theory Parsing

imports Base "Package/Simple_Inductive_Package"

begin

chapter {* Parsing *}

text {*

  Isabelle distinguishes between \emph{outer} and \emph{inner} syntax. 

  Theory commands, such as \isacommand{definition}, \isacommand{inductive} and so

  on, belong to the outer syntax, whereas items inside double quotation marks, such 

  as terms, types and so on, belong to the inner syntax. For parsing inner syntax, 

  Isabelle uses a rather general and sophisticated algorithm due to Earley, which 

  is driven by priority grammars. Parsers for outer syntax are built up by functional

  parsing combinators. These combinators are a well-established technique for parsing, 

  which has, for example, been described in Paulson's classic ML-book \cite{paulson-ml2}.

  Isabelle developers are usually concerned with writing these outer syntax parsers, 

  either for new definitional packages or for calling tactics with specific arguments. 

  \begin{readmore}

  The library 

  for writing parser combinators is split up, roughly, into two parts. 

  The first part consists of a collection of generic parser combinators defined

  in the structure @{ML_struct Scan} in the file 

  @{ML_file "Pure/General/scan.ML"}. The second part of the library consists of 

  combinators for dealing with specific token types, which are defined in the 

  structure @{ML_struct OuterParse} in the file 

  @{ML_file "Pure/Isar/outer_parse.ML"}.

  \end{readmore}

*}

section {* Building Generic Parsers *}

text {*

  Let us first have a look at parsing strings using generic parsing combinators. 

  The function @{ML "$$"} takes a string as argument and will ``consume'' this string from 

  a given input list of strings. ``Consume'' in this context means that it will 

  return a pair consisting of this string and the rest of the input list. 

  For example:

  @{ML_response [display,gray] "($$ \"h\") (explode \"hello\")" "(\"h\", [\"e\", \"l\", \"l\", \"o\"])"}

  @{ML_response [display,gray] "($$ \"w\") (explode \"world\")" "(\"w\", [\"o\", \"r\", \"l\", \"d\"])"}

  This function will either succeed (as in the two examples above) or raise the exception 

  @{text "FAIL"} if no string can be consumed. For example trying to parse

  @{ML_response_fake [display,gray] "($$ \"x\") (explode \"world\")" 

                               "Exception FAIL raised"}

  will raise the exception @{text "FAIL"}.

  There are three exceptions used in the parsing combinators:

  \begin{itemize}

  \item @{text "FAIL"} is used to indicate that alternative routes of parsing 

  might be explored. 

  \item @{text "MORE"} indicates that there is not enough input for the parser. For example 

  in @{text "($$ \"h\") []"}.

  \item @{text "ABORT"} is the exception that is raised when a dead end is reached. 

  It is used for example in the function @{ML "!!"} (see below).

  \end{itemize}

  However, note that these exceptions are private to the parser and cannot be accessed

  by the programmer (for example to handle them).

  Slightly more general than the parser @{ML "$$"} is the function @{ML

  Scan.one}, in that it takes a predicate as argument and then parses exactly

  one item from the input list satisfying this predicate. For example the

  following parser either consumes an @{text [quotes] "h"} or a @{text

  [quotes] "w"}:

@{ML_response [display,gray] 

"let 

  val hw = Scan.one (fn x => x = \"h\" orelse x = \"w\")

  val input1 = (explode \"hello\")

  val input2 = (explode \"world\")

in

    (hw input1, hw input2)

end"

    "((\"h\", [\"e\", \"l\", \"l\", \"o\"]),(\"w\", [\"o\", \"r\", \"l\", \"d\"]))"}

  Two parser can be connected in sequence by using the function @{ML "--"}. 

  For example parsing @{text "h"}, @{text "e"} and @{text "l"} in this 

  sequence you can achieve by:

  @{ML_response [display,gray] "(($$ \"h\") -- ($$ \"e\") -- ($$ \"l\")) (explode \"hello\")"

                          "(((\"h\", \"e\"), \"l\"), [\"l\", \"o\"])"}

  Note how the result of consumed strings builds up on the left as nested pairs.  

