Name
Marpa::R3::Scanless::DSL - The DSL for the Scanless interface
Synopsis
use Marpa::R3;
my $grammar = Marpa::R3::Scanless::G->new(
{ bless_package => 'My_Nodes',
source => \(<<'END_OF_SOURCE'),
:default ::= action => [values] bless => ::lhs
lexeme default = action => [ start, length, value ]
bless => ::name
:start ::= Script
Script ::= Expression+ separator => comma
comma ~ [,]
Expression ::=
Number bless => primary
| '(' Expression ')' bless => paren assoc => group
|| Expression '**' Expression bless => exponentiate assoc => right
|| Expression '*' Expression bless => multiply
| Expression '/' Expression bless => divide
|| Expression '+' Expression bless => add
| Expression '-' Expression bless => subtract
Number ~ [\d]+
:discard ~ whitespace
whitespace ~ [\s]+
# allow comments
:discard ~ <hash comment>
<hash comment> ~ <terminated hash comment> | <unterminated
final hash comment>
<terminated hash comment> ~ '#' <hash comment body> <vertical space char>
<unterminated final hash comment> ~ '#' <hash comment body>
<hash comment body> ~ <hash comment char>*
<vertical space char> ~ [\x{A}\x{B}\x{C}\x{D}\x{2028}\x{2029}]
<hash comment char> ~ [^\x{A}\x{B}\x{C}\x{D}\x{2028}\x{2029}]
END_OF_SOURCE
}
);About this document
This is the reference document for the domain-specific language (DSL) of Marpa's Scanless interface (SLIF). The SLIF's DSL is an extension of BNF. The SLIF DSL is used to specify other DSL's, and is therefore a "meta-DSL".
Lexical conventions
The SLIF source string consists of a series of rules, pseudo-rules and statements. Whitespace separates tokens, but is otherwise ignored.
Comment
A hash ("#") character starts a comment, which continues to the end of the line. Comments are equivalent to whitespace.
Symbol names
Symbol names can be either "bare" or enclosed in angle brackets. Bare symbol names must consist entirely of Perl word characters (alphanumerics, plus the underscore). Symbol names are case-sensitive.
The angle brackets, if used, serve to "quote" the symbol name, and will not be part of the explicit symbol name.
If angle brackets are used, symbol names may also contain whitespace, as in
<op comma>A whitespace sequence inside angle brackets can include any whitespace character that is legal in Perl, including newlines. This allows very long symbol names to be line wrapped, if necessary.
Unlike the angle brackets, the whitespace in a bracketed symbol token does become part of the explicit symbol name, but it does so in a "normalized" form. Leading and trailing whitespace in the name is discarded, and all other whitespace sequences are converted to a single ASCII space character. This means that
< op comma >
<op comma>
< op comma>and even
<op
comma>will all be regarded as the same symbol name. The explicit form of that symbol name is <op comma>, except that, again, the angle brackets are for clarity, and are not part of the explicit name.
Explicit, reserved and internal symbol names are often displayed between angle brackets, regardless of whether the symbol was originally specified in bracketed form.
When a SLIF symbol needs to be referred to by name in Perl code, it is the symbol's explicit name that is used.
Single-quoted strings
Expression ::=
Number bless => primary
| '(' Expression ')' bless => paren assoc => group
|| Expression '**' Expression bless => exponentiate assoc => right
|| Expression '*' Expression bless => multiply
| Expression '/' Expression bless => divide
|| Expression '+' Expression bless => add
| Expression '-' Expression bless => subtractChild ~ 'cHILd':iSingle quotes can be used in prioritized rules to indicate character strings. The characters inside the single quote will be matched in the input, literally and one-for-one. Single-quoted strings can contain any characters with the exception of single quotes and vertical whitespace.
Single-quoted strings do not allow "escaped" characters. A backslash ("\") represents itself and has no effect on the interpretation of the next character. If a rule needs to match one of the forbidden characters (single quote or vertical whitespace), it must use a character class.
