not" >> return PNot)] , [InfixR (reservedOp "&&" >> return pGAnd)] , [InfixR (reservedOp "||" >> return (\x y -> POr [x,y]))] , [InfixR (reservedOp "=>" >> return PImp)] , [InfixR (reservedOp "==>" >> return PImp)] , [InfixR (reservedOp "=" >> return PIff)] , [InfixR (reservedOp "<=>" >> return PIff)] , [InfixR (reservedOp "!=" >> return pNotIff)] , [InfixR (reservedOp "/=" >> return pNotIff)] ] pNotIff :: Expr -> Expr -> Expr pNotIff x y = PNot (PIff x y) -- | Parses a relation predicate. -- -- Binary relations connect expressions and predicates. -- predrP :: Parser Expr predrP = (\ e1 r e2 -> r e1 e2) <$> exprP <*> brelP <*> exprP -- | Parses a relation symbol. -- -- There is a built-in table of available relations. -- brelP :: Parser (Expr -> Expr -> Expr) brelP = (reservedOp "==" >> return (PAtom Eq)) <|> (reservedOp "=" >> return (PAtom Eq)) <|> (reservedOp "~~" >> return (PAtom Ueq)) <|> (reservedOp "!=" >> return (PAtom Ne)) <|> (reservedOp "/=" >> return (PAtom Ne)) <|> (reservedOp "!~" >> return (PAtom Une)) <|> (reservedOp "<" >> return (PAtom Lt)) <|> (reservedOp "<=" >> return (PAtom Le)) <|> (reservedOp ">" >> return (PAtom Gt)) <|> (reservedOp ">=" >> return (PAtom Ge)) -------------------------------------------------------------------------------- -- | BareTypes ----------------------------------------------------------------- -------------------------------------------------------------------------------- -- | Refa refaP :: Parser Expr refaP = try (pAnd <$> brackets (sepBy predP semi)) <|> predP -- | (Sorted) Refinements with configurable sub-parsers refBindP :: Parser Symbol -> Parser Expr -> Parser (Reft -> a) -> Parser a refBindP bp rp kindP = braces $ do x <- bp t <- kindP reservedOp "|" ra <- rp <* spaces return $ t (Reft (x, ra)) -- bindP = symbol <$> (lowerIdP <* colon) -- | Binder (lowerIdP <* colon) bindP :: Parser Symbol bindP = symbolP <* colon optBindP :: Symbol -> Parser Symbol optBindP x = try bindP <|> return x -- | (Sorted) Refinements refP :: Parser (Reft -> a) -> Parser a refP = refBindP bindP refaP -- | (Sorted) Refinements with default binder refDefP :: Symbol -> Parser Expr -> Parser (Reft -> a) -> Parser a refDefP x = refBindP (optBindP x) -------------------------------------------------------------------------------- -- | Parsing Data Declarations ------------------------------------------------- -------------------------------------------------------------------------------- dataFieldP :: Parser DataField dataFieldP = DField <$> locSymbolP <* colon <*> sortP dataCtorP :: Parser DataCtor dataCtorP = DCtor <$> locSymbolP <*> braces (sepBy dataFieldP comma) dataDeclP :: Parser DataDecl dataDeclP = DDecl <$> fTyConP <*> intP <* reservedOp "=" <*> brackets (many (reservedOp "|" *> dataCtorP)) -------------------------------------------------------------------------------- -- | Parsing Qualifiers -------------------------------------------------------- -------------------------------------------------------------------------------- -- | Qualifiers qualifierP :: Parser Sort -> Parser Qualifier qualifierP tP = do pos <- getSourcePos n <- upperIdP params <- parens $ sepBy1 (qualParamP tP) comma _ <- colon body <- predP return $ mkQual n params body pos qualParamP :: Parser Sort -> Parser QualParam qualParamP tP = do x <- symbolP pat <- qualPatP _ <- colon QP x pat <$> tP qualPatP :: Parser