  If, as in the previous example, you want to parse a particular string, 

  then one should use the function @{ML Scan.this_string}:

  @{ML_response [display,gray] "Scan.this_string \"hell\" (explode \"hello\")"

                          "(\"hell\", [\"o\"])"}

  Parsers that explore alternatives can be constructed using the function @{ML

  "||"}. For example, the parser @{ML "(p || q)" for p q} returns the

  result of @{text "p"}, in case it succeeds, otherwise it returns the

  result of @{text "q"}. For example:

@{ML_response [display,gray] 

"let 

  val hw = ($$ \"h\") || ($$ \"w\")

  val input1 = (explode \"hello\")

  val input2 = (explode \"world\")

in

  (hw input1, hw input2)

end"

  "((\"h\", [\"e\", \"l\", \"l\", \"o\"]), (\"w\", [\"o\", \"r\", \"l\", \"d\"]))"}

  The functions @{ML "|--"} and @{ML "--|"} work like the sequencing function 

  for parsers, except that they discard the item being parsed by the first (respectively second)

  parser. For example:

@{ML_response [display,gray]

"let 

  val just_e = ($$ \"h\") |-- ($$ \"e\") 

  val just_h = ($$ \"h\") --| ($$ \"e\") 

  val input = (explode \"hello\")  

in 

  (just_e input, just_h input)

end"

  "((\"e\", [\"l\", \"l\", \"o\"]),(\"h\", [\"l\", \"l\", \"o\"]))"}

  The parser @{ML "Scan.optional p x" for p x} returns the result of the parser 

  @{text "p"}, if it succeeds; otherwise it returns 

  the default value @{text "x"}. For example:

@{ML_response [display,gray]

"let 

  val p = Scan.optional ($$ \"h\") \"x\"

  val input1 = (explode \"hello\")

  val input2 = (explode \"world\")  

in 

  (p input1, p input2)

end" 

 "((\"h\", [\"e\", \"l\", \"l\", \"o\"]), (\"x\", [\"w\", \"o\", \"r\", \"l\", \"d\"]))"}

  The function @{ML Scan.option} works similarly, except no default value can

  be given. Instead, the result is wrapped as an @{text "option"}-type. For example:

@{ML_response [display,gray]

"let 

  val p = Scan.option ($$ \"h\")

  val input1 = (explode \"hello\")

  val input2 = (explode \"world\")  

in 

  (p input1, p input2)

end" "((SOME \"h\", [\"e\", \"l\", \"l\", \"o\"]), (NONE, [\"w\", \"o\", \"r\", \"l\", \"d\"]))"}

  The function @{ML "!!"} helps to produce appropriate error messages

  during parsing. For example if you want to parse that @{text p} is immediately 

  followed by @{text q}, or start a completely different parser @{text r},

  you might write:

  @{ML [display,gray] "(p -- q) || r" for p q r}

  However, this parser is problematic for producing an appropriate error

  message, in case the parsing of @{ML "(p -- q)" for p q} fails. Because in

  that case you lose the information that @{text p} should be followed by

  @{text q}. To see this consider the case in which @{text p} is present in

  the input, but not @{text q}. That means @{ML "(p -- q)" for p q} will fail

  and the alternative parser @{text r} will be tried. However in many

  circumstance this will be the wrong parser for the input ``p-followed-by-q''

  and therefore will also fail. The error message is then caused by the

  failure of @{text r}, not by the absence of @{text q} in the input. This

  kind of situation can be avoided when using the function @{ML "!!"}. 

  This function aborts the whole process of parsing in case of a

  failure and prints an error message. For example if you invoke the parser

  @{ML [display,gray] "(!! (fn _ => \"foo\") ($$ \"h\"))"}

  on @{text [quotes] "hello"}, the parsing succeeds

  @{ML_response [display,gray] 

                "(!! (fn _ => \"foo\") ($$ \"h\")) (explode \"hello\")" 

                "(\"h\", [\"e\", \"l\", \"l\", \"o\"])"}

  but if you invoke it on @{text [quotes] "world"}

  @{ML_response_fake [display,gray] "(!! (fn _ => \"foo\") ($$ \"h\")) (explode \"world\")"

                               "Exception ABORT raised"}

  then the parsing aborts and the error message @{text "foo"} is printed. In order to

  see the error message properly, you need to prefix the parser with the function 

  @{ML "Scan.error"}. For example:

  @{ML_response_fake [display,gray] "Scan.error (!! (fn _ => \"foo\") ($$ \"h\"))"

                               "Exception Error \"foo\" raised"}

  This ``prefixing'' is usually done by wrappers such as @{ML "OuterSyntax.command"} 

  (see Section~\ref{sec:newcommand} which explains this function in more detail). 