Single-quoted strings are always interpreted at the L0 level, but they may be used in either structural or lexical rules. When a single-quoted string is used in a structural rule, Marpa creates a virtual L0 rule on behalf of the application. This is handy, but it does have a real disadvantage -- the name of the virtual rule's LHS will be one assigned automatically by Marpa. When tracing and debugging parses and grammars, these virtual LHS's can be harder for a programmer to interpret.
A modifier can appear after the string. It must appear immediately after the string, with no intervening whitespace. Currently only the ":ic" and ":i" modifier are availables. These have exactly the same effect -- they make the string match case-insensitive.
Character classes
<vertical space char> ~ [\x{A}\x{B}\x{C}\x{D}\x{2028}\x{2029}]word ~ [\w]:ic +A character class in square brackets ("[]") can be used in a RHS alternative of a prioritized rule, a quantified rule or a discard pseudo-rule. Marpa character classes may contain anything acceptable to Perl, and follow the same escaping conventions as Perl's character classes.
Character classes are always interpreted at the L0 level, but they may be used in either structural or lexical rules. When a character class is used in a structural rule, Marpa creates a virtual L0 rule on behalf of the application. This is handy, but it does have a real disadvantage -- the name of the virtual rule's LHS will be one assigned automatically by Marpa. When tracing and debugging parses and grammars, these virtual LHS's can be harder for a programmer to interpret.
An implementation note: character classes are interpreted by Perl, but this involves minimal overhead when the parse is of any length. Each character class is passed to Perl to interpret exactly once and the result is memoized in a C language structure for future use.
The modifiers allowed after single-quoted strings are also allowed allowed after character classes. Modifiers must appear immediately after the closing square bracket, with no intervening whitespace. For more details, see the section on single-quoted strings.
Event name
The name of an event may be either a bare name, a single-quoted event name, or an event pseudo-name. A bare event name must be one or more word characters, starting with an alphabetic character.
A single-quoted event name may contain any character except a single quote or vertical space. The whitespace in single-quoted event names is normalized in similar fashion to the normalization of symbol names -- leading and trailing whitespace is removed, and all sequences of internal whitespace are changed to a single ASCII space character. Names containing single quotes (which, in any case, are impossible to add using current syntax) are reserved for future use.
A event pseudo-name is a colon, followed by one or more word characters. As present, there is only one event pseudo-name, :symbol. The :symbol pseudo-name is only allowed in discard pseudo-rules, and in the discard default statement.
If the name of an event is specified as the :symbol pseudo-name, an event's name will be based on the RHS of its discard rule. This will always be either a single symbol, or a character class. If the RHS is a single symbol, the actual event name will be the name of that symbol.
If the RHS is a character class, the actual event name will be the string specifying that character class in the DSL. The string specifying the event name for a character class is taken literally from the text specifying the DSL. This means that the character classes "[\x3B]" and "[:]" will have two different event names, event though both classes specify exactly the same set of characters.
Event initializer
event 'a' = completed A
event 'b'=off = completed B
event 'c'=on = completed C:discard ~ [,] event => comma=off
:discard ~ [;] event => 'semicolon'=on
:discard ~ [.] event => periodevent '!a' = nulled A
event '!b'=off = nulled B
event '!c'=on = nulled CAn event initializer is an event name, optionally with an explicit initialization. If there is an explicit initialization, it consists of the equal sign ('=') followed by a value indicating the event's initial activation setting (on or off).
If the initialization value is on, or if there is no explicit initialization, the event's activation setting is initially on. If the initialization value is off, the event's activation setting is initially off.
L0, G1 and lexemes
In reading this document, it is important to keep in mind the distinction, on one hand, between L0 and G1 rules and, on the other hand, between rules and lexemes. G1 rules have a semantics, which can be specified as described in this document. L0 rules simply recognize symbols in the input. L0 rules do not have a semantics.
Top-level L0 rules correspond to a string in the input. The top-level L0 rules are seen by G1 as lexemes, and the string to which a top-level L0 rule corresponds becomes the default value of the lexeme. The L0 grammar can be thought of as similar in behavior to a set of regular expressions with the lexemes being seen as similar to named captures.
