pt::json_language - The JSON Grammar Exchange Format
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In that case please read the overview provided by the Introduction to
Parser Tools. This document is the entrypoint to the whole system the
current package is a part of.
The json format for parsing expression grammars was written
as a data exchange format not bound to Tcl. It was defined to allow the
exchange of grammars with PackRat/PEG based parser generators for other
languages.
It is formally specified by the rules below:
- [1]
- The JSON of any PEG is a JSON object.
- [2]
- This object holds a single key, pt::grammar::peg, and its value.
This value holds the contents of the grammar.
- [3]
- The contents of the grammar are a JSON object holding the set of
nonterminal symbols and the starting expression. The relevant keys and
their values are
- rules
- The value is a JSON object whose keys are the names of the nonterminal
symbols known to the grammar.
- [1]
- Each nonterminal symbol may occur only once.
- [2]
- The empty string is not a legal nonterminal symbol.
- [3]
- The value for each symbol is a JSON object itself. The relevant keys and
their values in this dictionary are
- is
- The value is a JSON string holding the Tcl serialization of the parsing
expression describing the symbols sentennial structure, as specified in
the section PE serialization format.
- mode
- The value is a JSON holding holding one of three values specifying how a
parser should handle the semantic value produced by the symbol.
- value
- The semantic value of the nonterminal symbol is an abstract syntax tree
consisting of a single node node for the nonterminal itself, which has the
ASTs of the symbol's right hand side as its children.
- leaf
- The semantic value of the nonterminal symbol is an abstract syntax tree
consisting of a single node node for the nonterminal, without any
children. Any ASTs generated by the symbol's right hand side are
discarded.
- void
- The nonterminal has no semantic value. Any ASTs generated by the symbol's
right hand side are discarded (as well).
- start
- The value is a JSON string holding the Tcl serialization of the start
parsing expression of the grammar, as specified in the section PE
serialization format.
- [4]
- The terminal symbols of the grammar are specified implicitly as the set of
all terminal symbols used in the start expression and on the RHS of the
grammar rules.
As an aside to the advanced reader, this is pretty much the same
as the Tcl serialization of PE grammars, as specified in section PEG
serialization format, except that the Tcl dictionaries and lists of that
format are mapped to JSON objects and arrays. Only the parsing expressions
themselves are not translated further, but kept as JSON strings containing a
nested Tcl list, and there is no concept of canonicity for the JSON
either.
Assuming the following PEG for simple mathematical expressions
PEG calculator (Expression)
Digit <- '0'/'1'/'2'/'3'/'4'/'5'/'6'/'7'/'8'/'9' ;
Sign <- '-' / '+' ;
Number <- Sign? Digit+ ;
Expression <- '(' Expression ')' / (Factor (MulOp Factor)*) ;
MulOp <- '*' / '/' ;
Factor <- Term (AddOp Term)* ;
AddOp <- '+'/'-' ;
Term <- Number ;
END;
a JSON serialization for it is
{
"pt::grammar::peg" : {
"rules" : {
"AddOp" : {
"is" : "\/ {t -} {t +}",
"mode" : "value"
},
"Digit" : {
"is" : "\/ {t 0} {t 1} {t 2} {t 3} {t 4} {t 5} {t 6} {t 7} {t 8} {t 9}",
"mode" : "value"
},
"Expression" : {
"is" : "\/ {x {t (} {n Expression} {t )}} {x {n Factor} {* {x {n MulOp} {n Factor}}}}",
"mode" : "value"
},
"Factor" : {
"is" : "x {n Term} {* {x {n AddOp} {n Term}}}",
"mode" : "value"
},
"MulOp" : {
"is" : "\/ {t *} {t \/}",
"mode" : "value"
},
"Number" : {
"is" : "x {? {n Sign}} {+ {n Digit}}",
"mode" : "value"
},
"Sign" : {
"is" : "\/ {t -} {t +}",
"mode" : "value"
},
"Term" : {
"is" : "n Number",
"mode" : "value"
}
},
"start" : "n Expression"
}
}
and a Tcl serialization of the same is
pt::grammar::peg {
rules {
AddOp {is {/ {t -} {t +}} mode value}
Digit {is {/ {t 0} {t 1} {t 2} {t 3} {t 4} {t 5} {t 6} {t 7} {t 8} {t 9}} mode value}
Expression {is {/ {x {t (} {n Expression} {t )}} {x {n Factor} {* {x {n MulOp} {n Factor}}}}} mode value}
Factor {is {x {n Term} {* {x {n AddOp} {n Term}}}} mode value}
MulOp {is {/ {t *} {t /}} mode value}
Number {is {x {? {n Sign}} {+ {n Digit}}} mode value}
Sign {is {/ {t -} {t +}} mode value}
Term {is {n Number} mode value}
}
start {n Expression}
}
The similarity of the latter to the JSON should be quite
obvious.
