Name¶
Marpa::R2::Glade - Low-level interface to Marpa's Abstract Syntax Forests
(ASF's)
Synopsis¶
my $grammar = Marpa::R2::Scanless::G->new(
{ source => \(<<'END_OF_SOURCE'),
:start ::= pair
pair ::= duple | item item
duple ::= item item
item ::= Hesperus | Phosphorus
Hesperus ::= 'a'
Phosphorus ::= 'a'
END_OF_SOURCE
}
);
my $slr = Marpa::R2::Scanless::R->new( { grammar => $grammar } );
$slr->read( \'aa' );
my $asf = Marpa::R2::ASF->new( { slr => $slr } );
die 'No ASF' if not defined $asf;
my $output_as_array = asf_to_basic_tree($asf);
my $actual_output = array_display($output_as_array);
The code for "asf_to_basic_tree()" represents a user-supplied call
using the interface described below. An full example of
"ast_to_basic_tree()", which constructs a Perl array
"tree", is given below. "array_display()" displays the
tree in a compact form. The code for it is also given below. The return value
of "array_display()" is as follows:
Glade 2 has 2 symches
Glade 2, Symch 0, pair ::= duple
Glade 6, duple ::= item item
Glade 8 has 2 symches
Glade 8, Symch 0, item ::= Hesperus
Glade 13, Hesperus ::= 'a'
Glade 15, Symbol 'a': "a"
Glade 8, Symch 1, item ::= Phosphorus
Glade 1, Phosphorus ::= 'a'
Glade 17, Symbol 'a': "a"
Glade 7 has 2 symches
Glade 7, Symch 0, item ::= Hesperus
Glade 22, Hesperus ::= 'a'
Glade 24, Symbol 'a': "a"
Glade 7, Symch 1, item ::= Phosphorus
Glade 9, Phosphorus ::= 'a'
Glade 26, Symbol 'a': "a"
Glade 2, Symch 1, pair ::= item item
Glade 8 revisited
Glade 7 revisited
This INTERFACE is ALPHA and EXPERIMENTAL¶
The interface described in this document is very much a work in progress. It is
alpha and experimental. The bad side of this is that it is subject to radical
change without notice. The good side is that field is 100% open for users to
have feedback into the final interface.
About this document¶
This document describes the low-level interface to Marpa's abstract syntax
forests (ASF's). It assumes that you are already familiar with the high-level
interface. This low-level interface allows the maximum flexiblity in building
the forest, but requires the application to do much of the work.
Ambiguity: factoring versus symches¶
An abstract syntax forest (ASF) is similar to an abstract syntax tree (AST), but
it has an additional ability -- it can represent an ambiguous parse. Ambiguity
in a parse can come in two forms, and Marpa's ASF's treat the distinction as
important. An ambiguity can be a symbolic choice (a symch), or a factoring.
Symbolic choices are the kind of ambiguity that springs first to mind -- a
choice between rules, or a choice between a rule and token. Factorings involve
only one rule, but the RHS symbols of that rule divide the input up
("factor it") in different ways. I'll give examples below.
Symches and factorings are treated separately, because they behave very
differently:
- •
- Symches are less common than factorings.
- •
- Factorings are frequently not of interest; symches are almost always of
major interest.
- •
- Symches usually have just a few alternatives; the possible number of
factorings easily grows into the thousands.
- •
- In the worst case, the number of symches is a constant that depends on
size of the grammar. In the worst case, the number of factorings grows
exponentially with the length of the string being factored.
- •
- The constant limiting the number of symches will almost always be of
manageable size. The number of factorings can grow without limit.
