--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/ProgTutorial/Parsing.thy Thu Mar 19 13:28:16 2009 +0100
@@ -0,0 +1,1684 @@
+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, 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] "($$ \"w\") (explode \"world\")" "(\"w\", [\"o\", \"r\", \"l\", \"d\"])"}
+
+ The function @{ML "$$"} 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 you 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, for example, tokens. 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\") -- ($$ \"e\") >> double) (explode \"hello\")
+end"
+"((\"hh\", \"ee\"), [\"l\", \"l\", \"o\"])"}
+
+ doubles the two parsed input strings; or
+
+ @{ML_response [display,gray]
+"let
+ val p = Scan.repeat (Scan.one Symbol.not_eof)
+ val input = (explode \"foo bar foo\")
+in
+ Scan.finite Symbol.stopper (p >> implode) input
+end"
+"(\"foo bar foo\",[])"}
+
+ where the single-character strings in the parsed output are transformed
+ back into one string.
+
+ The function @{ML Scan.ahead} parses some input, but leaves the original
+ input unchanged. For example:
+
+ @{ML_response [display,gray]
+ "Scan.ahead (Scan.this_string \"foo\") (explode \"foo\")"
+ "(\"foo\", [\"f\", \"o\", \"o\"])"}
+
+ The function @{ML Scan.lift} takes a parser and a pair as arguments. This function applies
+ the given parser to the second component of the pair and leaves the first component
+ untouched. For example
+
+@{ML_response [display,gray]
+"Scan.lift (($$ \"h\") -- ($$ \"e\")) (1,(explode \"hello\"))"
+"((\"h\", \"e\"), (1, [\"l\", \"l\", \"o\"]))"}
+
+ (FIXME: In which situations is this useful? Give examples.)
+
+ \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}
+*}
+
+section {* Parsing Theory Syntax *}
+
+text {*
+ (FIXME: context parser)
+
+ Most of the time, however, Isabelle developers have to deal with parsing
+ tokens, not strings. These token parsers have the type:
+*}
+
+ML{*type 'a parser = OuterLex.token list -> 'a * OuterLex.token list*}
+
+text {*
+ The reason for using token parsers is that theory syntax, as well as the
+ parsers for the arguments of proof methods, use the type @{ML_type
+ OuterLex.token} (which is identical to the type @{ML_type
+ OuterParse.token}). However, 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 the argument @{ML "Position.none"}
+ 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.
+
+*}
+
+ML{*fun parse p input = Scan.finite OuterLex.stopper (Scan.error p) input *}
+
+text {*
+
+ The function @{ML "OuterParse.!!!"} can be used to force termination of the
+ parser in case of a dead end, just like @{ML "Scan.!!"} (see previous section),
+ except that the error message is fixed to be @{text [quotes] "Outer syntax error"}
+ with a relatively precise description of the failure. For example:
+
+@{ML_response_fake [display,gray]
+"let
+ val input = filtered_input \"in |\"
+ val parse_bar_then_in = OuterParse.$$$ \"|\" -- OuterParse.$$$ \"in\"
+in
+ parse (OuterParse.!!! parse_bar_then_in) input
+end"
+"Exception ERROR \"Outer syntax error: keyword \"|\" expected,
+but keyword in was found\" raised"
+}
+
+ \begin{exercise} (FIXME)
+ A type-identifier, for example @{typ "'a"}, is a token of
+ kind @{ML "Keyword" in OuterLex}. It can be parsed using
+ the function @{ML OuterParse.type_ident}.
+ \end{exercise}
+
+ (FIXME: or give parser for numbers)
+
+ Whenever there is a possibility that the processing of user input can fail,
+ it is a good idea to give as much information about where the error
+ occured. For this Isabelle can attach positional information to tokens
+ and then thread this information up the processing chain. To see this,
+ modify the function @{ML filtered_input} described earlier to
+*}
+
+ML{*fun filtered_input' str =
+ filter OuterLex.is_proper (OuterSyntax.scan (Position.line 7) str) *}
+
+text {*
+ where we pretend the parsed string starts on line 7. An example is
+
+@{ML_response_fake [display,gray]
+"filtered_input' \"foo \\n bar\""
+"[Token ((\"foo\", ({line=7, end_line=7}, {line=7})), (Ident, \"foo\"), \<dots>),
+ Token ((\"bar\", ({line=8, end_line=8}, {line=8})), (Ident, \"bar\"), \<dots>)]"}
+
+ in which the @{text [quotes] "\\n"} causes the second token to be in
+ line 8.
+
+ By using the parser @{ML OuterParse.position} you can decode the positional
+ information and return it as part of the parsed input. For example
+
+@{ML_response_fake [display,gray]
+"let
+ val input = (filtered_input' \"where\")
+in
+ parse (OuterParse.position (OuterParse.$$$ \"where\")) input
+end"
+"((\"where\", {line=7, end_line=7}), [])"}
+
+ \begin{readmore}
+ The functions related to positions are implemented in the file
+ @{ML_file "Pure/General/position.ML"}.
+ \end{readmore}
+
+*}
+
+section {* Parsing Inner Syntax *}
+
+text {*
+ There is usually no need to write your own parser for parsing inner syntax, that is
+ for terms and types: you can just call the pre-defined parsers. Terms can
+ be parsed using the function @{ML OuterParse.term}. For example:
+
+@{ML_response [display,gray]
+"let
+ val input = OuterSyntax.scan Position.none \"foo\"
+in
+ OuterParse.term input
+end"
+"(\"\\^E\\^Ftoken\\^Efoo\\^E\\^F\\^E\", [])"}
+
+ The function @{ML OuterParse.prop} is similar, except that it gives a different
+ error message, when parsing fails. As you can see, the parser not just returns
+ the parsed string, but also some encoded information. You can decode the
+ information with the function @{ML YXML.parse}. For example
+
+ @{ML_response [display,gray]
+ "YXML.parse \"\\^E\\^Ftoken\\^Efoo\\^E\\^F\\^E\""
+ "XML.Elem (\"token\", [], [XML.Text \"foo\"])"}
+
+ The result of the decoding is an XML-tree. You can see better what is going on if
+ you replace @{ML Position.none} by @{ML "Position.line 42"}, say:
+
+@{ML_response [display,gray]
+"let
+ val input = OuterSyntax.scan (Position.line 42) \"foo\"
+in
+ YXML.parse (fst (OuterParse.term input))
+end"
+"XML.Elem (\"token\", [(\"line\", \"42\"), (\"end_line\", \"42\")], [XML.Text \"foo\"])"}
+
+ The positional information is stored as part of an XML-tree so that code
+ called later on will be able to give more precise error messages.
+
+ \begin{readmore}
+ The functions to do with input and output of XML and YXML are defined
+ in @{ML_file "Pure/General/xml.ML"} and @{ML_file "Pure/General/yxml.ML"}.