  Let us now return to our example of parsing @{ML "(p -- q) || r" for p q

  r}. If you want to generate the correct error message for p-followed-by-q,

  then you have to write:

*}

ML{*fun p_followed_by_q p q r =

  let 

     val err_msg = (fn _ => p ^ " is not followed by " ^ q)

  in

    ($$ p -- (!! err_msg ($$ q))) || ($$ r -- $$ r)

  end *}

text {*

  Running this parser with the @{text [quotes] "h"} and @{text [quotes] "e"}, and 

  the input @{text [quotes] "holle"} 

  @{ML_response_fake [display,gray] "Scan.error (p_followed_by_q \"h\" \"e\" \"w\") (explode \"holle\")"

                               "Exception ERROR \"h is not followed by e\" raised"} 

  produces the correct error message. Running it with

  @{ML_response [display,gray] "Scan.error (p_followed_by_q \"h\" \"e\" \"w\") (explode \"wworld\")"

                          "((\"w\", \"w\"), [\"o\", \"r\", \"l\", \"d\"])"}

  yields the expected parsing. 

  The function @{ML "Scan.repeat p" for p} will apply a parser @{text p} as 

  often as it succeeds. For example:

  @{ML_response [display,gray] "Scan.repeat ($$ \"h\") (explode \"hhhhello\")" 

                "([\"h\", \"h\", \"h\", \"h\"], [\"e\", \"l\", \"l\", \"o\"])"}

  Note that @{ML "Scan.repeat"} stores the parsed items in a list. The function

  @{ML "Scan.repeat1"} is similar, but requires that the parser @{text "p"} 

  succeeds at least once.

  Also note that the parser would have aborted with the exception @{text MORE}, if

  you had run it only on just @{text [quotes] "hhhh"}. This can be avoided by using

  the wrapper @{ML Scan.finite} and the ``stopper-token'' @{ML Symbol.stopper}. With

  them you can write:

  @{ML_response [display,gray] "Scan.finite Symbol.stopper (Scan.repeat ($$ \"h\")) (explode \"hhhh\")" 

                "([\"h\", \"h\", \"h\", \"h\"], [])"}

  @{ML Symbol.stopper} is the ``end-of-input'' indicator for parsing strings;

  other stoppers need to be used when parsing tokens, for example. However, this kind of 

  manually wrapping is often already done by the surrounding infrastructure. 

  The function @{ML Scan.repeat} can be used with @{ML Scan.one} to read any 

  string as in

  @{ML_response [display,gray] 

"let 

   val p = Scan.repeat (Scan.one Symbol.not_eof)

   val input = (explode \"foo bar foo\") 

in

   Scan.finite Symbol.stopper p input

end" 

"([\"f\", \"o\", \"o\", \" \", \"b\", \"a\", \"r\", \" \", \"f\", \"o\", \"o\"], [])"}

  where the function @{ML Symbol.not_eof} ensures that we do not read beyond the 

  end of the input string (i.e.~stopper symbol).

  The function @{ML "Scan.unless p q" for p q} takes two parsers: if the first one can 

  parse the input, then the whole parser fails; if not, then the second is tried. Therefore

  @{ML_response_fake_both [display,gray] "Scan.unless ($$ \"h\") ($$ \"w\") (explode \"hello\")"

                               "Exception FAIL raised"}

  fails, while

  @{ML_response [display,gray] "Scan.unless ($$ \"h\") ($$ \"w\") (explode \"world\")"

                          "(\"w\",[\"o\", \"r\", \"l\", \"d\"])"}

  succeeds. 