An example of a symch¶
Hesperus is Venus's traditional name as an evening star, and Phosphorus (aka
Lucifer) is its traditional name as a morning star. For the grammar,
:start ::= planet
planet ::= hesperus
planet ::= phosphorus
hesperus ::= venus
phosphorus ::= venus
venus ~ 'venus'
and the input string '"venus"', the forest would look like
Symbol #0 planet has 2 symches
Symch #0.0
GL2 Rule 0: planet ::= hesperus
GL3 Rule 2: hesperus ::= venus
GL4 Symbol venus: "venus"
Symch #0.1
GL2 Rule 1: planet ::= phosphorus
GL5 Rule 3: phosphorus ::= venus
GL6 Symbol venus: "venus"
Notice the tags of the form ""GLn"", where
n is an
integer. These identify the glade. Glades will be described in detail below.
The rules allow the string '"venus"' to be parsed as either one of two
planets: '"hesperus"' or '"phosphorus"', depending on
whether rule 0 or rule 1 is used. The choice, at glade 2, between rules 0 and
1, is a symch.
An example of a factoring¶
For the grammar,
:start ::= top
top ::= b b
b ::= a a
b ::= a
a ~ 'a'
and the input '"aaa"', a successful parse will always have two
"b"'s. Of these two "b"'s one will always be short,
deriving a string of length 1: '"a"'. The other will always be long,
deriving a string of length 2: '"aa"'. But they can be in either
order, which means that the two "b"'s can divide up the input stream
in two different ways: long string first; or short string first.
These two different ways of dividing the input stream using the rule
top ::= b b
are called a
factoring. Here's Marpa's dump of the forest:
GL2 Rule 0: top ::= b b
Factoring #0
GL3 Rule 2: b ::= a
GL4 Symbol a: "a"
GL5 Rule 1: b ::= a a
GL6 Symbol a: "a"
GL7 Symbol a: "a"
Factoring #1
GL8 Rule 1: b ::= a a
GL9 Symbol a: "a"
GL10 Symbol a: "a"
GL11 Rule 2: b ::= a
GL12 Symbol a: "a"
The structure of a forest¶
An ASF can be pictured as a forest on a mountain. This mountain forest has
glades, and there are paths between the glades. The term "glade"
comes from the idea of a glade as a distinct place in a forest that is open to
light.
The paths between glades have a direction -- they are always thought of as
running one-way: downhill. If a path connects two glades, the one uphill is
called an upglade and the one downhill is called a downglade.
There is a glade at the top of mountain called the "peak". The peak
has no upglades.
The glade hierarchy¶
Every glade has the same internal structure, which is this hierarchy:
- •
- Glades contain symches. A symch is either for a rule or for a token.
- •
- Rule symches contain factorings.
- •
- Factorings contain factors.
- •
- A factor is the uphill end of a path which leads to a downglade. That
downglade will contain a glade hierarchy of its own.
Glades¶
Each glade node represents an instance of a symbol in one of the possible parse
trees. This means that each glade has a symbol (called the "glade
symbol"), and an "input span". An input span is an input start
location, and a length in characters. Because it has a start location and a
length, a span also specifies an end location in the input.
Symches¶
Every glade contains one or more symches. If a glade has only one symch, that
symch is said to be
trivial. A symch is either a token symch or a rule
symch. For a token symch, the glade symbol is the token symbol. For a rule
symch, the glade symbol is the LHS of the rule.
At most one of the symches in a glade can be a token symch. There can, however,
be many rule symches in a glade -- one for every rule with the glade symbol on
its LHS.
Factorings¶
Each rule symch contains one or more factorings. A factoring is a way of
dividing up the input span of the glade among its RHS symbols, which in this
context are called
factors. If a rule symch has only one factoring,
that factoring is said to be
trivial. A token symch contains no
factorings, which means that token symches are the
terminals of an ASF.
Because the number of factorings can get out of hand, factorings may be omitted.
A symch which omits factorings is said to be
truncated. By default,
every symch is truncated down to its first 42 factorings.
Factors¶
Every factoring has one or more factors. Each "factor" corresponds to
a symbol instance on the RHS of the rule. Each such RHS factor is also a
downglade, one which contains its own symches.