+ \end{readmore}
+
+*}
+
+section {* Parsing Specifications\label{sec:parsingspecs} *}
+
+text {*
+ There are a number of special purpose parsers that help with parsing
+ specifications of function definitions, inductive predicates and so on. In
+ Capter~\ref{chp:package}, for example, we will need to parse specifications
+ for inductive predicates of the form:
+*}
+
+simple_inductive
+ even and odd
+where
+ even0: "even 0"
+| evenS: "odd n \<Longrightarrow> even (Suc n)"
+| oddS: "even n \<Longrightarrow> odd (Suc n)"
+
+text {*
+ For this we are going to use the parser:
+*}
+
+ML %linenosgray{*val spec_parser =
+ OuterParse.fixes --
+ Scan.optional
+ (OuterParse.$$$ "where" |--
+ OuterParse.!!!
+ (OuterParse.enum1 "|"
+ (SpecParse.opt_thm_name ":" -- OuterParse.prop))) []*}
+
+text {*
+ Note that the parser does not parse the keyword \simpleinductive, even if it is
+ meant to process definitions as shown above. The parser of the keyword
+ will be given by the infrastructure that will eventually call @{ML spec_parser}.
+
+
+ To see what the parser returns, let us parse the string corresponding to the
+ definition of @{term even} and @{term odd}:
+
+@{ML_response [display,gray]
+"let
+ val input = filtered_input
+ (\"even and odd \" ^
+ \"where \" ^
+ \" even0[intro]: \\\"even 0\\\" \" ^
+ \"| evenS[intro]: \\\"odd n \<Longrightarrow> even (Suc n)\\\" \" ^
+ \"| oddS[intro]: \\\"even n \<Longrightarrow> odd (Suc n)\\\"\")
+in
+ parse spec_parser input
+end"
+"(([(even, NONE, NoSyn), (odd, NONE, NoSyn)],
+ [((even0,\<dots>), \"\\^E\\^Ftoken\\^Eeven 0\\^E\\^F\\^E\"),
+ ((evenS,\<dots>), \"\\^E\\^Ftoken\\^Eodd n \<Longrightarrow> even (Suc n)\\^E\\^F\\^E\"),
+ ((oddS,\<dots>), \"\\^E\\^Ftoken\\^Eeven n \<Longrightarrow> odd (Suc n)\\^E\\^F\\^E\")]), [])"}
+
+ As you see, the result is a pair consisting of a list of
+ variables with optional type-annotation and syntax-annotation, and a list of
+ rules where every rule has optionally a name and an attribute.
+
+ The function @{ML OuterParse.fixes} in Line 2 of the parser reads an
+ \isacommand{and}-separated
+ list of variables that can include optional type annotations and syntax translations.
+ For example:\footnote{Note that in the code we need to write
+ @{text "\\\"int \<Rightarrow> bool\\\""} in order to properly escape the double quotes
+ in the compound type.}
+
+@{ML_response [display,gray]
+"let
+ val input = filtered_input
+ \"foo::\\\"int \<Rightarrow> bool\\\" and bar::nat (\\\"BAR\\\" 100) and blonk\"
+in
+ parse OuterParse.fixes input
+end"
+"([(foo, SOME \"\\^E\\^Ftoken\\^Eint \<Rightarrow> bool\\^E\\^F\\^E\", NoSyn),
+ (bar, SOME \"\\^E\\^Ftoken\\^Enat\\^E\\^F\\^E\", Mixfix (\"BAR\", [], 100)),
+ (blonk, NONE, NoSyn)],[])"}
+*}
+
+text {*
+ Whenever types are given, they are stored in the @{ML SOME}s. The types are
+ not yet used to type the variables: this must be done by type-inference later
+ on. Since types are part of the inner syntax they are strings with some
+ encoded information (see previous section). If a syntax translation is
+ present for a variable, then it is stored in the @{ML Mixfix} datastructure;
+ no syntax translation is indicated by @{ML NoSyn}.
+
+ \begin{readmore}
+ The datastructre for sytax annotations is defined in @{ML_file "Pure/Syntax/mixfix.ML"}.
+ \end{readmore}
+
+ Lines 3 to 7 in the function @{ML spec_parser} implement the parser for a
+ list of introduction rules, that is propositions with theorem
+ annotations. The introduction rules are propositions parsed by @{ML
+ OuterParse.prop}. However, they can include an optional theorem name plus
+ some attributes. For example
+
+@{ML_response [display,gray] "let
+ val input = filtered_input \"foo_lemma[intro,dest!]:\"
+ val ((name, attrib), _) = parse (SpecParse.thm_name \":\") input
+in
+ (name, map Args.dest_src attrib)
+end" "(foo_lemma, [((\"intro\", []), \<dots>), ((\"dest\", [\<dots>]), \<dots>)])"}
+
+ The function @{ML opt_thm_name in SpecParse} is the ``optional'' variant of
+ @{ML thm_name in SpecParse}. Theorem names can contain attributes. The name
+ has to end with @{text [quotes] ":"}---see the argument of
+ the function @{ML SpecParse.opt_thm_name} in Line 7.
+
+ \begin{readmore}
+ Attributes and arguments are implemented in the files @{ML_file "Pure/Isar/attrib.ML"}
+ and @{ML_file "Pure/Isar/args.ML"}.
+ \end{readmore}
+*}
+
+section {* New Commands and Keyword Files\label{sec:newcommand} *}
+
+text {*
+ (FIXME: update to the right command setup)
+
+ Often new commands, for example for providing new definitional principles,
+ need to be implemented. While this is not difficult on the ML-level,
+ new commands, in order to be useful, need to be recognised by
+ ProofGeneral. This results in some subtle configuration issues, which we
+ will explain in this section.
+
+ To keep things simple, let us start with a ``silly'' command that does nothing
+ at all. We shall name this command \isacommand{foobar}. On the ML-level it can be
+ defined as:
+*}
+
+ML{*let
+ val do_nothing = Scan.succeed (Toplevel.theory I)
+ val kind = OuterKeyword.thy_decl
+in
+ OuterSyntax.command "foobar" "description of foobar" kind do_nothing
+end *}
+
+text {*
+ The crucial function @{ML OuterSyntax.command} expects a name for the command, a
+ short description, a kind indicator (which we will explain later on more thoroughly) and a
+ parser producing a top-level transition function (its purpose will also explained
+ later).
+
+ While this is everything you have to do on the ML-level, you need a keyword
+ file that can be loaded by ProofGeneral. This is to enable ProofGeneral to
+ recognise \isacommand{foobar} as a command. Such a keyword file can be
+ generated with the command-line:
+
+ @{text [display] "$ isabelle keywords -k foobar some_log_files"}
+
+ The option @{text "-k foobar"} indicates which postfix the name of the keyword file
+ will be assigned. In the case above the file will be named @{text
+ "isar-keywords-foobar.el"}. This command requires log files to be
+ present (in order to extract the keywords from them). To generate these log
+ files, you first need to package the code above into a separate theory file named
+ @{text "Command.thy"}, say---see Figure~\ref{fig:commandtheory} for the
+ complete code.