  The functions @{ML Scan.repeat} and @{ML Scan.unless} can be combined to read any

  input until a certain marker symbol is reached. In the example below the marker

  symbol is a @{text [quotes] "*"}.

  @{ML_response [display,gray]

"let 

  val p = Scan.repeat (Scan.unless ($$ \"*\") (Scan.one Symbol.not_eof))

  val input1 = (explode \"fooooo\")

  val input2 = (explode \"foo*ooo\")

in

  (Scan.finite Symbol.stopper p input1, 

   Scan.finite Symbol.stopper p input2)

end"

"(([\"f\", \"o\", \"o\", \"o\", \"o\", \"o\"], []),

 ([\"f\", \"o\", \"o\"], [\"*\", \"o\", \"o\", \"o\"]))"}

  After parsing is done, you nearly always want to apply a function on the parsed 

  items. One way to do this is the function @{ML "(p >> f)" for p f}, which runs 

  first the parser @{text p} and upon successful completion applies the 

  function @{text f} to the result. For example

@{ML_response [display,gray]

"let 

  fun double (x,y) = (x ^ x, y ^ y) 

in

  (($$ \"h\") -- ($$ \"e\") >> double) (explode \"hello\")

end"

"((\"hh\", \"ee\"), [\"l\", \"l\", \"o\"])"}

  doubles the two parsed input strings; or

  @{ML_response [display,gray] 

"let 

   val p = Scan.repeat (Scan.one Symbol.not_eof)

   val input = (explode \"foo bar foo\") 

in

   Scan.finite Symbol.stopper (p >> implode) input

end" 

"(\"foo bar foo\",[])"}

  where the single-character strings in the parsed output are transformed

  back into one string.

  \begin{exercise}\label{ex:scancmts}

  Write a parser that parses an input string so that any comment enclosed

  inside @{text "(*\<dots>*)"} is replaced by a the same comment but enclosed inside

  @{text "(**\<dots>**)"} in the output string. To enclose a string, you can use the

  function @{ML "enclose s1 s2 s" for s1 s2 s} which produces the string @{ML

  "s1 ^ s ^ s2" for s1 s2 s}.

  \end{exercise}

  The function @{ML Scan.ahead} parses some input, but leaves the original

  input unchanged. For example:

  @{ML_response [display,gray]

  "Scan.ahead (Scan.this_string \"foo\") (explode \"foo\")" 

  "(\"foo\", [\"f\", \"o\", \"o\"])"} 

  The function @{ML Scan.lift} takes a parser and a pair as arguments. This function applies

  the given parser to the second component of the pair and leaves the  first component 

  untouched. For example

@{ML_response [display,gray]

"Scan.lift (($$ \"h\") -- ($$ \"e\")) (1,(explode \"hello\"))"

"((\"h\", \"e\"), (1, [\"l\", \"l\", \"o\"]))"}

  (FIXME: In which situations is this useful? Give examples.) 

*}

section {* Parsing Theory Syntax *}

text {*

  Most of the time, however, Isabelle developers have to deal with parsing

  tokens, not strings.  This is because the parsers for the theory syntax, as

  well as the parsers for the arguments of proof methods the type @{ML_type OuterLex.token} 

  (which is identical to the type @{ML_type OuterParse.token}).  There are also handy 

  parsers for ML-expressions and ML-files.

  \begin{readmore}

  The parser functions for the theory syntax are contained in the structure

  @{ML_struct OuterParse} defined in the file @{ML_file  "Pure/Isar/outer_parse.ML"}.

  The definition for tokens is in the file @{ML_file "Pure/Isar/outer_lex.ML"}.

  \end{readmore}

  The structure @{ML_struct OuterLex} defines several kinds of tokens (for example 

  @{ML "Ident" in OuterLex} for identifiers, @{ML "Keyword" in OuterLex} for keywords and

  @{ML "Command" in OuterLex} for commands). Some token parsers take into account the 

  kind of tokens.