The glade ID¶
Each glade has a glade ID. This can be relied on to be a non-negative integer. A
glade ID may be zero. Glade ID's are obtained from the "
peak()" and "
factoring_downglades()" methods.
Techniques for traversing ASF's¶
Memoization¶
When traversing a forest, you should take steps to avoid traversing the same
glades twice. You can do this by memoizing the result of each glade, perhaps
using its glade ID to index an array. When a glade is visited, the array can
be checked to see if its result has been memoized. If so, the memoized result
should be used.
This memoization eliminates the need to revisit the downglades of an already
visited glade. It does not eliminate multiple visits to a glade, but it does
eliminate retraversal of the glades downhill from it. In practice, the
improvement in speed can be stunning. It will often be the difference between
an program which is unuseably slow even for very small inputs, and one which
is extremely fast even for large inputs.
Repeated subtraversals happen when two glades share the same downglades,
something that occurs frequently in ASF's. Additionally, some day the SLIF may
allow cycles. Memoization will prevent a cycle form causing an infinite loop.
The example in this POD includes a memoization scheme which is very simple, but
adequate for most purposes. The main logic of its memoization is shown here.
my ( $asf, $glade, $seen ) = @_;
return bless ["Glade $glade revisited"], 'My_Revisit'
if $seen->[$glade];
$seen->[$glade] = 1;
Putting memoization in one of the very first drafts of your code will save you
time and trouble.
Forest method¶
peak()¶
my $peak = $asf->peak();
Returns the glade ID of the peak. This may be zero. All failures are thrown as
exceptions.
Glade methods¶
glade_literal()¶
my $literal = $asf->glade_literal($glade);
Returns the literal substring of the input associated with the glade. Every
glade is associated with a span -- a start location in the input, and a
length. On failure, throws an exception.
The literal is determined by the range. This works as expected if your
application reads the input characters one-by-one in order. (We will call
applications which read in this fashion,
monotonic.) Most applications
are monotonic, and yours is, unless you've taken special pains to make it
otherwise. Computation of literal substrings for non-monotonic applications is
addressed in "Literals and G1 spans" in Marpa::R2::Scanless::R.
glade_span()¶
my ( $glade_start, $glade_length ) = $asf->glade_span($glade_id);
Returns the span of the input associated with the glade. Every glade is
associated with a span -- a start location in the input, and a length. On
failure, throws an exception.
The span will be as expected if your application reads the input characters
one-by-one in order. (We will call applications which read in this fashion,
monotonic.) Most applications are monotonic, and yours is, unless
you've taken special pains to make it otherwise. Computation of literal
substrings for non-monotonic applications is addressed in "Literals and
G1 spans" in Marpa::R2::Scanless::R.
glade_symch_count()¶
my $symch_count = $asf->glade_symch_count($glade);
Requires a glade ID as its only argument. Returns the number of symches
contained in the glade specified by the argument. On failure, throws an
exception.
glade_symbol_id()¶
my $symbol_id = $asf->glade_symbol_id($glade);
my $display_form = $grammar->symbol_display_form($symbol_id);
Requires a glade ID as its only argument. Returns the symbol ID of the
"glade symbol" for the glade specified by the argument. On failure,
throws an exception.
Symch methods¶
symch_rule_id()¶
my $rule_id = $asf->symch_rule_id( $glade, $symch_ix );
Requires two arguments: a glade ID and a zero-based symch index. These specify a
symch. If the symch specified is a rule symch, returns the rule ID. If it is a
token symch, returns -1.
Returns a Perl undef, if the glade exists, but the symch index is too high. On
other failure, throws an exception.
symch_is_truncated()¶
[ To be written. ]
symch_factoring_count()¶
my $factoring_count =
$asf->symch_factoring_count( $glade, $symch_ix );
Requires two arguments: a glade ID and a zero-based symch index. These specify a
symch. Returns the count of factorings if the specified symch is a rule symch.