Here we specify the format used by the Parser Tools to serialize
Parsing Expression Grammars as immutable values for transport, comparison,
etc.
We distinguish between regular and canonical
serializations. While a PEG may have more than one regular serialization
only exactly one of them will be canonical.
- regular
serialization
- [1]
- The serialization of any PEG is a nested Tcl dictionary.
- [2]
- This dictionary holds a single key, pt::grammar::peg, and its
value. This value holds the contents of the grammar.
- [3]
- The contents of the grammar are a Tcl dictionary holding the set of
nonterminal symbols and the starting expression. The relevant keys and
their values are
- rules
- The value is a Tcl dictionary whose keys are the names of the nonterminal
symbols known to the grammar.
- [1]
- Each nonterminal symbol may occur only once.
- [2]
- The empty string is not a legal nonterminal symbol.
- [3]
- The value for each symbol is a Tcl dictionary itself. The relevant keys
and their values in this dictionary are
- is
- The value is the serialization of the parsing expression describing the
symbols sentennial structure, as specified in the section PE
serialization format.
- mode
- The value can be one of three values specifying how a parser should handle
the semantic value produced by the symbol.
- value
- The semantic value of the nonterminal symbol is an abstract syntax tree
consisting of a single node node for the nonterminal itself, which has the
ASTs of the symbol's right hand side as its children.
- leaf
- The semantic value of the nonterminal symbol is an abstract syntax tree
consisting of a single node node for the nonterminal, without any
children. Any ASTs generated by the symbol's right hand side are
discarded.
- void
- The nonterminal has no semantic value. Any ASTs generated by the symbol's
right hand side are discarded (as well).
- start
- The value is the serialization of the start parsing expression of the
grammar, as specified in the section PE serialization format.
- [4]
- The terminal symbols of the grammar are specified implicitly as the set of
all terminal symbols used in the start expression and on the RHS of the
grammar rules.
- canonical
serialization
- The canonical serialization of a grammar has the format as specified in
the previous item, and then additionally satisfies the constraints below,
which make it unique among all the possible serializations of this
grammar.
- [1]
- The keys found in all the nested Tcl dictionaries are sorted in ascending
dictionary order, as generated by Tcl's builtin command lsort
-increasing -dict.
- [2]
- The string representation of the value is the canonical representation of
a Tcl dictionary. I.e. it does not contain superfluous whitespace.
Assuming the following PEG for simple mathematical expressions
PEG calculator (Expression)
Digit <- '0'/'1'/'2'/'3'/'4'/'5'/'6'/'7'/'8'/'9' ;
Sign <- '-' / '+' ;
Number <- Sign? Digit+ ;
Expression <- '(' Expression ')' / (Factor (MulOp Factor)*) ;
MulOp <- '*' / '/' ;
Factor <- Term (AddOp Term)* ;
AddOp <- '+'/'-' ;
Term <- Number ;
END;
then its canonical serialization (except for whitespace) is
pt::grammar::peg {
rules {
AddOp {is {/ {t -} {t +}} mode value}
Digit {is {/ {t 0} {t 1} {t 2} {t 3} {t 4} {t 5} {t 6} {t 7} {t 8} {t 9}} mode value}
Expression {is {/ {x {t (} {n Expression} {t )}} {x {n Factor} {* {x {n MulOp} {n Factor}}}}} mode value}
Factor {is {x {n Term} {* {x {n AddOp} {n Term}}}} mode value}
MulOp {is {/ {t *} {t /}} mode value}
Number {is {x {? {n Sign}} {+ {n Digit}}} mode value}
Sign {is {/ {t -} {t +}} mode value}
Term {is {n Number} mode value}
}
start {n Expression}
}
Here we specify the format used by the Parser Tools to serialize
Parsing Expressions as immutable values for transport, comparison, etc.
We distinguish between regular and canonical
serializations. While a parsing expression may have more than one regular
serialization only exactly one of them will be canonical.
- Regular
serialization
- Atomic Parsing
Expressions
- [1]
- The string epsilon is an atomic parsing expression. It matches the
empty string.
- [2]
- The string dot is an atomic parsing expression. It matches any
character.
- [3]
- The string alnum is an atomic parsing expression. It matches any
Unicode alphabet or digit character. This is a custom extension of PEs
based on Tcl's builtin command string is.