+
+
+ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+ \begin{figure}[t]
+ \begin{graybox}\small
+ \isacommand{theory}~@{text Command}\\
+ \isacommand{imports}~@{text Main}\\
+ \isacommand{begin}\\
+ \isacommand{ML}~@{text "\<verbopen>"}\\
+ @{ML
+"let
+ val do_nothing = Scan.succeed (Toplevel.theory I)
+ val kind = OuterKeyword.thy_decl
+in
+ OuterSyntax.command \"foobar\" \"description of foobar\" kind do_nothing
+end"}\\
+ @{text "\<verbclose>"}\\
+ \isacommand{end}
+ \end{graybox}
+ \caption{\small The file @{text "Command.thy"} is necessary for generating a log
+ file. This log file enables Isabelle to generate a keyword file containing
+ the command \isacommand{foobar}.\label{fig:commandtheory}}
+ \end{figure}
+ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+ For our purposes it is sufficient to use the log files of the theories
+ @{text "Pure"}, @{text "HOL"} and @{text "Pure-ProofGeneral"}, as well as
+ the log file for the theory @{text "Command.thy"}, which contains the new
+ \isacommand{foobar}-command. If you target other logics besides HOL, such
+ as Nominal or ZF, then you need to adapt the log files appropriately.
+
+ @{text Pure} and @{text HOL} are usually compiled during the installation of
+ Isabelle. So log files for them should be already available. If not, then
+ they can be conveniently compiled with the help of the build-script from the Isabelle
+ distribution.
+
+ @{text [display]
+"$ ./build -m \"Pure\"
+$ ./build -m \"HOL\""}
+
+ The @{text "Pure-ProofGeneral"} theory needs to be compiled with:
+
+ @{text [display] "$ ./build -m \"Pure-ProofGeneral\" \"Pure\""}
+
+ For the theory @{text "Command.thy"}, you first need to create a ``managed'' subdirectory
+ with:
+
+ @{text [display] "$ isabelle mkdir FoobarCommand"}
+
+ This generates a directory containing the files:
+
+ @{text [display]
+"./IsaMakefile
+./FoobarCommand/ROOT.ML
+./FoobarCommand/document
+./FoobarCommand/document/root.tex"}
+
+
+ You need to copy the file @{text "Command.thy"} into the directory @{text "FoobarCommand"}
+ and add the line
+
+ @{text [display] "use_thy \"Command\";"}
+
+ to the file @{text "./FoobarCommand/ROOT.ML"}. You can now compile the theory by just typing:
+
+ @{text [display] "$ isabelle make"}
+
+ If the compilation succeeds, you have finally created all the necessary log files.
+ They are stored in the directory
+
+ @{text [display] "~/.isabelle/heaps/Isabelle2008/polyml-5.2.1_x86-linux/log"}
+
+ or something similar depending on your Isabelle distribution and architecture.
+ One quick way to assign a shell variable to this directory is by typing
+
+ @{text [display] "$ ISABELLE_LOGS=\"$(isabelle getenv -b ISABELLE_OUTPUT)\"/log"}
+
+ on the Unix prompt. If you now type @{text "ls $ISABELLE_LOGS"}, then the
+ directory should include the files:
+
+ @{text [display]
+"Pure.gz
+HOL.gz
+Pure-ProofGeneral.gz
+HOL-FoobarCommand.gz"}
+
+ From them you can create the keyword files. Assuming the name
+ of the directory is in @{text "$ISABELLE_LOGS"},
+ then the Unix command for creating the keyword file is:
+
+@{text [display]
+"$ isabelle keywords -k foobar
+ $ISABELLE_LOGS/{Pure.gz,HOL.gz,Pure-ProofGeneral.gz,HOL-FoobarCommand.gz}"}
+
+ The result is the file @{text "isar-keywords-foobar.el"}. It should contain
+ the string @{text "foobar"} twice.\footnote{To see whether things are fine, check
+ that @{text "grep foobar"} on this file returns something
+ non-empty.} This keyword file needs to
+ be copied into the directory @{text "~/.isabelle/etc"}. To make Isabelle
+ aware of this keyword file, you have to start Isabelle with the option @{text
+ "-k foobar"}, that is:
+
+
+ @{text [display] "$ isabelle emacs -k foobar a_theory_file"}
+
+ If you now build a theory on top of @{text "Command.thy"},
+ then the command \isacommand{foobar} can be used.
+ Similarly with any other new command.
+
+
+ At the moment \isacommand{foobar} is not very useful. Let us refine it a bit
+ next by letting it take a proposition as argument and printing this proposition
+ inside the tracing buffer.
+
+ The crucial part of a command is the function that determines the behaviour
+ of the command. In the code above we used a ``do-nothing''-function, which
+ because of @{ML Scan.succeed} does not parse any argument, but immediately
+ returns the simple toplevel function @{ML "Toplevel.theory I"}. We can
+ replace this code by a function that first parses a proposition (using the
+ parser @{ML OuterParse.prop}), then prints out the tracing
+ information (using a new top-level function @{text trace_top_lvl}) and
+ finally does nothing. For this you can write:
+*}
+
+ML{*let
+ fun trace_top_lvl str =
+ Toplevel.theory (fn thy => (tracing str; thy))
+
+ val trace_prop = OuterParse.prop >> trace_top_lvl
+
+ val kind = OuterKeyword.thy_decl
+in
+ OuterSyntax.command "foobar" "traces a proposition" kind trace_prop
+end *}
+
+text {*
+ Now you can type
+
+ \begin{isabelle}
+ \isacommand{foobar}~@{text [quotes] "True \<and> False"}\\
+ @{text "> \"True \<and> False\""}
+ \end{isabelle}
+
+ and see the proposition in the tracing buffer.
+
+ Note that so far we used @{ML thy_decl in OuterKeyword} as the kind indicator
+ for the command. This means that the command finishes as soon as the
+ arguments are processed. Examples of this kind of commands are
+ \isacommand{definition} and \isacommand{declare}. In other cases,
+ commands are expected to parse some arguments, for example a proposition,
+ and then ``open up'' a proof in order to prove the proposition (for example
+ \isacommand{lemma}) or prove some other properties (for example
+ \isacommand{function}). To achieve this kind of behaviour, you have to use the kind
+ indicator @{ML thy_goal in OuterKeyword}. Note, however, once you change the
+ ``kind'' of a command from @{ML thy_decl in OuterKeyword} to @{ML thy_goal in OuterKeyword}
+ then the keyword file needs to be re-created!
