deliverables/report/pars.tex

   1 \section{Lexing \& parsing}\label{sec:pars}
   2 \subsection{\Yard}
   3 For both lexing and parsing we use proof of concept
   4 %state of the art
   5 minimal
   6 parser combinators library called \Yard. \Yard{} is inspired by the well-known
   7 \textsc{Parsec} library. Where \Yard{} only has 7 primitive parser (combinators)
   8 \textsc{Parsec} already has 9 categories of parser combinators with in every
   9 category there are numerous combinators.
  10
  11 Parsers implemented in Yard parse left to right and are greedy, that is they
  12 always try to consume as
  13 much input as possible, starting from the left most encountered token.
  14 Yards parsers also automatically apply backtracking,
  15 when the left parser combined with \CI{<|>} fails, then any input it might
  16 have consumed is restored and the right parser is executed.
  17
  18 \begin{lstlisting}[language=Clean]
  19 :: Error = PositionalError Int Int String | Error String
  20 :: Parser a b = Parser ([a] -> (Either Error b, [a]))
  21
  22 (<?>) :: (Parser a b) Error -> Parser a b
  23 fail :: Parser a b
  24 top :: Parser a a
  25 peek :: Parser a a
  26 eof :: Parser a Void
  27 pure :: b -> Parser a b
  28 (>>=) :: (Parser a b) (b -> Parser a c) -> Parser a c
  29 (<|>) :: (Parer a b) (Parser a b) -> Parser a b
  30 --derived parser functions
  31 satisfy :: (a -> Bool) -> Parser a a
  32 check :: (a -> Bool) -> Parser a a
  33 (until) infix 2 :: (Parser a b) (Parser a c) -> Parser a [b]
  34 item :: a -> Parser a a | Eq a
  35 list :: [a] -> Parser a [a] | Eq a
  36 \end{lstlisting}
  37
  38 \subsection{Lexing \& Grammar}
  39 The existing \SPL{} grammar was not suitable for parsing and lexing. The
  40 grammar listed in Listing~\ref{lst:grammar} shows the current and final
  41 grammar. The grammar for \SPLC{} has been extended to accommodate for the
  42 syntactic sugar \SPLC{} introduces, such as string and list literals,
  43 and for anonymous lambda functions.
  44 Moreover we have applied transformation on the grammar including eliminating
  45 left recursion, fixing operator priority and associativity.
  46
  47 To make the parsing more easy we first lex the character input into tokens. In
  48 this way the parser can be simplified a lot and some more complex constructs
  49 can be lexed as one token such as literal characters.
  50
  51 As said, the lexer uses a \Yard{} parser. The parser takes a list of characters
  52 and returns a list of \CI{Token}s. A token is a \CI{TokenValue} accompanied
  53 with a position and the \emph{ADT} used is shown in Listing~\ref{lst:lextoken}.
  54 Parser combinators make it very easy to account for arbitrary white space and
  55 it is much less elegant to do this in a regular way.
  56 Listing~\ref{lst:lexerwhite} shows the way we handle white space and recalculate
  57 positions. By choosing to lex with parser combinators the speed of the phase
  58 decreases. However due to the simplicity of the lexer this is barely
  59 measurable.
  60
  61 \begin{lstlisting}[
  62         language=Clean,
  63         label={lst:lexerwhite},
  64         caption={Lexer whitespace handling}]
  65 lexProgram :: Int Int -> Parser Char [Token]
  66 lexProgram line column = lexToken >>= \t->case t of
  67         LexEOF = pure []
  68         LexNL = lexProgram (line+1) 1
  69         (LexSpace l c) = lexProgram (line+l) (column+c)
  70         (LexItemError e) = fail <?>
  71                 PositionalError line column ("LexerError: " +++ e)
  72         (LexToken c t) = lexProgram line (column+c)
  73                 >>= \rest->pure [({line=line,col=column}, t):rest]
  74 \end{lstlisting}
  75
  76 \begin{lstlisting}[
  77         language=Clean,
  78         label={lst:lextoken},
  79         caption={Lexer token ADT}]
  80 :: Pos = {line :: Int, col :: Int}
  81 :: Token :== (Pos, TokenValue)
  82 :: TokenValue
  83         //Value tokens
  84         = IdentToken String
  85         | NumberToken Int
  86         | CharToken Char
  87         | StringToken [Char]
  88         //Keyword tokens
  89         | VarToken
  90         | ReturnToken
  91         | IfToken
  92         | ...
  93 \end{lstlisting}
  94
  95 A lexer written with parser combinators is pretty straight forward and in
  96 practice it is just a very long list of \texttt{alternative} monadic
  97 combinators. However the order is very important since some tokens are very
  98 greedy. Almost all tokens can be lexed trivially with the \CI{list} combinator
  99 for matching literal strings. Comments and literals are the only exception that
 100 require a non trivial parser.
 101
 102 \subsection{Parsing}
 103 The parsing phase is the second phase of the parser and is yet again a \Yard{}
 104 parser that transforms a list of tokens to an Abstract Syntax Tree(\AST). The
 105 full abstract syntax tree is listed in Listing~\ref{lst:ast} which closely
 106 resembles the grammar.
