Rules with a Guard

Guards specify applicability conditions of rewrite rules. The syntax of a rule with a guard is:

\( \textit{Head}\ \texttt{:-}\ \textit{Guard}\ \texttt{|}\ \textit{Body} \)

where \( \textit{Guard} \) is a multiset of type constraints of the form \( c(\texttt{\$}p_1, \dots, \texttt{\$}p_n) \).

Type constraints constrains the shapes of processes (or the names of unary atoms) received by the process contexts \( \texttt{\$}p_1, \dots, \texttt{\$}p_n \). 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(\( \texttt{\$}p_1, \dots, \texttt{\$}p_n \)) 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 are 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 $pk occurs exactly twice in the rule. For example,

p($n) :- $n>$z, 0($z) | ok

can be abbreviated to:

p($n) :- $n>0 | ok

A process context constrained in Guard is said to be a typed process context.

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.

Type checking

check if $i[X] is an integer.
check if $f[X] is a floating-point number.
check if $u[X] is a unary atom. Note that int and float are subtypes of unary.
check if $g[X1,...,Xn] (n>0) is a connected graph whose free links are exactly X1,...,Xn. Note that unary is a subtype of ground.


check if $u[X1,...,Xn] and $v[Y1,...,Yn] are connected graphs with the same structure.
check if $u[X1,...,Xn] and $v[Y1,...,Ym] are connected graphs with different structures.
check if $u[X] and $v[Y] are unary atoms with the same name.
check if $u[X] and $v[Y] are unary atoms with different names (if either of them are not unary, the check fails.)
float comparison; also: '>.', '=<.', '>=.', '=:=.', '=\=.'.
integer comparison; also: '>', '=<', '>=', '=:=', '=\='.


make sure that $u[X] and $v[Y] are unary atoms with the same name.
same as above.
cast to int.
cast to float.
defined for every integer (not only with 345).
defined for every float.
integer operation; also: '-', '*', '/', mod.
float operation; also: '-.', '*.', '/.'.

Avoiding Infinite Rule Application

A constraint of the form uniq($p1, ..., $pn) succeeds if each $pk is a ground structure (connected graph with exactly one free link; see below) and the rule has not been applied to the tuple $p1, ..., $pn before.

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.

uniqueness constraint; checks if the rule has not been applied to the tuple $g1[X1], ..., $gn[Xn] (n>=0).

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Last-modified: 2019-05-02 (Thu) 12:06:54 (870d)