+
+ Below we change \isacommand{foobar} so that it takes a proposition as
+ argument and then starts a proof in order to prove it. Therefore in Line 13,
+ we set the kind indicator to @{ML thy_goal in OuterKeyword}.
+*}
+
+ML%linenosgray{*let
+ fun set_up_thm str ctxt =
+ let
+ val prop = Syntax.read_prop ctxt str
+ in
+ Proof.theorem_i NONE (K I) [[(prop,[])]] ctxt
+ end;
+
+ val prove_prop = OuterParse.prop >>
+ (fn str => Toplevel.print o
+ Toplevel.local_theory_to_proof NONE (set_up_thm str))
+
+ val kind = OuterKeyword.thy_goal
+in
+ OuterSyntax.command "foobar" "proving a proposition" kind prove_prop
+end *}
+
+text {*
+ The function @{text set_up_thm} in Lines 2 to 7 takes a string (the proposition to be
+ proved) and a context as argument. The context is necessary in order to be able to use
+ @{ML Syntax.read_prop}, which converts a string into a proper proposition.
+ In Line 6 the function @{ML Proof.theorem_i} starts the proof for the
+ proposition. Its argument @{ML NONE} stands for a locale (which we chose to
+ omit); the argument @{ML "(K I)"} stands for a function that determines what
+ should be done with the theorem once it is proved (we chose to just forget
+ about it). Lines 9 to 11 contain the parser for the proposition.
+
+ If you now type \isacommand{foobar}~@{text [quotes] "True \<and> True"}, you obtain the following
+ proof state:
+
+ \begin{isabelle}
+ \isacommand{foobar}~@{text [quotes] "True \<and> True"}\\
+ @{text "goal (1 subgoal):"}\\
+ @{text "1. True \<and> True"}
+ \end{isabelle}
+
+ and you can build the proof
+
+ \begin{isabelle}
+ \isacommand{foobar}~@{text [quotes] "True \<and> True"}\\
+ \isacommand{apply}@{text "(rule conjI)"}\\
+ \isacommand{apply}@{text "(rule TrueI)+"}\\
+ \isacommand{done}
+ \end{isabelle}
+
+
+
+ (FIXME What do @{ML "Toplevel.theory"}
+ @{ML "Toplevel.print"}
+ @{ML Toplevel.local_theory} do?)
+
+ (FIXME read a name and show how to store theorems)
+
+*}
+
+section {* Methods *}
+
+text {*
+ Methods are a central concept in Isabelle. They are the ones you use for example
+ in \isacommand{apply}. To print out all currently known methods you can use the
+ Isabelle command.
+*}
+
+print_methods
+
+text {*
+ An example of a very simple method is the following code.
+*}
+
+method_setup %gray foobar_meth =
+ {* Scan.succeed
+ (K (SIMPLE_METHOD ((etac @{thm conjE} THEN' rtac @{thm conjI}) 1))) *}
+ "foobar method"
+
+text {*
+ It defines the method @{text foobar_meth}, which takes no arguments (therefore the
+ parser @{ML Scan.succeed}) and
+ only applies the tactic @{thm [source] conjE} and then @{thm [source] conjI}.
+ This method can be used in the following proof
+*}
+
+lemma shows "A \<and> B \<Longrightarrow> C \<and> D"
+apply(foobar_meth)
+txt {*
+ where it results in the goal state
+
+ \begin{minipage}{\textwidth}
+ @{subgoals}
+ \end{minipage} *}
+(*<*)oops(*>*)
+
+text {*
+ (FIXME: explain a version of rule-tac)
+*}
+
+(*<*)
+
+chapter {* Parsing *}
+
+text {*
+
+ Lots of Standard ML code is given in this document, for various reasons,
+ including:
+ \begin{itemize}
+ \item direct quotation of code found in the Isabelle source files,
+ or simplified versions of such code
+ \item identifiers found in the Isabelle source code, with their types
+ (or specialisations of their types)
+ \item code examples, which can be run by the reader, to help illustrate the
+ behaviour of functions found in the Isabelle source code
+ \item ancillary functions, not from the Isabelle source code,
+ which enable the reader to run relevant code examples
+ \item type abbreviations, which help explain the uses of certain functions
+ \end{itemize}
+
+*}
+
+section {* Parsing Isar input *}
+
+text {*
+
+ The typical parsing function has the type
+ \texttt{'src -> 'res * 'src}, with input
+ of type \texttt{'src}, returning a result
+ of type \texttt{'res}, which is (or is derived from) the first part of the
+ input, and also returning the remainder of the input.
+ (In the common case, when it is clear what the ``remainder of the input''
+ means, we will just say that the functions ``returns'' the
+ value of type \texttt{'res}).
+ An exception is raised if an appropriate value
+ cannot be produced from the input.
+ A range of exceptions can be used to identify different reasons
+ for the failure of a parse.
+
+ This contrasts the standard parsing function in Standard ML,
+ which is of type
+ \texttt{type ('res, 'src) reader = 'src -> ('res * 'src) option};
+ (for example, \texttt{List.getItem} and \texttt{Substring.getc}).
+ However, much of the discussion at
+ FIX file:/home/jeremy/html/ml/SMLBasis/string-cvt.html
+ is relevant.
+
+ Naturally one may convert between the two different sorts of parsing functions
+ as follows:
+ \begin{verbatim}
+ open StringCvt ;
+ type ('res, 'src) ex_reader = 'src -> 'res * 'src
+ ex_reader : ('res, 'src) reader -> ('res, 'src) ex_reader
+ fun ex_reader rdr src = Option.valOf (rdr src) ;
+ reader : ('res, 'src) ex_reader -> ('res, 'src) reader
+ fun reader exrdr src = SOME (exrdr src) handle _ => NONE ;
+ \end{verbatim}
+
+*}
+
+section{* The \texttt{Scan} structure *}
+
+text {*
+ The source file is \texttt{src/General/scan.ML}.
+ This structure provides functions for using and combining parsing functions
+ of the type \texttt{'src -> 'res * 'src}.
+ Three exceptions are used:
+ \begin{verbatim}
+ exception MORE of string option; (*need more input (prompt)*)
+ exception FAIL of string option; (*try alternatives (reason of failure)*)
+ exception ABORT of string; (*dead end*)
+ \end{verbatim}
+ Many functions in this structure (generally those with names composed of
+ symbols) are declared as infix.
+
+ Some functions from that structure are
+ \begin{verbatim}
+ |-- : ('src -> 'res1 * 'src') * ('src' -> 'res2 * 'src'') ->
+ 'src -> 'res2 * 'src''
+ --| : ('src -> 'res1 * 'src') * ('src' -> 'res2 * 'src'') ->
+ 'src -> 'res1 * 'src''
+ -- : ('src -> 'res1 * 'src') * ('src' -> 'res2 * 'src'') ->
+ 'src -> ('res1 * 'res2) * 'src''
+ ^^ : ('src -> string * 'src') * ('src' -> string * 'src'') ->
+ 'src -> string * 'src''
+ \end{verbatim}
+ These functions parse a result off the input source twice.