This count will always be one or greater. Returns zero if the specified symch
is a token symch.
Returns a Perl undef, if the glade exists, but the symch index is too high. On
other failure, throws an exception.
Factoring methods¶
factoring_downglades()¶
my $downglades =
$asf->factoring_downglades( $glade, $symch_ix,
$factoring_ix );
Requires three arguments: a glade ID, the zero-based index of a symch and the
zero-based index of a factoring. These specify a factoring. On success,
returns a reference to an array. The array contains the glade IDs of the the
downglades in the factoring specified.
Returns a Perl undef, if the glade and symch exist, but the factoring index is
too high. On other failure, throws an exception. In particular, exceptions are
thrown if the symch is for a token; and if the glade exists, but the symch
index is too high.
Methods for reporting ambiguity¶
if ( $recce->ambiguity_metric() > 1 ) {
my $asf = Marpa::R2::ASF->new( { slr => $recce } );
die 'No ASF' if not defined $asf;
my $ambiguities = Marpa::R2::Internal::ASF::ambiguities($asf);
# Only report the first two
my @ambiguities = grep {defined} @{$ambiguities}[ 0 .. 1 ];
$actual_value = 'Application grammar is ambiguous';
$actual_result =
Marpa::R2::Internal::ASF::ambiguities_show( $asf, \@ambiguities );
last PROCESSING;
} ## end if ( $recce->ambiguity_metric() > 1 )
ambiguities()¶
my $ambiguities = Marpa::R2::Internal::ASF::ambiguities($asf);
Returns a reference to an array of ambiguity reports in the ASF. The first and
only argument must be an ASF object. The array returned will be be zero length
if the parse was not ambiguous. Ambiguity reports are as described below.
While the "ambiguities()" method can be called to determine whether or
not ambiguities exist, it is the more expensive way to do it. The $slr->
ambiguity_metric() method tests an already-existing boolean and is
therefore extremely fast. If you are simply testing for ambiguity, or if you
can save time when you know that a parse is unambiguous, you will usually want
to test for ambiguity with the "ambiguity_metric()" method before
calling the "ambiguities()" method.
ambiguities_show()¶
$actual_result =
Marpa::R2::Internal::ASF::ambiguities_show( $asf, \@ambiguities );
Returns a string which contains a description of the ambiguities in its
arguments. Takes two arguments, both required. The first is an ASF, and the
second is a reference to an array of ambiguities, in the format returned by
the
ambiguities() method.
Major applications will often have their own customized ambiguity formatting
routine, one which can formulate error messages based, not just on the names
of the rules and symbols, but on knowledge of the role that the rules and
symbols play in the application. This method is intended for applications
which do not have their own customized ambiguity handling. For those which do,
it can be used as a fallback for handling those reports that the customized
method does not recognize or that do not need special handling. The format of
the returned string is subject to change.
Ambiguity reports¶
The ambiguity reports returned by the "ambiguities()" method are of
two kinds: symch reports and factoring reports.
Symch reports¶
A symch report is issued whenever, in a top-down traversal of the ASF, an
non-trivial symch is encountered. A symch report takes the form
[ 'symch', $glade ]
where $glade is the ID of the glade with the symch ambiguity. With this and the
accessor methods in this document, an application can report full details of
the symch ambiguity.
Typically, when there is more than one kind of ambiguity in an input span, only
one is of real interest. Symch ambiguities are usually of more interest than
factorings. And if one ambiguity is uphill from another, the downhill
ambiguity is usually a side effect of the uphill one and of little interest.
Accordingly, if a glade has both a symch ambiguity and a factoring ambiguity,
only the symch ambiguity is reported. And if two ambiguities in the ASF
overlap, only the one closest to the peak is reported.