Lexemes are the symbols which form the interface between G1 and L0. Lexemes, like G1 rules, have a semantics. The semantics of lexemes is specified separately from the semantics of G1 rules, as described below.
Statements
The SLIF DSL consists of a series of statements. The statements are of three kinds, as indicated by their declarator:
G1 rule
The BNF operator ("
::="), coming between the LHS and the first RHS alternative of a rule, indicates that the rule is a G1 rule.L0 rule
The match operator ("
~"), coming between the LHS and the first RHS alternative of a rule, indicates a L0 rule.Global statements
Global statements are signified by the assignment operator ("
="). The location of a statement in the DSL source will never affect the result.
Rules differ from statements in that the effect of a rule is sometimes lexical -- that is, the effect may vary depending on the position of the rule in the DSL source. Some rules are called pseudo-rules. Pseudo-rules do not correspond to BNF rules, but instead use the rule format as a convenient way to express other information.
The structure of rules
Every rule declaration consists of, in order:
A left hand side (LHS). This will be a symbol or a pseudo-symbol.
A declaration operator ("
::=" or "~").A right side declaration, which contains one or more RHS alternatives. Details of the right side declaration vary by the type of rule. For each type of rule, the right side declaration is described in detail below.
RHS alternatives
The right side declaration of a rule will often contain one or more RHS alternatives. A RHS alternative is a series of RHS primaries, where a RHS primary may be a symbol name, a character class, or a single-quoted string. A list of one or more adverbs is often associated with the RHS alternatives. Each adverb consists of a keyword, the adverb operator ("=>"), and the adverb's value.
Within an alternative, primaries may be enclosed in parentheses. A primary enclosed in parentheses is hidden from Marpa's semantics. A set of parentheses may contain more than one primary, in which case the entire sequence of primaries is hidden, as if they had been enclosed in parentheses individually. "Hiding" primaries in this way can be convenient for primaries whose values the semantics will ignore, perhaps because the value is constant.
For example, in the following rule
a ::= b (',' c) d action => ::firstthere is
A LHS, in this case the symbol "
a".A declarator, "
::=", which indicates this is a G1 rule.A RHS alternative consisting of four RHS primaries. The first RHS primary is the symbol "
b". The second RHS primary is a short single-quoted string','. The third and fourth RHS primaries are symbols: "c" and "d". The parentheses around the second and third RHS primaries "hide" them from the semantics. Marpa's semantics will see this as a rule with only two RHS values.The adverb list associated with the RHS alternative, consisting of a single adverb. The adverb consists of its keyword "
action", followed by the adverb operator ("=>"), and the adverb's value "::first".
The rule in the above example is one of a very common type: a trivial prioritized rule. A prioritized rule is one that contains one or more prioritized RHS alternatives. Prioritized rules are the only rules which may contain more than one RHS alternative, but even prioritized rules usually have only one RHS alternative. If there is only one RHS alternative, as in this case, the prioritization is trivial -- there is only one priority.
Start rule
:start ::= ScriptBy default, the start symbol of the grammar is the LHS of the first G1 rule. This default can be make explicit or overriden by using an explicit start rule. The LHS of this rule is the :start pseudo-symbol. Only one RHS alternative is allowed. This RHS alternative must contain only one symbol name, and that symbol will be the start symbol of the G1 grammar. No adverbs should be associated with the RHS alternative. Start rules must be G1 rules.
Empty rule
An empty rule is a rule with an empty RHS. The empty RHS, technically, is a RHS alternative, one with zero RHS primaries. The action and bless adverbs are allowed for the empty RHS alternative, but no others. A empty rule makes its LHS symbol a nullable symbol.
Quantified rule
Script ::= Expression+ separator => commaA quantified rule has only one RHS alternative, which is followed by a quantifier. The RHS alternative must consist of a single RHS primary. This RHS primary must be a symbol name or a character class. The quantifer is either a star ("*"), or a plus sign ("+") indicating, respectively, that the sequence rule has a minimum length of 0 or 1.