 107
 108 The parser uses the standard \Yard{} combinators. Due to the modularity of
 109 combinators it was and is very easy to add functionality to the parser. The
 110 parser also handles some syntactic sugar(Section~\ref{ssec:synsugar}). For
 111 example the parser expands the literal lists and literal strings to the
 112 according list or string representation. Moreover the parser transforms the let
 113 expressions to real functions representing constant values.
 114
 115 As an example we show the parsing of a \CI{FunDecl} in
 116 Listing~\ref{lst:fundecl}. The \CI{FunDecl} is one of the most complex parsers
 117 and is composed of as complex subparsers. A \CI{FunDecl} parser exactly one
 118 complete function.
 119
 120 First we do the non consuming \CI{peekPos} to get the position of the first
 121 token without consuming it, after that the identifier is parsed
 122 which is basically a parser that transforms an \CI{IdToken} into a \CI{String}.
 123
 124 \CI{parseBBraces} is a parser combinator built from the basic combinators that
 125 parses a parser when the contents are surrounded by braces. This is followed by
 126 a yet another helper function to parse comma separated items.
 127
 128 Since the next element of the \ADT{} is a \CI{Maybe} the next parser is
 129 combined with the optional combinator since the type of a function is optional
 130 and when not given it will be inferred later.
 131
 132 A function consists of \emph{many} \CI{VarDecl}s and then \emph{many}
 133 \CI{Stmt}s. The word \emph{many} in \Yard{} means zero or more while the word
 134 \emph{some} means one or more. Thus we allow a function to be empty. The reason
 135 why \CI{flatten} is mapped on to the last argument of the \CI{liftM6} is
 136 because the \CI{parseStmt} returns possibly multiple \CI{Stmt}s. This is
 137 because in the parsing phase we expand the \CI{print} functions into multiple
 138 instances and thus it can be the case that from one \CI{Stmt} we actually get
 139 multiple.
 140
 141 \begin{lstlisting}[
 142         language=Clean,
 143         label={lst:fundecl},
 144         caption={Parsing a \CI{FunDecl}}]
 145 :: FunDecl = FunDecl Pos String [String] (Maybe Type) [VarDecl] [Stmt]
 146
 147 parseFunDecl :: Parser Token FunDecl
 148 parseFunDecl = liftM6 FunDecl
 149     (peekPos)
 150     (parseIdent)
 151         (parseBBraces $ parseSepList CommaToken parseIdent)
 152         (optional (satTok DoubleColonToken *> parseFunType))
 153         (satTok CBraceOpenToken *> many parseVarDecl)
 154         (flatten <$> (many parseStmt <* satTok CBraceCloseToken))
 155 \end{lstlisting}
 156
 157 \subsection{Sugars} \label{ssec:synsugar}
 158 Some syntactic sugars are procesessed in the lexing or parsing phase. Entering
 159 literal lists and strings is a tedious job because you can only glue them
 160 together with cons opererators. Thus we introduced a literal lists notation as
 161 visible in the grammar. Literal strings are lexed as single tokens and expanded
 162 during parsing in to normal lists of characters. Literal lists are processed in
 163 the parsing phase and expanded to their similar form with the \texttt{Cons}
 164 operator. An example of this is shown in Listing~\ref{lst:litlist}
 165
 166 \begin{lstlisting}[
 167         language=SPLCode,
 168         caption={Literal lists},
 169         label={lst:litlist}]
 170 //Before transformation
 171 var a = "Hello world!";
 172 var b = [3, 1, 4, 1, 5];
 173
 174 //After transformation
 175 var a = 'H':'e':'l':'l':'o':' ':'w':'o':'r':'l':'d':'!':[]
 176 var b = 3 : 1 : 4 : 1 : 5 : [];
 177 \end{lstlisting}
 178
 179 Another sugar added is variable arguments printing. To enable the user to
 180 pretty print data the number of arguments of the \SI{print} function is not
 181 fixed and it is expanded at compiletime. With this sugar the programmer can
 182 print several different types in one line. Listing~\ref{lst:varprint} shows an
 183 example of the sugar. In the semantic analysis phase these statements are
 184 actually refined even more to represent the specific print function per type
 185 since the compiler allows printing of \SI{Int}, \SI{Bool}, \SI{Char} and
 186 \SI{[Char]}
 187 \begin{lstlisting}[
 188         language=SPLCode,
 189         caption={Variable arguments printing},
 190         label={lst:varprint}]
 191 //Before transformation
 192 print("abc", 42, 'c', "da\n");
 193
 194 //After transformation
 195 print('a':'b':'c':[]);
 196 print(42);
 197 print('c');
 198 print('d':'a':'\n':[]);
 199 \end{lstlisting}
 200
 201 The last sugar processed in the parsing or lexing phase are the \SI{let}
 202 constructions. These constructions provide an easy way of defining global
 203 constants without real constants. While we do not allow global variables one
 204 might want to introduce global constants and with these constructs this can be
 205 done very easily. Listing~\ref{lst:letgl} shows the expansion of \SI{let}
 206 declarations.
 207 \begin{lstlisting}[
 208         language=SPLCode,
 209         caption={\SI{let} expansion},
 210         label={lst:letgl}]
 211 //Before transformation
 212 let Int x = 42;
 213
 214 //After transformation
 215 x() :: -> Int{
 216         return 42;
 217 }
 218 \end{lstlisting}