*}  

text {*

  The first example shows how to generate a token list out of a string using

  the function @{ML "OuterSyntax.scan"}. It is given below @{ML "Position.none"}

  as argument since, at the moment, we are not interested in generating

  precise error messages. The following code

@{ML_response_fake [display,gray] "OuterSyntax.scan Position.none \"hello world\"" 

"[Token (\<dots>,(Ident, \"hello\"),\<dots>), 

 Token (\<dots>,(Space, \" \"),\<dots>), 

 Token (\<dots>,(Ident, \"world\"),\<dots>)]"}

  produces three tokens where the first and the last are identifiers, since

  @{text [quotes] "hello"} and @{text [quotes] "world"} do not match any

  other syntactic category.\footnote{Note that because of a possible a bug in

  the PolyML runtime system the result is printed as @{text [quotes] "?"}, instead of

  the tokens.} The second indicates a space.

  Many parsing functions later on will require spaces, comments and the like

  to have already been filtered out.  So from now on we are going to use the 

  functions @{ML filter} and @{ML OuterLex.is_proper} do this. For example:

@{ML_response_fake [display,gray]

"let

   val input = OuterSyntax.scan Position.none \"hello world\"

in

   filter OuterLex.is_proper input

end" 

"[Token (\<dots>,(Ident, \"hello\"), \<dots>), Token (\<dots>,(Ident, \"world\"), \<dots>)]"}

  For convenience we define the function:

*}

ML{*fun filtered_input str = 

       filter OuterLex.is_proper (OuterSyntax.scan Position.none str) *}

text {*

  If you now parse

@{ML_response_fake [display,gray] 

"filtered_input \"inductive | for\"" 

"[Token (\<dots>,(Command, \"inductive\"),\<dots>), 

 Token (\<dots>,(Keyword, \"|\"),\<dots>), 

 Token (\<dots>,(Keyword, \"for\"),\<dots>)]"}

  you obtain a list consisting of only a command and two keyword tokens.

  If you want to see which keywords and commands are currently known to Isabelle, type in

  the following code (you might have to adjust the @{ML print_depth} in order to

  see the complete list):

@{ML_response_fake [display,gray] 

"let 

  val (keywords, commands) = OuterKeyword.get_lexicons ()

in 

  (Scan.dest_lexicon commands, Scan.dest_lexicon keywords)

end" 

"([\"}\",\"{\",\<dots>],[\"\<rightleftharpoons>\",\"\<leftharpoondown>\",\<dots>])"}

  The parser @{ML "OuterParse.$$$"} parses a single keyword. For example:

@{ML_response [display,gray]

"let 

  val input1 = filtered_input \"where for\"

  val input2 = filtered_input \"| in\"

in 

  (OuterParse.$$$ \"where\" input1, OuterParse.$$$ \"|\" input2)

end"

"((\"where\",\<dots>),(\"|\",\<dots>))"}

  Like before, you can sequentially connect parsers with @{ML "--"}. For example: 

@{ML_response [display,gray]

"let 

  val input = filtered_input \"| in\"

in 

  (OuterParse.$$$ \"|\" -- OuterParse.$$$ \"in\") input

end"

"((\"|\",\"in\"),[])"}

  The parser @{ML "OuterParse.enum s p" for s p} parses a possibly empty 

  list of items recognised by the parser @{text p}, where the items being parsed

  are separated by the string @{text s}. For example:

@{ML_response [display,gray]

"let 

  val input = filtered_input \"in | in | in foo\"

in 

  (OuterParse.enum \"|\" (OuterParse.$$$ \"in\")) input

end" 

"([\"in\",\"in\",\"in\"],[\<dots>])"}

  @{ML "OuterParse.enum1"} works similarly, except that the parsed list must

  be non-empty. Note that we had to add a string @{text [quotes] "foo"} at the

  end of the parsed string, otherwise the parser would have consumed all

  tokens and then failed with the exception @{text "MORE"}. Like in the

  previous section, we can avoid this exception using the wrapper @{ML

  Scan.finite}. This time, however, we have to use the ``stopper-token'' @{ML

  OuterLex.stopper}. We can write:

@{ML_response [display,gray]

"let 

  val input = filtered_input \"in | in | in\"

in 

  Scan.finite OuterLex.stopper 

         (OuterParse.enum \"|\" (OuterParse.$$$ \"in\")) input

end" 

"([\"in\",\"in\",\"in\"],[])"}

  The following function will help to run examples.