Factoring reports¶
A symch report is issued whenever, in a top-down traversal of the ASF, an
sequence of symbols is found which has more than one factoring. Factoring
reports are specific -- they identify not just rules, but the specific
sequences within the RHS which are differently factored --
multifactored
stretches. Sequence rules especially have long stretches where the symbols
are in sync with each other, broken by other stretches where they are out of
sync. Marpa reports each of the ambiguous stretches. (A detailed definition of
multifactored stretches is below.)
A factoring report takes the form
[ 'factoring', $glade, $symch_ix, $factor_ix1, $factoring_ix2, $factor_ix2 ];
where $glade is the ID of the glade with the factoring ambiguity, and $symch_ix
is the index of the symch involved. The multifactored stretch is described by
two "identifying factors". Both factors are at the beginning of the
stretch, and therefore have the same input start location. They differ in
length.
The first of the two identifying factors has factoring index of 0, and its
factor index is $factor_ix1. The second identifying factor has a factoring
index of $factoring_ix2, and its factor index is $factor_ix2.
The identifying factors will usually be enough for error reporting, which is the
usual application of these reports. Full details of the stretch are not given
because they can be extremely large; are usually not of interest; and can be
determined by following up on the information in the factoring report using
the accessor methods described in this document.
Ambiguities in rules and symbols downhill from an ambiguously factored stretch
are not reported. If a glade has both a symch ambiguity and a factoring
ambiguity, only the symch ambiguity is reported.
The code for the synopsis¶
The asf_to_basic_tree() code¶
sub asf_to_basic_tree {
my ( $asf, $glade ) = @_;
my $peak = $asf->peak();
return glade_to_basic_tree( $asf, $peak, [] );
} ## end sub asf_to_basic_tree
sub glade_to_basic_tree {
my ( $asf, $glade, $seen ) = @_;
return bless ["Glade $glade revisited"], 'My_Revisit'
if $seen->[$glade];
$seen->[$glade] = 1;
my $grammar = $asf->grammar();
my @symches = ();
my $symch_count = $asf->glade_symch_count($glade);
SYMCH: for ( my $symch_ix = 0; $symch_ix < $symch_count; $symch_ix++ ) {
my $rule_id = $asf->symch_rule_id( $glade, $symch_ix );
if ( $rule_id < 0 ) {
my $literal = $asf->glade_literal($glade);
my $symbol_id = $asf->glade_symbol_id($glade);
my $display_form = $grammar->symbol_display_form($symbol_id);
push @symches,
bless [qq{Glade $glade, Symbol $display_form: "$literal"}],
'My_Token';
next SYMCH;
} ## end if ( $rule_id < 0 )
# ignore any truncation of the factorings
my $factoring_count =
$asf->symch_factoring_count( $glade, $symch_ix );
my @symch_description = ("Glade $glade");
push @symch_description, "Symch $symch_ix" if $symch_count > 1;
push @symch_description, $grammar->rule_show($rule_id);
my $symch_description = join q{, }, @symch_description;
my @factorings = ($symch_description);
for (
my $factoring_ix = 0;
$factoring_ix < $factoring_count;
$factoring_ix++
)
{
my $downglades =
$asf->factoring_downglades( $glade, $symch_ix,
$factoring_ix );
push @factorings,
bless [ map { glade_to_basic_tree( $asf, $_, $seen ) }
@{$downglades} ], 'My_Rule';
} ## end for ( my $factoring_ix = 0; $factoring_ix < $factoring_count...)
if ( $factoring_count > 1 ) {
push @symches,
bless [
"Glade $glade, symch $symch_ix has $factoring_count factorings",
@factorings
],
'My_Factorings';
next SYMCH;
} ## end if ( $factoring_count > 1 )
push @symches, bless [ @factorings[ 0, 1 ] ], 'My_Factorings';
} ## end SYMCH: for ( my $symch_ix = 0; $symch_ix < $symch_count; ...)