+
+ \texttt{|--} and \texttt{--|}
+ return the first result and the second result, respectively.
+
+ \texttt{--} returns both.
+
+ \verb|^^| returns the result of concatenating the two results
+ (which must be strings).
+
+ Note how, although the types
+ \texttt{'src}, \texttt{'src'} and \texttt{'src''} will normally be the same,
+ the types as shown help suggest the behaviour of the functions.
+ \begin{verbatim}
+ :-- : ('src -> 'res1 * 'src') * ('res1 -> 'src' -> 'res2 * 'src'') ->
+ 'src -> ('res1 * 'res2) * 'src''
+ :|-- : ('src -> 'res1 * 'src') * ('res1 -> 'src' -> 'res2 * 'src'') ->
+ 'src -> 'res2 * 'src''
+ \end{verbatim}
+ These are similar to \texttt{|--} and \texttt{--|},
+ except that the second parsing function can depend on the result of the first.
+ \begin{verbatim}
+ >> : ('src -> 'res1 * 'src') * ('res1 -> 'res2) -> 'src -> 'res2 * 'src'
+ || : ('src -> 'res_src) * ('src -> 'res_src) -> 'src -> 'res_src
+ \end{verbatim}
+ \texttt{p >> f} applies a function \texttt{f} to the result of a parse.
+
+ \texttt{||} tries a second parsing function if the first one
+ fails by raising an exception of the form \texttt{FAIL \_}.
+
+ \begin{verbatim}
+ succeed : 'res -> ('src -> 'res * 'src) ;
+ fail : ('src -> 'res_src) ;
+ !! : ('src * string option -> string) ->
+ ('src -> 'res_src) -> ('src -> 'res_src) ;
+ \end{verbatim}
+ \texttt{succeed r} returns \texttt{r}, with the input unchanged.
+ \texttt{fail} always fails, raising exception \texttt{FAIL NONE}.
+ \texttt{!! f} only affects the failure mode, turning a failure that
+ raises \texttt{FAIL \_} into a failure that raises \texttt{ABORT ...}.
+ This is used to prevent recovery from the failure ---
+ thus, in \texttt{!! parse1 || parse2}, if \texttt{parse1} fails,
+ it won't recover by trying \texttt{parse2}.
+
+ \begin{verbatim}
+ one : ('si -> bool) -> ('si list -> 'si * 'si list) ;
+ some : ('si -> 'res option) -> ('si list -> 'res * 'si list) ;
+ \end{verbatim}
+ These require the input to be a list of items:
+ they fail, raising \texttt{MORE NONE} if the list is empty.
+ On other failures they raise \texttt{FAIL NONE}
+
+ \texttt{one p} takes the first
+ item from the list if it satisfies \texttt{p}, otherwise fails.
+
+ \texttt{some f} takes the first
+ item from the list and applies \texttt{f} to it, failing if this returns
+ \texttt{NONE}.
+
+ \begin{verbatim}
+ many : ('si -> bool) -> 'si list -> 'si list * 'si list ;
+ \end{verbatim}
+ \texttt{many p} takes items from the input until it encounters one
+ which does not satisfy \texttt{p}. If it reaches the end of the input
+ it fails, raising \texttt{MORE NONE}.
+
+ \texttt{many1} (with the same type) fails if the first item
+ does not satisfy \texttt{p}.
+
+ \begin{verbatim}
+ option : ('src -> 'res * 'src) -> ('src -> 'res option * 'src)
+ optional : ('src -> 'res * 'src) -> 'res -> ('src -> 'res * 'src)
+ \end{verbatim}
+ \texttt{option}:
+ where the parser \texttt{f} succeeds with result \texttt{r}
+ or raises \texttt{FAIL \_},
+ \texttt{option f} gives the result \texttt{SOME r} or \texttt{NONE}.
+
+ \texttt{optional}: if parser \texttt{f} fails by raising \texttt{FAIL \_},
+ \texttt{optional f default} provides the result \texttt{default}.
+
+ \begin{verbatim}
+ repeat : ('src -> 'res * 'src) -> 'src -> 'res list * 'src
+ repeat1 : ('src -> 'res * 'src) -> 'src -> 'res list * 'src
+ bulk : ('src -> 'res * 'src) -> 'src -> 'res list * 'src
+ \end{verbatim}
+ \texttt{repeat f} repeatedly parses an item off the remaining input until
+ \texttt{f} fails with \texttt{FAIL \_}
+
+ \texttt{repeat1} is as for \texttt{repeat}, but requires at least one
+ successful parse.
+
+ \begin{verbatim}
+ lift : ('src -> 'res * 'src) -> ('ex * 'src -> 'res * ('ex * 'src))
+ \end{verbatim}
+ \texttt{lift} changes the source type of a parser by putting in an extra
+ component \texttt{'ex}, which is ignored in the parsing.
+
+ The \texttt{Scan} structure also provides the type \texttt{lexicon},
+ HOW DO THEY WORK ?? TO BE COMPLETED
+ \begin{verbatim}
+ dest_lexicon: lexicon -> string list ;
+ make_lexicon: string list list -> lexicon ;
+ empty_lexicon: lexicon ;
+ extend_lexicon: string list list -> lexicon -> lexicon ;
+ merge_lexicons: lexicon -> lexicon -> lexicon ;
+ is_literal: lexicon -> string list -> bool ;
+ literal: lexicon -> string list -> string list * string list ;
+ \end{verbatim}
+ Two lexicons, for the commands and keywords, are stored and can be retrieved
+ by:
+ \begin{verbatim}
+ val (command_lexicon, keyword_lexicon) = OuterSyntax.get_lexicons () ;
+ val commands = Scan.dest_lexicon command_lexicon ;
+ val keywords = Scan.dest_lexicon keyword_lexicon ;
+ \end{verbatim}
+*}
+
+section{* The \texttt{OuterLex} structure *}
+
+text {*
+ The source file is @{text "src/Pure/Isar/outer_lex.ML"}.
+ In some other source files its name is abbreviated:
+ \begin{verbatim}
+ structure T = OuterLex;
+ \end{verbatim}
+ This structure defines the type \texttt{token}.
+ (The types
+ \texttt{OuterLex.token},
+ \texttt{OuterParse.token} and
+ \texttt{SpecParse.token} are all the same).
+
+ Input text is split up into tokens, and the input source type for many parsing
+ functions is \texttt{token list}.