Adverbs may be associated with the RHS alternative. The adverb list must follow the quantifier. The adverbs allowed are action, bless, proper and separator.
Prioritized rule
Expression ::=
Number bless => primary
| '(' Expression ')' bless => paren assoc => group
|| Expression '**' Expression bless => exponentiate assoc => right
|| Expression '*' Expression bless => multiply
| Expression '/' Expression bless => divide
|| Expression '+' Expression bless => add
| Expression '-' Expression bless => subtractA prioritized rule contains a series of one or more RHS alternatives, separated by either the alternation operator ("|") or the loosen operators ("||"). In a typical grammar, most rules are prioritized rules, but they are often trivially prioritized, consisting of only one RHS alternative. For brevity, RHS alternatives are often called alternatives.
Each alternative may be followed by a list of associated adverbs. The action, assoc and bless adverbs are allowed.
The RHS alternatives in a prioritized right hand side proceed from tightest (highest) priority to loosest. The double "or" symbol ("||") is the "loosen" operator -- the alternatives after it have a looser (lower) priority than the alternatives before it. The single "or" symbol ("|") is the ordinary "alternative" operator -- alternatives on each side of it have the same priority. Associativity is specified using adverbs, as described below.
Discard pseudo-rule
:discard ~ whitespace:discard ~ whitespace event => wsA discard pseudo-rule is a rule whose LHS is the :discard pseudo-symbol, and which has only one RHS alternative. The RHS alternative must contain
exactly one symbol name, or
exactly one character class.
The symbol specified by the RHS of a discard pseudo-rule is called the discarded symbol. Discard pseudo-rules indicate that the discarded symbol is a top-level L0 symbol, but one which is not a lexeme. When a discarded symbol is recognized, it is not passed as a lexeme to the G1 parser, but is (as the name suggests) discarded. Discard pseudo-rules must be L0 rules.
Only the event adverb is allowed. Its value must be an event initializer. The format of an event initializer is described above. If present, it defines a discard event, as described in the document on SLIF parse events.
Default pseudo-rule
:default ::= action => [values] bless => ::lhs:default ::= action => [symbol, name, values]The purpose of the default pseudo-rule is to change the defaults for rule adverbs. Technically, it has one RHS alternative, but this must always contain zero RHS primaries. Default pseudo-rules do not affect the defaults for L0 rules or for lexemes. There may be more than one default pseudo-rule. The scope of default pseudo-rules is lexical, applying only to rules that appear afterwards in the DSL source.
Currently only the action and bless adverbs can be specified in a default pseudo-rule. Each default pseudo-rule creates a completely new set of defaults -- if an adverb is not specified, the default is reset to its implicit value, the value which it had prior to any explicit settings.
Lexeme pseudo-rule
:lexeme ~ <say keyword> priority => 1The purpose of the :lexeme pseudo-rule is to allow adverbs to change the treatment of a lexeme. This pseudo-rule always has exactly one RHS alternative, and that RHS alternative must contain exactly one symbol. This RHS symbol identifies the lexeme which the adverbs will affect. The only adverbs allowed in a :lexeme rule are event, pause, and priority.
As a side effect, a :lexeme pseudo-rule declares that its RHS symbol is expected to be a lexeme. This declaration does not "force" lexeme status -- if the symbol does not meet the criteria for a lexeme based on its use in L0 and G1 rules, the result will be a fatal error. Applications may find this ability to "declare" lexemes useful for debugging, and for documenting grammars.
Discard default statement
discard default = event => :symbol=ondiscard default = event => :symbolThe discard default statement changes the defaults for discard pseudo-rules. Only the default for the event adverb can be specified in a lexeme default statement. Only one discard default statement is allowed in a grammar.
Typically in a discard default statement, the event name will be the pseudo-name :symbol. For details about event pseudo-names, see the section on event names.
