**Rules with a Guard

The syntax of a rule with a guard is:
>'''Head''' :- '''Guard''' | '''Body'''

where '''Guard''' is a multiset of ''type constraints'' of the form:
'''c'''($'''p'''&size(10){1};, ..., $'''p'''&size(10){'''n'''};).

Type constraints constrains the shapes of processes
(or the names of unary atoms)
received by the process contexts $'''p'''&size(10){1};, ..., $'''p'''&size(10){'''n'''};.
The ''type constraint name'' '''c''' is drawn from a built-in set and specifies which kind of constraints is imposed.

A constraint of the form ''uniq''($'''p'''&size(10){1};, ..., $'''p'''&size(10){'''n'''};) is
also allowed.  This is a control structure rather than a type constraint
and used to avoid infinite rule application (see below).


Here is an example rule with guard:

 waitint(X), $p[X] :- int($p) | ok.

This can be abbreviated to

 waitint($p) :- int($p) | ok.

and can be thought of representing the following infinite number of rules:

 waitint(0)  :- ok.
 waitint(1)  :- ok.
 waitint(-1) :- ok.
 waitint(2)  :- ok.
 waitint(-2) :- ok.

The following list contains examples of some type constraints that can be written in '''Guard''':

- int($p) --- specifies that $p must be an integer atom.
- 4($p) --- specifies that $p must be a unary integer atom of value 4 (i.e., 4(X)).
- $p < $q --- specifies that $p and $q are integer atoms
such that the value of $p is less than that of $q.
- $r = $p +. $q --- specifies that $p, $q, and $r are floating
point number atoms
such that the sum of the values of $p and $q is equal to the value of $r. 


Each type constraint name (such as int or <)
has its own mode of usage
that specifies which of its arguments are input arguments.
The effect of the constraint specified by a type constraint
is enabled only after the shapes (or values)
of its input arguments are all determined.
For example, $r = $p + $q proceeds only when $p and $q are determined.

The same abbreviation scheme as defined for atoms
applies to type constraints when a process context name
occurs exactly twice in the rule.
For example, p($n) :- $n>$z, 0($z) | ok can be abbreviated
to p($n) :- $n>0 | ok.

**Typed Process Contexts

A process context constrained in '''Guard'''
is said to be a ''typed process context''.
// As a syntactic sugar,
// typed process context names can be written as link names.
// For inscance, the above example can be written as:
//  waitint(X) :- int(X) | ok.
// // ( Res = gen(N) :- N > 0 | Res = [N|gen(N-1)] ), p(gen(10))
// However, the original form, waitint($p) :- int($p) | ok, is preferred
// because, unlike link names, typed process context names has no constraints
// on the number of their occurrences.

**Avoiding Infinite Rule Application

A constraint of the form
''uniq''($'''p'''&size(10){1};, ..., $'''p'''&size(10){'''n'''};)
succeeds if each $'''p'''&size(10){'''k'''}; is a '''ground''' structure
(connected graph with exactly one free link; see below) 
and the rule has not
been applied to the tuple
$'''p'''&size(10){1};, ..., $'''p'''&size(10){'''n'''};

As a special case of '''n'''=0,
''uniq'' succeeds if the rule in question has not been used
before.  The ''uniq''() test is a general tool for avoiding 
infinite application of rules whose right-hand side is a 
super(multi)set of the left-hand side.

**Guard Library

The following type constraints can be used in guards.
The + (input) sign preceding a process context name means that the name should
appear in the head, while the - (output) sign means that the name should not
appear in the head.

 '='(+$u,-$v)                  - make sure that $u[X] and $v[Y] are unary atoms
                                 with the same name
 '='(-$u,+$v)                  - same as above
 '=='(+$u,+$v)                 - check if $u[X] and $v[Y] are unary atoms with
                                 the same name
 unary(+$u)                    - check if $u[X] is a unary atom
 ground(+$g)                   - check if $g[X1,...,Xn] (n>0) is a connected
                                 graph whose free links are exactly X1,...,Xn 
 int(+$i)                      - check if $i[X] is an integer
 float(+$f)                    - check if $f[X] is a float
 int(+$float,-$int)            - cast
 float(+$int,-$float)          - cast
 345(-$int)                    - defined for every integer (not only with 345)
 '-3.14'(-$float)              - defined for every float
 '<'(+$int,+$int)              - integer comparison; also: > =< >= =:= =\=
 '+'(+$int,+$int,-$int)        - integer operation;  also: - * / mod
 '<.'(+$float,+$float)         - float comparison;   also: >. =<. >=. =:=. =\=.
 '+.'(+$float,+$float,-$float) - float operation;    also: -. *. /.
 uniq(+$g1,...,+$gn)           - uniqueness constraint; checks if the rule has
                                 not been applied to the tuple $g1[X1], ..., $gn[Xn] (n>=0)

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