+
+ The datatype definition (which is not published in the signature) is
+ \begin{verbatim}
+ datatype token = Token of Position.T * (token_kind * string);
+ \end{verbatim}
+ but here are some runnable examples for viewing tokens:
+
+*}
+
+
+
+
+ML{*
+ val toks = OuterSyntax.scan Position.none
+ "theory,imports;begin x.y.z apply ?v1 ?'a 'a -- || 44 simp (* xx *) { * fff * }" ;
+*}
+
+ML{*
+ print_depth 20 ;
+*}
+
+ML{*
+ map OuterLex.text_of toks ;
+*}
+
+ML{*
+ val proper_toks = filter OuterLex.is_proper toks ;
+*}
+
+ML{*
+ map OuterLex.kind_of proper_toks
+*}
+
+ML{*
+ map OuterLex.unparse proper_toks ;
+*}
+
+ML{*
+ OuterLex.stopper
+*}
+
+text {*
+
+ The function \texttt{is\_proper : token -> bool} identifies tokens which are
+ not white space or comments: many parsing functions assume require spaces or
+ comments to have been filtered out.
+
+ There is a special end-of-file token:
+ \begin{verbatim}
+ val (tok_eof : token, is_eof : token -> bool) = T.stopper ;
+ (* end of file token *)
+ \end{verbatim}
+
+*}
+
+section {* The \texttt{OuterParse} structure *}
+
+text {*
+ The source file is \texttt{src/Pure/Isar/outer\_parse.ML}.
+ In some other source files its name is abbreviated:
+ \begin{verbatim}
+ structure P = OuterParse;
+ \end{verbatim}
+ Here the parsers use \texttt{token list} as the input source type.
+
+ Some of the parsers simply select the first token, provided that it is of the
+ right kind (as returned by \texttt{T.kind\_of}): these are
+ \texttt{ command, keyword, short\_ident, long\_ident, sym\_ident, term\_var,
+ type\_ident, type\_var, number, string, alt\_string, verbatim, sync, eof}
+ Others select the first token, provided that it is one of several kinds,
+ (eg, \texttt{name, xname, text, typ}).
+
+ \begin{verbatim}
+ type 'a tlp = token list -> 'a * token list ; (* token list parser *)
+ $$$ : string -> string tlp
+ nat : int tlp ;
+ maybe : 'a tlp -> 'a option tlp ;
+ \end{verbatim}
+
+ \texttt{\$\$\$ s} returns the first token,
+ if it equals \texttt{s} \emph{and} \texttt{s} is a keyword.
+
+ \texttt{nat} returns the first token, if it is a number, and evaluates it.
+
+ \texttt{maybe}: if \texttt{p} returns \texttt{r},
+ then \texttt{maybe p} returns \texttt{SOME r} ;
+ if the first token is an underscore, it returns \texttt{NONE}.
+
+ A few examples:
+ \begin{verbatim}
+ P.list : 'a tlp -> 'a list tlp ; (* likewise P.list1 *)
+ P.and_list : 'a tlp -> 'a list tlp ; (* likewise P.and_list1 *)
+ val toks : token list = OuterSyntax.scan "44 ,_, 66,77" ;
+ val proper_toks = List.filter T.is_proper toks ;
+ P.list P.nat toks ; (* OK, doesn't recognize white space *)
+ P.list P.nat proper_toks ; (* fails, doesn't recognize what follows ',' *)
+ P.list (P.maybe P.nat) proper_toks ; (* fails, end of input *)
+ P.list (P.maybe P.nat) (proper_toks @ [tok_eof]) ; (* OK *)
+ val toks : token list = OuterSyntax.scan "44 and 55 and 66 and 77" ;
+ P.and_list P.nat (List.filter T.is_proper toks @ [tok_eof]) ; (* ??? *)
+ \end{verbatim}
+
+ The following code helps run examples:
+ \begin{verbatim}
+ fun parse_str tlp str =
+ let val toks : token list = OuterSyntax.scan str ;
+ val proper_toks = List.filter T.is_proper toks @ [tok_eof] ;
+ val (res, rem_toks) = tlp proper_toks ;
+ val rem_str = String.concat
+ (Library.separate " " (List.map T.unparse rem_toks)) ;
+ in (res, rem_str) end ;
+ \end{verbatim}
+
+ Some examples from \texttt{src/Pure/Isar/outer\_parse.ML}
+ \begin{verbatim}
+ val type_args =
+ type_ident >> Library.single ||
+ $$$ "(" |-- !!! (list1 type_ident --| $$$ ")") ||
+ Scan.succeed [];
+ \end{verbatim}
+ There are three ways parsing a list of type arguments can succeed.
+ The first line reads a single type argument, and turns it into a singleton
+ list.
+ The second line reads "(", and then the remainder, ignoring the "(" ;
+ the remainder consists of a list of type identifiers (at least one),
+ and then a ")" which is also ignored.
+ The \texttt{!!!} ensures that if the parsing proceeds this far and then fails,
+ it won't try the third line (see the description of \texttt{Scan.!!}).
+ The third line consumes no input and returns the empty list.
+
+ \begin{verbatim}
+ fun triple2 (x, (y, z)) = (x, y, z);
+ val arity = xname -- ($$$ "::" |-- !!! (
+ Scan.optional ($$$ "(" |-- !!! (list1 sort --| $$$ ")")) []
+ -- sort)) >> triple2;
+ \end{verbatim}
+ The parser \texttt{arity} reads a typename $t$, then ``\texttt{::}'' (which is
+ ignored), then optionally a list $ss$ of sorts and then another sort $s$.
+ The result $(t, (ss, s))$ is transformed by \texttt{triple2} to $(t, ss, s)$.
+ The second line reads the optional list of sorts:
+ it reads first ``\texttt{(}'' and last ``\texttt{)}'', which are both ignored,
+ and between them a comma-separated list of sorts.
+ If this list is absent, the default \texttt{[]} provides the list of sorts.
+
+ \begin{verbatim}
+ parse_str P.type_args "('a, 'b) ntyp" ;
+ parse_str P.type_args "'a ntyp" ;
+ parse_str P.type_args "ntyp" ;
+ parse_str P.arity "ty :: tycl" ;
+ parse_str P.arity "ty :: (tycl1, tycl2) tycl" ;
+ \end{verbatim}
+
+*}
+
+section {* The \texttt{SpecParse} structure *}
+
+text {*
+ The source file is \texttt{src/Pure/Isar/spec\_parse.ML}.
+ This structure contains token list parsers for more complicated values.
