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# pt::json_language(n) 1.1 tcllib "Parser Tools"

## Name

pt::json_language - The JSON Grammar Exchange Format

## Synopsis

- package require Tcl 8.5 9

## Description

Are you lost ? Do you have trouble understanding this document ? 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.

### Example

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 <- Term (AddOp Term)*                            ;
        MulOp      <- '*' / '/'                                     ;
        Term       <- Factor (MulOp Factor)*                        ;
        AddOp      <- '+'/'-'                                       ;
        Factor     <- '(' Expression ')' / 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 {n Term} {* {x {n AddOp} {n Term}}}}                                        mode value}
            Factor     {is {/ {x {t (} {n Expression} {t )}} {n Number}}                                  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 {x {n Factor} {* {x {n MulOp} {n Factor}}}}                                    mode value}
        }
        start {n Expression}
    }

The similarity of the latter to the JSON should be quite obvious.

## PEG serialization format

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.

### Example

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 <- Term (AddOp Term)*                            ;
        MulOp      <- '*' / '/'                                     ;
        Term       <- Factor (MulOp Factor)*                        ;
        AddOp      <- '+'/'-'                                       ;
        Factor     <- '(' Expression ')' / 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 {n Term} {* {x {n AddOp} {n Term}}}}                                        mode value}
            Factor     {is {/ {x {t (} {n Expression} {t )}} {n Number}}                                  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 {x {n Factor} {* {x {n MulOp} {n Factor}}}}                                    mode value}
        }
        start {n Expression}
    }

## PE serialization format

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).

### Example

Assuming the parsing expression shown on the right-hand side of the rule

        Expression <- Term (AddOp Term)*

then its canonical serialization (except for whitespace) is

        {x {n Term} {* {x {n AddOp} {n Term}}}}

## Bugs, Ideas, Feedback

This document, and the package it describes, will undoubtedly contain bugs and other problems. Please report such in the category pt of the Tcllib Trackers. Please also report any ideas for enhancements you may have for either package and/or documentation.

When proposing code changes, please provide unified diffs, i.e the output of diff -u.

Note further that attachments are strongly preferred over inlined patches. Attachments can be made by going to the Edit form of the ticket immediately after its creation, and then using the left-most button in the secondary navigation bar.

## Keywords

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

## Category

Parsing and Grammars

## Copyright

Copyright © 2009 Andreas Kupries <andreas_kupries@users.sourceforge.net>