return bless [ "Glade $glade has $symch_count symches", @symches ],
'My_Symches'
if $symch_count > 1;
return $symches[0];
} ## end sub glade_to_basic_tree
The array_display() code¶
Because of the blessings in this example, a standard dump of the output array is
too cluttered for comfortable reading. The following code displays the output
from "asf_to_basic_tree()" in a more compact form. Note that this
code makes no use of Marpa, and works for all Perl arrays. It is included for
completeness, and as a simple example of array traversal.
sub array_display {
my ($array) = @_;
my ( undef, @lines ) = @{ array_lines_display($array) };
my $text = q{};
for my $line (@lines) {
my ( $indent, $body ) = @{$line};
$indent -= 6;
$text .= ( q{ } x $indent ) . $body . "\n";
}
return $text;
} ## end sub array_display
sub array_lines_display {
my ($array) = @_;
my $reftype = Scalar::Util::reftype($array) // '!undef!';
return [ [ 0, $array ] ] if $reftype ne 'ARRAY';
my @lines = ();
ELEMENT: for my $element ( @{$array} ) {
for my $line ( @{ array_lines_display($element) } ) {
my ( $indent, $body ) = @{$line};
push @lines, [ $indent + 2, $body ];
}
} ## end ELEMENT: for my $element ( @{$array} )
return \@lines;
} ## end sub array_lines_display
Details¶
This section contains some elaborations of the above, some of them in
mathematical terms. These details are segregated because they are not
essential to using this interface, and while some readers find them more
helpful than distracting, for many others it is the reverse.
An alternative way of defining glade terminology¶
Here's a way of defining some of the above terms which is less intuitive, but
more precise. First, define the
glade length from glades A to glade B
in an ASF as the number of glades on the shortest path from A to B, not
including glade A. (Recall that paths are directional.) If there is no path
between glades A and B, the glade length is undefined. Glade B is a
downglade of glade A, and glade A is an
upglade of glade B, if
and only if the glade length from A to B is 1.
A glade A is
uphill with respect to glade B, and a glade B is
downhill with respect to glade A, if and only if the glade length from
A to B is defined.
A
peak of an ASF is a node without upglades. By construction of the ASF,
there is only one peak. A glade with a token symch is
trivial if it has
no rule symches. A glade without a token symch is
trivial if it has
exactly one downglade.
The
distance-to-peak of a glade "A" is the glade length from
the peak to glade "A". Glade "A" is said to have a higher
altitude than glade "B" if the distance-to-peak of glade
"A" is less than that of glade "B". Glade "A"
has a lower
altitude than glade "B" if the distance-to-peak
of glade "A" is greater than that of glade "B". Glade
"A" has the same
altitude as glade "B" if the
distance-to-peak of glade "A" is equal to that of glade
"B".
Cycles¶
In the current SLIF implementation, a forest is a directed acyclic graph (DAG).
(In the mathematical literature a DAG is also called a "tree", but
that use is confusing in the present context.) The underlying Marpa algorithm
allows parse trees with cycles, and someday the SLIF probably will as well.
When that happens, ASF's will no longer be "acyclic" and therefore
will no longer be DAG's. This document talks about ASF's as if that day had
already come -- it assumes that the ASF's might contain cycles.
In an ASF that contains one or more cycles, the concepts of uphill and downhill
become much less useful for describing the relative positions of glades. For
example, if glade A cycles back to itself through glade B, then
- •
- Glade A will be uphill from glade B, and
- •
- Glade B will be uphill from glade A; so that
- •
- Glade B will be downhill from glade A, and
- •
- Glade A will be downhill from glade B; and
- •
- Glade A will be both downhill and uphill from itself; and
- •
- Glade B will be both downhill and uphill from itself.
ASF's will always be constructed so that the peak has no upglades. Because of
this, the peak can never be part of a cycle. This means that altitude will
always be well defined in the sense that, for any two glades "A" and
"B", one and only one of the following statements will be true:
- •
- Glade "A" is lower in altitude than glade "B".
- •
- Glade "A" is higher in altitude than glade "B".