+ For example,
+ \begin{verbatim}
+ open SpecParse ;
+ attrib : Attrib.src tok_rdr ;
+ attribs : Attrib.src list tok_rdr ;
+ opt_attribs : Attrib.src list tok_rdr ;
+ xthm : (thmref * Attrib.src list) tok_rdr ;
+ xthms1 : (thmref * Attrib.src list) list tok_rdr ;
+
+ parse_str attrib "simp" ;
+ parse_str opt_attribs "hello" ;
+ val (ass, "") = parse_str attribs "[standard, xxxx, simp, intro, OF sym]" ;
+ map Args.dest_src ass ;
+ val (asrc, "") = parse_str attrib "THEN trans [THEN sym]" ;
+
+ parse_str xthm "mythm [attr]" ;
+ parse_str xthms1 "thm1 [attr] thms2" ;
+ \end{verbatim}
+
+ As you can see, attributes are described using types of the \texttt{Args}
+ structure, described below.
+*}
+
+section{* The \texttt{Args} structure *}
+
+text {*
+ The source file is \texttt{src/Pure/Isar/args.ML}.
+ The primary type of this structure is the \texttt{src} datatype;
+ the single constructors not published in the signature, but
+ \texttt{Args.src} and \texttt{Args.dest\_src}
+ are in fact the constructor and destructor functions.
+ Note that the types \texttt{Attrib.src} and \texttt{Method.src}
+ are in fact \texttt{Args.src}.
+
+ \begin{verbatim}
+ src : (string * Args.T list) * Position.T -> Args.src ;
+ dest_src : Args.src -> (string * Args.T list) * Position.T ;
+ Args.pretty_src : Proof.context -> Args.src -> Pretty.T ;
+ fun pr_src ctxt src = Pretty.string_of (Args.pretty_src ctxt src) ;
+
+ val thy = ML_Context.the_context () ;
+ val ctxt = ProofContext.init thy ;
+ map (pr_src ctxt) ass ;
+ \end{verbatim}
+
+ So an \texttt{Args.src} consists of the first word, then a list of further
+ ``arguments'', of type \texttt{Args.T}, with information about position in the
+ input.
+ \begin{verbatim}
+ (* how an Args.src is parsed *)
+ P.position : 'a tlp -> ('a * Position.T) tlp ;
+ P.arguments : Args.T list tlp ;
+
+ val parse_src : Args.src tlp =
+ P.position (P.xname -- P.arguments) >> Args.src ;
+ \end{verbatim}
+
+ \begin{verbatim}
+ val ((first_word, args), pos) = Args.dest_src asrc ;
+ map Args.string_of args ;
+ \end{verbatim}
+
+ The \texttt{Args} structure contains more parsers and parser transformers
+ for which the input source type is \texttt{Args.T list}. For example,
+ \begin{verbatim}
+ type 'a atlp = Args.T list -> 'a * Args.T list ;
+ open Args ;
+ nat : int atlp ; (* also Args.int *)
+ thm_sel : PureThy.interval list atlp ;
+ list : 'a atlp -> 'a list atlp ;
+ attribs : (string -> string) -> Args.src list atlp ;
+ opt_attribs : (string -> string) -> Args.src list atlp ;
+
+ (* parse_atl_str : 'a atlp -> (string -> 'a * string) ;
+ given an Args.T list parser, to get a string parser *)
+ fun parse_atl_str atlp str =
+ let val (ats, rem_str) = parse_str P.arguments str ;
+ val (res, rem_ats) = atlp ats ;
+ in (res, String.concat (Library.separate " "
+ (List.map Args.string_of rem_ats @ [rem_str]))) end ;
+
+ parse_atl_str Args.int "-1-," ;
+ parse_atl_str (Scan.option Args.int) "x1-," ;
+ parse_atl_str Args.thm_sel "(1-,4,13-22)" ;
+
+ val (ats as atsrc :: _, "") = parse_atl_str (Args.attribs I)
+ "[THEN trans [THEN sym], simp, OF sym]" ;
+ \end{verbatim}
+
+ From here, an attribute is interpreted using \texttt{Attrib.attribute}.
+
+ \texttt{Args} has a large number of functions which parse an \texttt{Args.src}
+ and also refer to a generic context.
+ Note the use of \texttt{Scan.lift} for this.
+ (as does \texttt{Attrib} - RETHINK THIS)
+
+ (\texttt{Args.syntax} shown below has type specialised)
+
+ \begin{verbatim}
+ type ('res, 'src) parse_fn = 'src -> 'res * 'src ;
+ type 'a cgatlp = ('a, Context.generic * Args.T list) parse_fn ;
+ Scan.lift : 'a atlp -> 'a cgatlp ;
+ term : term cgatlp ;
+ typ : typ cgatlp ;
+
+ Args.syntax : string -> 'res cgatlp -> src -> ('res, Context.generic) parse_fn ;
+ Attrib.thm : thm cgatlp ;
+ Attrib.thms : thm list cgatlp ;
+ Attrib.multi_thm : thm list cgatlp ;
+
+ (* parse_cgatl_str : 'a cgatlp -> (string -> 'a * string) ;
+ given a (Context.generic * Args.T list) parser, to get a string parser *)
+ fun parse_cgatl_str cgatlp str =
+ let
+ (* use the current generic context *)
+ val generic = Context.Theory thy ;
+ val (ats, rem_str) = parse_str P.arguments str ;
+ (* ignore any change to the generic context *)
+ val (res, (_, rem_ats)) = cgatlp (generic, ats) ;
+ in (res, String.concat (Library.separate " "
+ (List.map Args.string_of rem_ats @ [rem_str]))) end ;
+ \end{verbatim}
+*}
+
+section{* Attributes, and the \texttt{Attrib} structure *}
+
+text {*
+ The type \texttt{attribute} is declared in \texttt{src/Pure/thm.ML}.
+ The source file for the \texttt{Attrib} structure is
+ \texttt{src/Pure/Isar/attrib.ML}.
+ Most attributes use a theorem to change a generic context (for example,
+ by declaring that the theorem should be used, by default, in simplification),
+ or change a theorem (which most often involves referring to the current
+ theory).
+ The functions \texttt{Thm.rule\_attribute} and
+ \texttt{Thm.declaration\_attribute} create attributes of these kinds.
+
+ \begin{verbatim}
+ type attribute = Context.generic * thm -> Context.generic * thm;
+ type 'a trf = 'a -> 'a ; (* transformer of a given type *)
+ Thm.rule_attribute : (Context.generic -> thm -> thm) -> attribute ;
+ Thm.declaration_attribute : (thm -> Context.generic trf) -> attribute ;
+
+ Attrib.print_attributes : theory -> unit ;
+ Attrib.pretty_attribs : Proof.context -> src list -> Pretty.T list ;
+
+ List.app Pretty.writeln (Attrib.pretty_attribs ctxt ass) ;
+ \end{verbatim}
+
+ An attribute is stored in a theory as indicated by:
+ \begin{verbatim}
+ Attrib.add_attributes :
+ (bstring * (src -> attribute) * string) list -> theory trf ;
+ (*
+ Attrib.add_attributes [("THEN", THEN_att, "resolution with rule")] ;
+ *)
+ \end{verbatim}
+ where the first and third arguments are name and description of the attribute,
+ and the second is a function which parses the attribute input text
+ (including the attribute name, which has necessarily already been parsed).