- [4]
- The string alpha is an atomic parsing expression. It matches any
Unicode alphabet character. This is a custom extension of PEs based on
Tcl's builtin command string is.
- [5]
- The string ascii is an atomic parsing expression. It matches any
Unicode character below U0080. This is a custom extension of PEs based on
Tcl's builtin command string is.
- [6]
- The string control is an atomic parsing expression. It matches any
Unicode control character. This is a custom extension of PEs based on
Tcl's builtin command string is.
- [7]
- The string digit is an atomic parsing expression. It matches any
Unicode digit character. Note that this includes characters outside of the
[0..9] range. This is a custom extension of PEs based on Tcl's builtin
command string is.
- [8]
- The string graph is an atomic parsing expression. It matches any
Unicode printing character, except for space. This is a custom extension
of PEs based on Tcl's builtin command string is.
- [9]
- The string lower is an atomic parsing expression. It matches any
Unicode lower-case alphabet character. This is a custom extension of PEs
based on Tcl's builtin command string is.
- [10]
- The string print is an atomic parsing expression. It matches any
Unicode printing character, including space. This is a custom extension of
PEs based on Tcl's builtin command string is.
- [11]
- The string punct is an atomic parsing expression. It matches any
Unicode punctuation character. This is a custom extension of PEs based on
Tcl's builtin command string is.
- [12]
- The string space is an atomic parsing expression. It matches any
Unicode space character. This is a custom extension of PEs based on Tcl's
builtin command string is.
- [13]
- The string upper is an atomic parsing expression. It matches any
Unicode upper-case alphabet character. This is a custom extension of PEs
based on Tcl's builtin command string is.
- [14]
- The string wordchar is an atomic parsing expression. It matches any
Unicode word character. This is any alphanumeric character (see alnum),
and any connector punctuation characters (e.g. underscore). This is a
custom extension of PEs based on Tcl's builtin command string
is.
- [15]
- The string xdigit is an atomic parsing expression. It matches any
hexadecimal digit character. This is a custom extension of PEs based on
Tcl's builtin command string is.
- [16]
- The string ddigit is an atomic parsing expression. It matches any
decimal digit character. This is a custom extension of PEs based on Tcl's
builtin command regexp.
- [17]
- The expression [list t x] is an atomic parsing expression. It
matches the terminal string x.
- [18]
- The expression [list n A] is an atomic parsing expression. It
matches the nonterminal A.
- Combined Parsing
Expressions
- [1]
- For parsing expressions e1, e2, ... the result of [list /
e1 e2 ... ] is a parsing expression as well. This is the
ordered choice, aka prioritized choice.
- [2]
- For parsing expressions e1, e2, ... the result of [list x
e1 e2 ... ] is a parsing expression as well. This is the
sequence.
- [3]
- For a parsing expression e the result of [list * e] is a
parsing expression as well. This is the kleene closure, describing
zero or more repetitions.
- [4]
- For a parsing expression e the result of [list + e] is a
parsing expression as well. This is the positive kleene closure,
describing one or more repetitions.
- [5]
- For a parsing expression e the result of [list & e] is a
parsing expression as well. This is the and lookahead
predicate.
- [6]
- For a parsing expression e the result of [list ! e] is a
parsing expression as well. This is the not lookahead
predicate.
- [7]
- For a parsing expression e the result of [list ? e] is a
parsing expression as well. This is the optional input.
- Canonical
serialization
- The canonical serialization of a parsing expression has the format as
specified in the previous item, and then additionally satisfies the
constraints below, which make it unique among all the possible
serializations of this parsing expression.
- [1]
- The string representation of the value is the canonical representation of
a pure Tcl list. I.e. it does not contain superfluous whitespace.
- [2]
- Terminals are not encoded as ranges (where start and end of the
range are identical).
Assuming the parsing expression shown on the right-hand side of
the rule
Expression <- '(' Expression ')'
/ Factor (MulOp Factor)*
then its canonical serialization (except for whitespace) is
{/ {x {t (} {n Expression} {t )}} {x {n Factor} {* {x {n MulOp} {n Factor}}}}}
This document, and the package it describes, will undoubtedly
contain bugs and other problems. Please report such in the category
pt of the Tcllib SF Trackers
[http://sourceforge.net/tracker/?group_id=12883]. Please also report any
ideas for enhancements you may have for either package and/or
documentation.
EBNF, LL(k), PEG, TDPL, context-free languages, expression,
grammar, matching, parser, parsing expression, parsing expression grammar,
push down automaton, recursive descent, state, top-down parsing languages,
transducer
Copyright (c) 2009 Andreas Kupries <andreas_kupries@users.sourceforge.net>