Hyperlinks

Hyperlinks and hypergraphs †

LMNtal links represent point-to-point connection between atoms and form an ordinary graph. In some applications, however, natural modeling calls for hyperlinks, namely links that interconnect more than two atoms. A graph structure with hyperlinks forms a (hierarchical) hypergraph.

Accordingly, LMNtal now provides the syntax and operations for hypergraphs. The language with this extension is also called HyperLMNtal.

Creating a hyperlink †

A hyperlink is created by a new construct specified in a guard.

hoge.
hoge :- new($h) | a($h), b($h).

Since each hyperlink can be regarded as a unary atom with a fresh local name, we use the syntax of process contexts (starting with a '$') to represent it.

Another view of hyperlinks is a generalization of ordinary links, and they can be written also by attaching '!' to link names as

hoge.
hoge :- a(!H), b(!H).

or just

a(!H), b(!H).

The result of all the above programs will be

a(!H4), b(!H4).

That is, a hyperlink will be printed as a '!H' followed by a system-generated hexadecimal number.

Type checking †

The type constraint hlink($x) checks if $x represents a hyperlink.

main.
main :- new($x) | a($y).
a($x) :- hlink($x) | b($x,$x).

or

a(!Y).
a(!X) :- b(!X,!X).

Result:

b(!H4,!H4).

Equality checking †

Since an occurrence of a hyperlink is regarded as a unary atom with a special private name, the constructs == and \== can be used for comparing two hyperlinks, e.g.,

a($x), b($y) :- hlink($x), hlink($y), $x == $y | ok.

The above rule can be written also as

a($x), b($x) :- ok.

or

a(!X), b(!X) :- ok.

Fusing two hyperlinks †

Two hyperlinks can be fused into one using the "><" operator.

main.
main :- new($x), new($y) | a($x), b($z).
a($x), b($y) :- $x \== $y | ab($x,$y), $x >< $y.

or

a(!X), b(!Z).
a(!X), b(!Y) :- !X \== !Y | ab(!X,!Y), !X >< !Y.

If $x and $y represent different hyperlinks (i.e., have different hyperlink names), they will be merged into one; that is, they are made to have the same hyperlink name.

Number of occurrences †

The num construct in a guard will return the number of occurrences of the specified hyperlink.

main.
main :- new($x) | a($x), b($x).
a($h) :- $n = num($h) | occurrences($n).

or

a(!X), b(!X).
a(!H) :- $n = num(!H) | occurrences($n).

Result:

b(!H4), occurrences(2). 

Another use:

a(!X).
a(!H) :- num(!H) < 5 | a(!H), a(!H).

Result:

a(!H4), a(!H4), a(!H4), a(!H4), a(!H4).

Yet another use:

flag(!X), a(!X), a(!X), a(!X), a(!X), a(!X).
a(!H) :- .
flag(!H) :- num(!H) =:= 1 | ok.

Result:

ok. // ok is created when all a(!H1)'s are removed

In this way, using hyperlinks, one can check the absence of a particular hyperlink.

How to use †

LaViT †

When you execute your program under LaViT (recommended), select the Option tab and turn on the following checkboxes:

• Compile Option: --slimcode and --hl-opt
• Slim Option: --hl

Please see below for the details of those options.

Compiling †

Currently, programs with hyperlinks can be executed only under SLIM. To compile them, both --slimcode and --hl (or --hl-opt) options need be specified, e.g.,

lmntal --slimcode --hl hoge.lmn > hoge.il

• --hl : turn on hyperlinks.
• --hl-opt : turn on hyperlinks and optimize graph matching using hyperlink connection.

Execution †

Specify --hl when running SLIM, e.g.,

slim --hl --show-hl hoge.il

• --hl : turn on hyperlinks.
• --show-hl : prints the details of hyperlinks.
  • Without this option, different occurrences of a hyperlink are printed with the same name.
  • With this option, each occurrence of a hyperlink is printed with its own ID. In addition, a table of hyperlink occurrences will be printed.