Lexeme default statement
lexeme default = action => [ start, length, value ]
bless => ::namelexeme default = action => [ name, value ]The lexeme default statement changes the defaults for lexeme adverbs. It only changes the defaults for lexemes, and does not affect rules. Only the defaults for the action, and bless adverbs can be specified in a lexeme default statement. Only one lexeme default statement is allowed in a grammar.
Named event statement
event 'a' = completed A
event 'b'=off = completed B
event 'c'=on = completed C
event 'd' = completed Devent '!a' = nulled A
event '!b'=off = nulled B
event '!c'=on = nulled C
event '!d' = nulled Devent '^a' = predicted A
event '^b'=off = predicted B
event '^c'=on = predicted C
event '^d' = predicted DThe named event statement sets up a SLIF parse event. A named event statement consists of, in order
The
eventkeyword.An event initializer, as described in the section on event initializers.
An equal sign ('
=').A keyword, which is one of
completed,nulled, orpredicted, to indicate the event type.A symbol name.
The SLIF's event-triggering methods are the Scanless recognizer's read(), resume(), lexeme_complete(), and lexeme_read(). If the condition described by the named event statement occurs during an event-triggering method, the method will return immediately, with the current location at the trigger location. Once triggered, named events may be queried using the Scanless recognizer's events() method. For details, see the document on SLIF parse events.
Inaccessible symbol statement
inaccessible is ok by defaultinaccessible is fatal by defaultInaccessible symbols are symbols which cannot be reached from the start symbol. Often, they are the result of an error in grammar writing. But inaccessible symbols can also occur for legitimate reasons -- for example, you may have rules and symbols in grammar intended for future use.
The default can be specified or changed with a statement of the form:
inaccessible is TREATMENT by defaultwhere TREATMENT is one of warn, ok, or fatal.
fatal indicates that an inaccessible symbol should be a fatal error. warn indicates that Marpa should print a warning message, but proceed with the parse. warn is the default. ok indicates that the parse should proceed without warning messages.
Ambiguity
Marpa parses ambiguous grammars and the design of the SLIF exploits this. A flexible, but potentially ambiguous, syntax is used. Actual ambiguities are obvious to the human eye, and users will create them, so that the techniques of this section will rarely be needed.
If and when an actual ambiguity does occur, an error message reports the ambiguity and its exact location. It will always be possible to disambiguate a SLIF DSL, and there will always be more than one way to do this.
Separating statements with semicolons
:default ::= action => ::array
quartet ::= a a a a;
inaccessible is warn by default
a ~ 'a'A statement may be terminated with a semicolon (";").
Grouping statements in curly braces
{
:default ::= action => ::array
quartet ::= a a a a
}
inaccessible is warn by default
a ~ 'a'Statements can be grouped, using curly braces. These do not create scopes -- the curly braces serve merely to group and to separate groups of statements.
Other ways to disambiguate
There are many other ways to disambiguate SLIF statements. If the ambiguity is between keywords and symbol names, enclosing a symbol name in angle brackets will force it to be treated only as a symbol name. And while it is never necessary, statements can be re-ordered.
Adverbs
Adverbs consist of a keyword, the adverb operator ("=>"), and the adverb's value. The keyword must be one of those described in this section. The adverb's value must be as described for each keyword.
action
The action adverb is allowed for
An RHS alternative, in which the action is for the alternative.
The default pseudo-rule, in which case the action is for all rules which do not have their own action explicitly specified.
The lexeme default statement, in which case the action is for all lexemes.
The action adverb is not allowed for L0 rules. The possible values of actions are described, along with other details of the semantics, in a separate document.
assoc
The assoc adverb is only valid in a prioritized rule. Its value must be one of left, right or group. Its effect will be as described below.
bless
The bless adverb causes the result of the semantics to be blessed into the class indicated by the value of the adverb. Details of its use may be found in the semantics document.
event
:lexeme ~ <a> pause => before event => 'before a'
:lexeme ~ <b> pause => after event => 'after b'=on
:lexeme ~ <c> pause => before event => 'before c'=off
:lexeme ~ <d> pause => after event => 'after d'The event adverb applies only to lexemes and is only allowed in a :lexeme pseudo-rule. It names the event specified by the pause adverb. It is a fatal error to specify the event adverb if the pause adverb is not also specified.