+ Here, \texttt{THEN\_att} is a function declared in the code for the
+ structure \texttt{Attrib}, but not published in its signature.
+ The source file \texttt{src/Pure/Isar/attrib.ML} shows the use of
+ \texttt{Attrib.add\_attributes} to add a number of attributes.
+
+ \begin{verbatim}
+ FullAttrib.THEN_att : src -> attribute ;
+ FullAttrib.THEN_att atsrc (generic, ML_Context.thm "sym") ;
+ FullAttrib.THEN_att atsrc (generic, ML_Context.thm "all_comm") ;
+ \end{verbatim}
+
+ \begin{verbatim}
+ Attrib.syntax : attribute cgatlp -> src -> attribute ;
+ Attrib.no_args : attribute -> src -> attribute ;
+ \end{verbatim}
+ When this is called as \texttt{syntax scan src (gc, th)}
+ the generic context \texttt{gc} is used
+ (and potentially changed to \texttt{gc'})
+ by \texttt{scan} in parsing to obtain an attribute \texttt{attr} which would
+ then be applied to \texttt{(gc', th)}.
+ The source for parsing the attribute is the arguments part of \texttt{src},
+ which must all be consumed by the parse.
+
+ For example, for \texttt{Attrib.no\_args attr src}, the attribute parser
+ simply returns \texttt{attr}, requiring that the arguments part of
+ \texttt{src} must be empty.
+
+ Some examples from \texttt{src/Pure/Isar/attrib.ML}, modified:
+ \begin{verbatim}
+ fun rot_att_n n (gc, th) = (gc, rotate_prems n th) ;
+ rot_att_n : int -> attribute ;
+ val rot_arg = Scan.lift (Scan.optional Args.int 1 : int atlp) : int cgatlp ;
+ val rotated_att : src -> attribute =
+ Attrib.syntax (rot_arg >> rot_att_n : attribute cgatlp) ;
+
+ val THEN_arg : int cgatlp = Scan.lift
+ (Scan.optional (Args.bracks Args.nat : int atlp) 1 : int atlp) ;
+
+ Attrib.thm : thm cgatlp ;
+
+ THEN_arg -- Attrib.thm : (int * thm) cgatlp ;
+
+ fun THEN_att_n (n, tht) (gc, th) = (gc, th RSN (n, tht)) ;
+ THEN_att_n : int * thm -> attribute ;
+
+ val THEN_att : src -> attribute = Attrib.syntax
+ (THEN_arg -- Attrib.thm >> THEN_att_n : attribute cgatlp);
+ \end{verbatim}
+ The functions I've called \texttt{rot\_arg} and \texttt{THEN\_arg}
+ read an optional argument, which for \texttt{rotated} is an integer,
+ and for \texttt{THEN} is a natural enclosed in square brackets;
+ the default, if the argument is absent, is 1 in each case.
+ Functions \texttt{rot\_att\_n} and \texttt{THEN\_att\_n} turn these into
+ attributes, where \texttt{THEN\_att\_n} also requires a theorem, which is
+ parsed by \texttt{Attrib.thm}.
+ Infix operators \texttt{--} and \texttt{>>} are in the structure \texttt{Scan}.
+
+*}
+
+section{* Methods, and the \texttt{Method} structure *}
+
+text {*
+ The source file is \texttt{src/Pure/Isar/method.ML}.
+ The type \texttt{method} is defined by the datatype declaration
+ \begin{verbatim}
+ (* datatype method = Meth of thm list -> cases_tactic; *)
+ RuleCases.NO_CASES : tactic -> cases_tactic ;
+ \end{verbatim}
+ In fact \texttt{RAW\_METHOD\_CASES} (below) is exactly the constructor
+ \texttt{Meth}.
+ A \texttt{cases\_tactic} is an elaborated version of a tactic.
+ \texttt{NO\_CASES tac} is a \texttt{cases\_tactic} which consists of a
+ \texttt{cases\_tactic} without any further case information.
+ For further details see the description of structure \texttt{RuleCases} below.
+ The list of theorems to be passed to a method consists of the current
+ \emph{facts} in the proof.
+
+ \begin{verbatim}
+ RAW_METHOD : (thm list -> tactic) -> method ;
+ METHOD : (thm list -> tactic) -> method ;
+
+ SIMPLE_METHOD : tactic -> method ;
+ SIMPLE_METHOD' : (int -> tactic) -> method ;
+ SIMPLE_METHOD'' : ((int -> tactic) -> tactic) -> (int -> tactic) -> method ;
+
+ RAW_METHOD_CASES : (thm list -> cases_tactic) -> method ;
+ METHOD_CASES : (thm list -> cases_tactic) -> method ;
+ \end{verbatim}
+ A method is, in its simplest form, a tactic; applying the method is to apply
+ the tactic to the current goal state.
+
+ Applying \texttt{RAW\_METHOD tacf} creates a tactic by applying
+ \texttt{tacf} to the current {facts}, and applying that tactic to the
+ goal state.
+
+ \texttt{METHOD} is similar but also first applies
+ \texttt{Goal.conjunction\_tac} to all subgoals.
+
+ \texttt{SIMPLE\_METHOD tac} inserts the facts into all subgoals and then
+ applies \texttt{tacf}.
+
+ \texttt{SIMPLE\_METHOD' tacf} inserts the facts and then
+ applies \texttt{tacf} to subgoal 1.
+
+ \texttt{SIMPLE\_METHOD'' quant tacf} does this for subgoal(s) selected by
+ \texttt{quant}, which may be, for example,
+ \texttt{ALLGOALS} (all subgoals),
+ \texttt{TRYALL} (try all subgoals, failure is OK),
+ \texttt{FIRSTGOAL} (try subgoals until it succeeds once),
+ \texttt{(fn tacf => tacf 4)} (subgoal 4), etc
+ (see the \texttt{Tactical} structure, FIXME) %%\cite[Chapter 4]{ref}).
+
+ A method is stored in a theory as indicated by:
+ \begin{verbatim}
+ Method.add_method :
+ (bstring * (src -> Proof.context -> method) * string) -> theory trf ;
+ ( *
+ * )
+ \end{verbatim}
+ where the first and third arguments are name and description of the method,
+ and the second is a function which parses the method input text
+ (including the method name, which has necessarily already been parsed).
+
+ Here, \texttt{xxx} is a function declared in the code for the
+ structure \texttt{Method}, but not published in its signature.
+ The source file \texttt{src/Pure/Isar/method.ML} shows the use of
+ \texttt{Method.add\_method} to add a number of methods.
+
+
+*}
+(*>*)
+end
\ No newline at end of file