- •
- Glade "A" is equal in altitude to glade "b".
Token symches¶
In the current SLIF implementation, a symbol is always either a token or the LHS
of a rule. This means that any glade that contains a token symch cannot
contain any rule symches. It also means that any glade that contains a rule
symch will not contain a token symch.
However, the underlying Marpa algorithm allows LHS terminals, and someday the
SLIF probably will as well. This document is written as if that day has
already come, and describes glades as if they could contain both rule symches
and a token symch.
Maximum symches per glade¶
Above, the point is made that the number of symches in a glade, even in the
worst case, is a very manageable number. For a particular case, it is not hard
to work out the exact maximum. Here are the details.
There can be at most one token symch. There can be only rule symch for every
rule. In addition, all rules in a glade must have the glade symbol as their
LHS. Let the number of rules with the glade symbol on their LHS be
"r". The maximum number of symches in a glade is "r+1".
Multifactored stretches¶
Marpa locates factoring ambiguities, not just by rule, but by RHS symbol. It
finds
multifactored stretches, input spans where a sequence of symbols
within the RHS of a rule have multiple factorings. A multifactored stretch
will sometimes encompass the entire RHS of a rule. In other cases, the RHS of
a single rule might contain many multifactored stretches. This is often the
case with sequence rules. Sequence rules can have a very long RHS, and in
those situations narrowing down factoring ambiguities to specific input spans
is necessary for precise error reporting.
The main body of this document worked with an intuitive "know one when I
see one" idea of multifactored stretches. The exact definition follows.
First we will need a series of preliminary definitions.
Consider the case of a arbitrary rule symch. Intuitively, a
factoring
position is a location within the factors of one of the factorings of that
symch. It can be seen as a duple "<factoring_ix, factor_ix>"
where "<factoring_ix>" is the index of a factoring within the
symch, and "<factor_ix>" is the index of one of the factors of
the factoring.
Let "SP" be a function that maps the symch's set of factoring indexes
to the non-negative integers, such that for a factoring index "i"
and factor index "j", "SP(i)=j", "j" is a valid
factor index within the factoring "i". The function "SP"
can be called a
symch position.
Every
symch position is equivalent to a set of factoring positions. The
initial symch position is the symch position all of whose factoring
positions have a factor index of 0. Equivalently, it is the constant function
"ISP", where "ISP(i)=0" for all factoring indexes
"i".
The factor with index "factor_ix" in the factoring with index
"factoring_ix" is said to be the factor at factoring position
"<factoring_ix, factor_ix>". A factor is one of the factors of
a symch position if and only if it is a factor at one of its factoring
positions.
An
aligned symch position is a factoring position all of whose factors
have the same start location. The location of an aligned symch position is
that start location. The
initial symch position is always an aligned
factoring position. A
synced symch position is an aligned symch
position all of whose factors have the same length and symbol ID. A
unsynced symch position is an aligned symch position that is not a
synced symch position.
We are now in a position to define a
multifactored stretch. Intuitively,
a multifactored stretch is a longest possible input span that contains at
least one unsynced symch position, but no synced symch positions. More
formally, a multifactored stretch of a symch is a span of start locations
within that symch, such that:
- •
- Its first location is the location of unsynced symch position.
- •
- Its first location is the initial symch position, or the first symch
positiion after a synched symch position.
- •
- Its end location is the end location of the symch, or a synced symch
position, whichever occurs first.
Note that multifactored stretch are aligned in terms of input locations, but
they do not have to be aligned in terms of factor indexes. The factoring
positions of a multifactored stretch can have many different factor indexes.
This is true of all rules, but it is particularly likely for a sequence rule,
where the RHS consists of repetitions of a single symbol.
Copyright and License¶
Copyright 2014 Jeffrey Kegler
This file is part of Marpa::R2. Marpa::R2 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::R2 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::R2. If not, see
http://www.gnu.org/licenses/.