The value of the event adverb is an event initializer. Event initializers are as described above.
When an event declared with the the pause adverb is not named using the event adverb, an unnamed event results. An unnamed event cannot be accessed by normal methods and the use of unnamed events is strongly discouraged. SLIF parse events are described in detail in a separate document.
name
start ::= number1 number2 name => top
number1 ::= <forty two> name => 'number 1'
number2 ::= <forty three> name => 'number 2'The name adverb applies only to rules and rule alternatives. When specified, it defines a name for that rule alternative.
null-ranking
S ::= A A A A null-ranking => highThe null-ranking adverb applies only to G1 rules (L0 rules do not have a semantics) and is ignored unless the SLIF recognizer's ranking_method named argument is set to something other than its default. Some rule alternatives can match the same input in several ways, depending on which symbols are nulled. These different ways of nulling symbols in a rule are called its null variants. The null-ranking named argument allows the application to control the order in which null variants are returned by the value() method.
If null-ranking is undefined, the order of the null variants will be arbitrary. This is the default, and is acceptable to most applications. For details on using the null-ranking adverb, see the document on parse order.
pause
:lexeme ~ <a> pause => before event => 'before a'
:lexeme ~ <b> pause => after event => 'after b'=on
:lexeme ~ <c> pause => before event => 'before c'=off
:lexeme ~ <d> pause => after event => 'after d'The pause adverb applies only to lexemes and is only allowed in a :lexeme pseudo-rule. The pause adverb declares a SLIF parse event. The event adverb names the SLIF parse event declared by the pause adverb.
When an event declared with the the pause adverb is not named using the event adverb, an unnamed event results. An unnamed event cannot be accessed by normal methods and the use of unnamed events is strongly discouraged.
priority
The priority adverb is only allowed in a :lexeme pseudo-rule. It sets the lexeme priority for the lexeme. The priority must be an integer, but it may be negative. An increase in numerical value means a higher priority. For example, a priority of 1 is greater than a priority of 0. A priority of 0, in turn, is greater than a priority of -1. The default priority is zero.
Where more than one lexeme can be accepted at a location, the lexeme priority limits the lexemes that will be considered. Only lexemes with the highest priority are considered. If several lexemes have the same priority, all of them will be accepted.
The only effect of the lexeme priority is on the choice of lexemes when
all of them would be accepted;
all started at the same string location;
all end at the same string location; and therefore
all have the same length.
Lexeme priorities only have an effect when lexemes are accepted. The intent of this scheme is to avoid situations where a lexeme with a high priority is rejected, and causes a parse to fail, even though another lower priority lexeme is acceptable and would allow the parse to continue.
For example, suppose that "say" can be both a keyword (<say keyword>), and a variable name (<variable>). Suppose further that the grammar specifies that <say keyword> has a priority of 1, and <variable> is left at the default priority of 0. When L0 finds a occurrence of "say", where both the say keyword and a variable name would be accepted by G1, then only the say keyword is read by G1, because of the priorities.
But, suppose instead that the parse is at a location where G1 is not accepting the <say keyword>. Since only lexeme priorites of acceptable lexemes are considered, <variable> lexeme has the highest priority, and the literal string "say" will be read as a <variable> token.
proper
The proper keyword is only valid for a quantified right side, and its value must be a boolean, in the form of a binary digit (0 or 1). It is only relevant if a separator is defined and is 1 if proper separation is required, and 0 if Perl separation is allowed. "Perl separation" allows a final separator. "Proper separation" is so called, because it requires that separators be "proper" in the sense that they must actually separate sequence items.
rank
unspecial ::= ('I' 'am' 'special') words ('--' 'NOT!' ';') rank => 1
special ::= words (';') rank => -1rank is ignored unless the recognizer's ranking_method named argument is set to something other than its default. The range allowed for rank is implementation-defined, but numbers in the range between -134,217,727 and 134,217,727 will always be allowed. rank is 0 by default. For details on using the rank named argument, see the document on parse order.
separator
The separator keyword is only valid for a quantified right side, and its value must be a single symbol -- either a single symbol name, or a character class. If specified, the separator must separate items of the sequence. A separator may not be nullable.
