An LMNtal program is written as an LMNtal process, and an LMNtal process is a multiset (bag) of the following:

atomsp(X1, ..., Xn)a graph node with a symbolic name p and an ordered sequence of links Xi
cells{ Process }
m{ Process }
a process enclosed with a membrane (curly braces),
optionally with a membrane name m
rules( Head :- Body )a rewrite rule for processes, explained below

The elements of a multiset are either separated by commas (e.g., a(X), b(X)) or terminated by periods (e.g., a(X). b(X).) .

Links names are written using alphanumeric tokens starting with capital letters (e.g., X, Res). The other alpha-numeric tokens are treated as atom or membrane names (e.g., foo, 123). Quoted symbols can also be used for atom or membrane names (e.g., "foo", 'bar', [:baz:]).

Since link names stand for endpoints of one-to-one links, each link name in a well-formed process must occur at most twice, and each link name in a well-formed rule must occur exactly twice.

Term Notation

Since each link name occurs at most twice, we can abbreviate

p(s1, ..., sm), q(t1, ..., tn)


p(s1, ..., sk-1, q(t1, ..., tn-1), sk+1, ..., sm)

if tn and sk are the same link name. For example,


is an abbreviation of


This can be written also as


because the semantics of LMNtal regards c(1,c(2,n),L0) and L0=L1, c(1,c(2,n),L1) as identical (see Connectors below) and we can apply term abbreviation to the latter to obtain L0=c(1,c(2,n)) .

For an atom name p and a membrane, p(..., {...}, ...) stands for a process p(..., X, ...), {+X, ...} .

List Notation

The Prolog list syntax can be used in LMNtal. List constructor atoms have three arguments and the name '.' .

X=[A,B|Rest], Rest=[]



are abbreviated forms of

'.'(A,Tmp,X), '.'(B,Rest,Tmp), '[]'(Rest).


Binary atoms of the form X=Y are called connector atoms or connectors. A connector states that the two links are interconnected (in zero steps). For example, ( p(A,X,C), X=B ) is equivalent to p(A,B,C), as well as to ( p(A,B,X), C=X ) and C=p(A,B).

Connectors are typically used in the base case of a recursive definition:

( append([],Y,Res)    :- Res=Y ),
( append([A|X],Y,Res) :- Res=[A|R], append(X,Y,R)] )


The basic syntax of a rule is

( Head :- Body ).

The enclosing parentheses can be omitted if periods are used to delimit the rule. Both of Head and Body are process templates.

Head specifies processes to be rewritten and Body specifies the result of rewriting. Rules work only for the processes residing in the same membrane.

The full syntax of a rule that contains Guards will be explained later in a separate section.

Process Templates

A process template is a multiset of the following:

atomsp(X1, ..., Xn)same as in a process
cells{ Template }
{ Template }/
m{ Template }
m{ Template }/
a process template enclosed with a membrane
rules( Head :- Body )allowed only in a Body
process contexts$p
$p[X1, ..., Xn]
$p[X1, ..., Xn|*X]
matches a multiset of atoms and cells (see below)
rule contexts@pmatches a multiset of rules

A cell template with a membrane name only matches a cell with the same membrane name. A cell template with '/' (the stable flag) only matches a stable cell, i.e., a cell containing no applicable rules inside it.

Process Contexts

A process context represents a multiset of atoms and cells. The arguments X1, ..., Xn specify the set of free links that must exist in the matched process. The optional *X represents an arbitrary number of extra free links.

The form $p is an abbreviation of $p[|*X], i.e., a multiset of atoms and cells with no constraints on the occurrences of free links.

A process context must occur within a membrane in a head. Alternatively, it may either occur

Process contexts of the latter kinds are called typed process contexts; see Guards for details.

You can abbreviate

p(s1, ..., sk-1, X, sk+1, ..., sm), $q[X]


p(s1, ..., sk-1, $q, sk+1, ..., sm).

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