QualPattern qualPatP = (reserved "as" >> qualStrPatP) <|> return PatNone qualStrPatP :: Parser QualPattern qualStrPatP = (PatExact <$> symbolP) <|> parens ( (uncurry PatPrefix <$> pairP symbolP dot qpVarP) <|> (uncurry PatSuffix <$> pairP qpVarP dot symbolP) ) qpVarP :: Parser Int qpVarP = char '$' *> intP symBindP :: Parser a -> Parser (Symbol, a) symBindP = pairP symbolP colon pairP :: Parser a -> Parser z -> Parser b -> Parser (a, b) pairP xP sepP yP = (,) <$> xP <* sepP <*> yP --------------------------------------------------------------------- -- | Axioms for Symbolic Evaluation --------------------------------- --------------------------------------------------------------------- autoRewriteP :: Parser AutoRewrite autoRewriteP = do args <- sepBy sortedReftP spaces _ <- spaces _ <- reserved "=" _ <- spaces (lhs, rhs) <- braces $ pairP exprP (reserved "=") exprP return $ AutoRewrite args lhs rhs defineP :: Parser Equation defineP = do name <- symbolP params <- parens $ sepBy (symBindP sortP) comma sort <- colon *> sortP body <- reserved "=" *> braces ( if sort == boolSort then predP else exprP ) return $ mkEquation name params body sort matchP :: Parser Rewrite matchP = SMeasure <$> symbolP <*> symbolP <*> many symbolP <*> (reserved "=" >> exprP) pairsP :: Parser a -> Parser b -> Parser [(a, b)] pairsP aP bP = brackets $ sepBy (pairP aP (reserved ":") bP) semi --------------------------------------------------------------------- -- | Parsing Constraints (.fq files) -------------------------------- --------------------------------------------------------------------- -- Entities in Query File data Def a = Srt !Sort | Cst !(SubC a) | Wfc !(WfC a) | Con !Symbol !Sort | Dis !Symbol !Sort | Qul !Qualifier | Kut !KVar | Pack !KVar !Int | IBind !Int !Symbol !SortedReft !a | EBind !Int !Symbol !Sort !a | Opt !String | Def !Equation | Mat !Rewrite | Expand ![(Int,Bool)] | Adt !DataDecl | AutoRW !Int !AutoRewrite | RWMap ![(Int,Int)] deriving (Show, Generic) -- Sol of solbind -- Dep of FixConstraint.dep fInfoOptP :: Parser (FInfoWithOpts ()) fInfoOptP = do ps <- many defP return $ FIO (defsFInfo ps) [s | Opt s <- ps] fInfoP :: Parser (FInfo ()) fInfoP = defsFInfo <$> {- SCC "many-defP" -} many defP defP :: Parser (Def ()) defP = Srt <$> (reserved "sort" >> colon >> sortP) <|> Cst <$> (reserved "constraint" >> colon >> {- SCC "subCP" -} subCP) <|> Wfc <$> (reserved "wf" >> colon >> {- SCC "wfCP" -} wfCP) <|> Con <$> (reserved "constant" >> symbolP) <*> (colon >> sortP) <|> Dis <$> (reserved "distinct" >> symbolP) <*> (colon >> sortP) <|> Pack <$> (reserved "pack" >> kvarP) <*> (colon >> intP) <|> Qul <$> (reserved "qualif" >> qualifierP sortP) <|> Kut <$> (reserved "cut" >> kvarP) <|> EBind <$> (reserved "ebind" >> intP) <*> symbolP <*> (colon >> braces sortP) <*> pure () <|> IBind <$> (reserved "bind" >> intP) <*> symbolP <*> (colon >> sortedReftP) <*> pure () <|> Opt <$> (reserved "fixpoint" >> stringLiteral) <|> Def <$> (reserved "define" >> defineP) <|> Mat <$> (reserved "match" >> matchP) <|> Expand <$> (reserved "expand" >> pairsP intP boolP) <|> Adt <$> (reserved "data" >> dataDeclP) <|> AutoRW <$> (reserved "autorewrite" >> intP) <*> autoRewriteP <|> RWMap <$> (reserved "rewrite" >> pairsP intP intP) sortedReftP :: Parser SortedReft sortedReftP = refP (RR <$> (sortP <* spaces)) wfCP :: Parser (WfC ()) wfCP = do reserved "env" env <- envP reserved "reft" r <- sortedReftP case wfC env r () of [w] -> return w [] -> error "Unexpected empty list in wfCP" _:_:_ -> error "Expected a single element list in wfCP" subCP :: Parser (SubC ()) subCP = do pos <- getSourcePos reserved "env" env <- envP reserved "lhs" lhs <- sortedReftP reserved "rhs" rhs <- sortedReftP reserved "id" i <- natural <* spaces tag <- tagP subC' env lhs rhs i tag pos <$> getSourcePos subC' :: IBindEnv -> SortedReft -> SortedReft -> Integer -> Tag -> SourcePos -> SourcePos -> SubC () subC' env lhs rhs i tag l l' = case cs of [c] -> c _ -> die $ err sp $ "RHS without single conjunct at" <+> pprint l' where cs = subC env lhs rhs (Just i) tag () sp = SS l l' tagP :: Parser [Int] tagP = reserved "tag" >> spaces >> brackets (sepBy intP semi) envP :: Parser IBindEnv envP = do binds <- brackets $ sepBy (intP <* spaces) semi return $ insertsIBindEnv binds emptyIBindEnv intP :: Parser Int intP = fromInteger <$> natural boolP :: Parser Bool boolP = (reserved "True" >> return True) <|> (reserved "False" >> return False) defsFInfo :: [Def a] -> FInfo a defsFInfo defs = {- SCC "defsFI" -} Types.FI cm ws bs ebs lts dts kts qs binfo adts mempty mempty ae where cm = Misc.safeFromList "defs-cm" [(cid c, c) | Cst c <- defs] ws = Misc.safeFromList "defs-ws" [(i, w) | Wfc w <- defs, let i = Misc.thd3 (wrft w)] bs = bindEnvFromList $ exBinds ++ [(n,(x,r,a)) | IBind n x r a <- defs] ebs = [ n | (n,_) <- exBinds] exBinds = [(n, (x, RR t mempty, a)) | EBind n x t a <- defs] lts = fromListSEnv [(x, t) | Con x t <- defs] dts = fromListSEnv [(x, t) | Dis x t <- defs] kts = KS $ S.fromList [k | Kut k <- defs] qs = [q | Qul q <- defs] binfo = mempty expand = M.fromList [(fromIntegral i, f)| Expand fs <- defs, (i,f) <- fs] eqs = [e | Def e <- defs] rews = [r | Mat r <- defs] autoRWs = M.fromList [(arId , s) | AutoRW arId s <- defs] rwEntries = [(i, f) | RWMap fs <- defs, (i,f) <- fs] rwMap = foldl' insert (M.fromList []) rwEntries where insert map' (cid', arId) = case M.lookup arId autoRWs of Just rewrite -> M.insertWith (++) (fromIntegral cid') [rewrite] map' Nothing -> map' cid = fromJust . sid ae = AEnv eqs rews expand rwMap adts = [d | Adt d <- defs] -- msg = show $ "#Lits = " ++ (show $ length consts) --------------------------------------------------------------------- -- | Interacting with Fixpoint -------------------------------------- --------------------------------------------------------------------- fixResultP :: Parser a -> Parser (FixResult a) fixResultP pp = (reserved "SAT" >> return (Safe mempty)) <|> (reserved "UNSAT" >> Unsafe mempty <$> brackets (sepBy pp comma)) <|> (reserved "CRASH" >> crashP pp) crashP :: Parser a -> Parser (FixResult a) crashP pp = do i <- pp msg <- takeWhileP Nothing (const True) -- consume the rest of the input return $ Crash [(i, Nothing)] msg predSolP :: Parser Expr predSolP = parens (predP <* (comma >> iQualP)) iQualP :: Parser [Symbol] iQualP = upperIdP >> parens (sepBy symbolP comma) solution1P :: Parser (KVar, Expr) solution1P = do reserved "solution:" k <- kvP reservedOp ":=" ps <- brackets $ sepBy predSolP semi return (k, simplify $ PAnd ps) where kvP = try kvarP <|> (KV <$> symbolP) solutionP :: Parser (M.HashMap KVar Expr) solutionP = M.fromList <$> sepBy solution1P spaces solutionFileP :: Parser (FixResult Integer, M.HashMap KVar Expr) solutionFileP = (,) <$> fixResultP natural <*> solutionP -------------------------------------------------------------------------------- -- | Parse via the given parser, and obtain the rest of the input -- as well as the final source position. -- remainderP :: Parser a -> Parser (a, String, SourcePos) remainderP p = do res <- p str <- getInput pos <- getSourcePos return (res, str, pos) -- | Initial parser state. initPState :: Maybe Expr -> PState initPState cmpFun = PState { fixityTable = bops cmpFun , empList = Nothing , singList = Nothing , fixityOps = [] , supply = 0 , layoutStack = Empty , numTyCons = S.empty } -- | Entry point for parsing, for testing. -- -- Take the top-level parser, the source file name, and the input as a string. -- Fails with an exception on a parse error. -- doParse' :: Parser a -> SourceName -> String -> a doParse' parser fileName input = case runParser (evalStateT (spaces *> parser <* eof) (initPState Nothing)) fileName input of Left peb@(ParseErrorBundle errors posState) -> -- parse errors; we extract the first error from the error bundle let ((_, pos) :| _, _) = attachSourcePos errorOffset errors posState in die $ err (SS pos pos) (dErr peb) Right r -> r -- successful parse with no remaining input where -- Turns the multiline error string from megaparsec into a pretty-printable Doc. dErr :: ParseErrorBundle String Void -> Doc dErr e = vcat (map text (lines (errorBundlePretty e))) -- | Function to test parsers interactively. parseTest' :: Show a => Parser a -> String -> IO () parseTest' parser input = parseTest (evalStateT parser (initPState Nothing)) input -- errorSpan :: ParseError -> SrcSpan -- errorSpan e = SS l l where l = errorPos e parseFromFile :: Parser b -> SourceName -> IO b parseFromFile p f = doParse' p f <$> readFile f parseFromStdIn :: Parser a -> IO a parseFromStdIn p = doParse' p "stdin" . T.unpack <$> T.getContents -- | Obtain a fresh integer during the parsing process. freshIntP :: Parser Integer freshIntP = do n <- gets supply modify (\ s -> s{supply = n + 1}) return n --------------------------------------------------------------------- -- Standalone SMTLIB2 commands -------------------------------------- --------------------------------------------------------------------- commandsP :: Parser [Command] commandsP = sepBy commandP semi commandP :: Parser Command commandP = (reserved "var" >> cmdVarP) <|> (reserved "push" >> return Push) <|> (reserved "pop" >> return Pop) <|> (reserved "check" >> return CheckSat) <|> (reserved "assert" >> (Assert Nothing <$> predP)) <|> (reserved "distinct" >> (Distinct <$> brackets (sepBy exprP comma))) cmdVarP :: Parser Command cmdVarP = error "UNIMPLEMENTED: cmdVarP" -- do -- x <- bindP -- t <- sortP -- return $ Declare x [] t --------------------------------------------------------------------- -- Bundling Parsers into a Typeclass -------------------------------- --------------------------------------------------------------------- class Inputable a where rr :: String -> a rr' :: String -> String -> a rr' _ = rr rr = rr' "" instance Inputable Symbol where rr' = doParse' symbolP instance Inputable Constant where rr' = doParse' constantP instance Inputable Expr where rr' = doParse' exprP instance Inputable (FixResult Integer) where rr' = doParse' $ fixResultP natural instance Inputable (FixResult Integer, FixSolution) where rr' = doParse' solutionFileP