Precedence
Marpa's precedence is a generalization beyond the traditional ideas of precedence. Traditional precedence parsing required the classification of operators as postfix, infix, etc. Marpa's precedence parsing is NOT based on the special treatment of operators.
For the purpose of precedence, an operand is an occurrence in a RHS alternative of the LHS symbol. An operator is considered to be anything that is not an operand. The arity of an alternative is the number of operands that it contains. All arities are allowed, from zero to the arbitrary number imposed by system limits such as memory and file size.
For example, in the synopsis, the LHS symbol is Expression. The alternative
'(' Expression ')'contains one occurrence of Expression and therefore has an arity of one. The <op lparen> and <op rparen> are considered operators.
In the RHS alternative
Expression '**' ExpressionExpression occurs twice, and therefore the arity is 2. <op pow> is considered to be an operator.
Because for this purpose an operator is defined as anything that is not an operand, Marpa treats some symbols as operators that would not be considered operators in the traditional approach. For example, in the RHS alternative
Numberthere are no occurrences of Expression, so that the alternative has an arity of zero -- it is nullary. The symbol Number is considered to be an operator.
An alternative with arity 0 is nullary. Precedence and associativity are meaningless in this case and will be ignored.
An alternative with arity 1 is unary. Precedence will have effect, but left and right associativity will not.
An alternative with arity 2 is binary. Precedence will have effect, and left and right associativity will behave in the traditional way. The traditional behavior for binary alternatives is exactly as described next for the N-ary case.
An alternative with an arity of N, where N is 2 or greater, is N-ary. Precedence will have effect. For left associativity, only the leftmost operand of an N-ary alternative associates -- operands after the first will have the next-tightest priority level. For right associativity, only the rightmost operand of an N-ary alternative associates -- all operands except the last will have the next-tightest priority level.
Marpa also allows "group" associativity. In "group" associativity, all operands associate at the loosest (lowest) priority. That is, in an alternative with group associativity, each operand may be a full expression of the kind defined by the prioritized rule. "Group" associativity is used, for example, in implementing the traditional function of parentheses in Marpa. Group associativity is meaningless for nullary alternatives, and is ignored.
Precedence and ambiguous grammars
Marpa's generalization of precedence works for all grammars that can be defined by prioritized rules. It is efficient (linear) for all grammars that could be parsed by the traditional precedence parsing methods. Marpa also allows you to define alternatives not allowed by traditional methods. Many of these are useful, and most of the useful ones can be parsed efficiently.
Because of the many forms of recursion allowed, it is possible to define highly ambiguous grammars using the precedence mechanism. This can occur even by accident.
The user should especially be careful with right hand side alternatives in which all the symbols are operands. These can be useful. For example, an implicit operation can be defined using a binary alternative with no non-operands, and this could implement, for example, the standard notation for concatenation or multiplication. But to do this efficiently requires either avoiding ambiguity, or controlling its use carefully.
Marpa does catch the case where an alternative consists only of a single operand -- a "unit rule". This causes a fatal error. Unit rules are easy to define by accident in the SLIF. The author knows of no practical use for them, and their presence in a grammar is usually unintentional. Note that, in the event an application does find a use for a grammar with unit rules, the NAIF and the Thin interface can parse it.
Copyright and License
Copyright 2016 Jeffrey Kegler
This file is part of Marpa::R3. Marpa::R3 is free software: you can
redistribute it and/or modify it under the terms of the GNU Lesser
General Public License as published by the Free Software Foundation,
either version 3 of the License, or (at your option) any later version.
Marpa::R3 is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
Lesser General Public License for more details.
You should have received a copy of the GNU Lesser
General Public License along with Marpa::R3. If not, see
http://www.gnu.org/licenses/.