pt::json_language(n)

💖 pt::json_language 💖

okay bestie, welcome to pt::json_language(n) — the JSON Grammar Exchange Format page from Parser Tools ✨ it's giving "grammars but make them portable" and honestly? iconic.

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🦋 SYNOPSIS 🦋

package require Tcl 8.5 9

that's it. that's the whole vibe check. two Tcl versions, no drama. 💅

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🌸 DESCRIPTION 🌸

Are you lost ? Do you have trouble understanding this document ? 😭 bestie, same energy, but listen — if that's you, go read the overview in the Introduction to Parser Tools. That doc is the entrypoint to the whole system this package lives in, fr fr. Like, it's the main character of the docs and this page is its cute sidekick. 🫶

okay so. The json format for parsing expression grammars was written as a data exchange format that is not bound to Tcl. The whole point? To let people exchange grammars with PackRat/PEG based parser generators for other languages. no Tcl required, we're being ✨international✨.

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.

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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. so don't come for me about formatting, it's free-form, periodt. 💀

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🎀 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. fr fr, they're twins 💖✨

🦋 PEG SERIALIZATION FORMAT 🦋

okay bestie, so this whole section is about the format the Parser Tools use to serialize Parsing Expression Grammars as immutable values — like, for transport, for comparison, whatever. Basically turning your grammar into a chill little blob of data that can travel. ✈️✨

And the way that we do it, there are two flavors: regular and canonical. A PEG can have more than one regular serialization, but only exactly one of them is canonical. So canonical is the main character, periodt. 👑

---

regular serialization

1. The serialization of any PEG is a nested Tcl dictionary. yes, nested. it's giving inception but make it data 💅
2. This dictionary holds a single key, pt::grammar::peg, and its value. That 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, bestie, listen up:
   • 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. no duplicates, we don't do that here 🙅
     2. The empty string is not a legal nonterminal symbol. like, "" is not a name, girl, give it an actual name.
     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 symbol's sentential structure, as specified in the section PE serialization format. (spelled "sentennial" in the og text, we keep the vibe 🫶)
        • 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 for the nonterminal itself, which has the ASTs of the symbol's right hand side as its children. so like, the node is the parent, the RHS stuff hangs off it 🌳
          • leaf — The semantic value of the nonterminal symbol is an abstract syntax tree consisting of a single node for the nonterminal, without any children. Any ASTs generated by the symbol's right hand side are discarded. bye bye children 👋
          • void — The nonterminal has no semantic value. Any ASTs generated by the symbol's right hand side are discarded (as well). nothing to see here, it's giving void fr fr 💀
   • 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. no separate list, they're just vibing in there ✨

---

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 is what makes it unique among all the possible serializations of this grammar. one of one. iconic. 🎀

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. tidy queen 🧹✨

---

EXAMPLE

say we have 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}
}

look at that alignment, the keys all sorted, no superfluous whitespace — she ate and left no crumbs 🍽️💅 lowkey obsessed with how clean that is ngl 🌸

✨ PE SERIALIZATION FORMAT ✨

okay so here's where 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. [1] The string epsilon is an atomic parsing expression. It matches the empty string. ✨
2. [2] The string dot is an atomic parsing expression. It matches any character. 🦋
3. [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. [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. [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. [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. [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. [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. [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. [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. [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. [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. [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. [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. [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. [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. [17] The expression [list t x] is an atomic parsing expression. It matches the terminal string x. 🦋
18. [18] The expression [list n A] is an atomic parsing expression. It matches the nonterminal A. 💅

💫 Combined Parsing Expressions

1. [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. [2] For parsing expressions e1, e2, ... the result of [list x e1 e2 ... ] is a parsing expression as well. This is the sequence. 🌸
3. [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. [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. [5] For a parsing expression e the result of [list & e] is a parsing expression as well. This is the and lookahead predicate. 🎀
6. [6] For a parsing expression e the result of [list ! e] is a parsing expression as well. This is the not lookahead predicate. 🧚
7. [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. [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. [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 http://core.tcl.tk/tcllib/reportlist. 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 (c) 2009 Andreas Kupries <andreas_kupries@users.sourceforge.net>

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That's the whole vibe, bestie! Source/version: tcllib 1.1, page: pt::json_language(n), and the date is whatever that footer line says. Mwah! 💖✨👑