instance Inputable (FInfo ()) where rr' = {- SCC "fInfoP" -} doParse' fInfoP instance Inputable (FInfoWithOpts ()) where rr' = {- SCC "fInfoWithOptsP" -} doParse' fInfoOptP instance Inputable Command where rr' = doParse' commandP instance Inputable [Command] where rr' = doParse' commandsP {- --------------------------------------------------------------- --------------------------- Testing --------------------------- --------------------------------------------------------------- -- A few tricky predicates for parsing -- myTest1 = "((((v >= 56320) && (v <= 57343)) => (((numchars a o ((i - o) + 1)) == (1 + (numchars a o ((i - o) - 1)))) && (((numchars a o (i - (o -1))) >= 0) && (((i - o) - 1) >= 0)))) && ((not (((v >= 56320) && (v <= 57343)))) => (((numchars a o ((i - o) + 1)) == (1 + (numchars a o (i - o)))) && ((numchars a o (i - o)) >= 0))))" -- -- myTest2 = "len x = len y - 1" -- myTest3 = "len x y z = len a b c - 1" -- myTest4 = "len x y z = len a b (c - 1)" -- myTest5 = "x >= -1" -- myTest6 = "(bLength v) = if n > 0 then n else 0" -- myTest7 = "(bLength v) = (if n > 0 then n else 0)" -- myTest8 = "(bLength v) = (n > 0 ? n : 0)" sa = "0" sb = "x" sc = "(x0 + y0 + z0) " sd = "(x+ y * 1)" se = "_|_ " sf = "(1 + x + _|_)" sg = "f(x,y,z)" sh = "(f((x+1), (y * a * b - 1), _|_))" si = "(2 + f((x+1), (y * a * b - 1), _|_))" s0 = "true" s1 = "false" s2 = "v > 0" s3 = "(0 < v && v < 100)" s4 = "(x < v && v < y+10 && v < z)" s6 = "[(v > 0)]" s6' = "x" s7' = "(x <=> y)" s8' = "(x <=> a = b)" s9' = "(x <=> (a <= b && b < c))" s7 = "{ v: Int | [(v > 0)] }" s8 = "x:{ v: Int | v > 0 } -> {v : Int | v >= x}" s9 = "v = x+y" s10 = "{v: Int | v = x + y}" s11 = "x:{v:Int | true } -> {v:Int | true }" s12 = "y : {v:Int | true } -> {v:Int | v = x }" s13 = "x:{v:Int | true } -> y:{v:Int | true} -> {v:Int | v = x + y}" s14 = "x:{v:a | true} -> y:{v:b | true } -> {v:a | (x < v && v < y) }" s15 = "x:Int -> Bool" s16 = "x:Int -> y:Int -> {v:Int | v = x + y}" s17 = "a" s18 = "x:a -> Bool" s20 = "forall a . x:Int -> Bool" s21 = "x:{v : GHC.Prim.Int# | true } -> {v : Int | true }" r0 = (rr s0) :: Pred r0' = (rr s0) :: [Refa] r1 = (rr s1) :: [Refa] e1, e2 :: Expr e1 = rr "(k_1 + k_2)" e2 = rr "k_1" o1, o2, o3 :: FixResult Integer o1 = rr "SAT " o2 = rr "UNSAT [1, 2, 9,10]" o3 = rr "UNSAT []" -- sol1 = doParse solution1P "solution: k_5 := [0 <= VV_int]" -- sol2 = doParse solution1P "solution: k_4 := [(0 <= VV_int)]" b0, b1, b2, b4, b5, b6, b7, b8, b9, b10, b11, b12, b13 :: BareType b0 = rr "Int" b1 = rr "x:{v:Int | true } -> y:{v:Int | true} -> {v:Int | v = x + y}" b2 = rr "x:{v:Int | true } -> y:{v:Int | true} -> {v:Int | v = x - y}" b4 = rr "forall a . x : a -> Bool" b5 = rr "Int -> Int -> Int" b6 = rr "(Int -> Int) -> Int" b7 = rr "({v: Int | v > 10} -> Int) -> Int" b8 = rr "(x:Int -> {v: Int | v > x}) -> {v: Int | v > 10}" b9 = rr "x:Int -> {v: Int | v > x} -> {v: Int | v > 10}" b10 = rr "[Int]" b11 = rr "x:[Int] -> {v: Int | v > 10}" b12 = rr "[Int] -> String" b13 = rr "x:(Int, [Bool]) -> [(String, String)]" -- b3 :: BareType -- b3 = rr "x:Int -> y:Int -> {v:Bool | ((v is True) <=> x = y)}" m1 = ["len :: [a] -> Int", "len (Nil) = 0", "len (Cons x xs) = 1 + len(xs)"] m2 = ["tog :: LL a -> Int", "tog (Nil) = 100", "tog (Cons y ys) = 200"] me1, me2 :: Measure.Measure BareType Symbol me1 = (rr $ intercalate "\n" m1) me2 = (rr $ intercalate "\n" m2) -}