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#author("2019-05-02T21:06:54+09:00","default:LMNtal","LMNtal")
//[[Documentation]]

*Guards
#mathjax

**Rules with a Guard
*Guards [#v398323a]

**Rules with a Guard [#x7373323]

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 '''Guard''' is a multiset of ''type constraints'' of the form
'''c'''($'''p'''&size(10){1};, ...,$'''p'''&size(10){'''n'''};).
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 $'''p'''&size(10){1};, ...,$'''p'''&size(10){'''n'''};.
The ''type constraint name'' '''c''' is drawn from a built-in set and specifies which kind of constraints is imposed.
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''($'''p'''&size(10){1};, ...,$'''p'''&size(10){'''n'''};) is
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).

***Examples
***Examples [#oc28c486]

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.
...
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''':

-&color(#8B4513){int($p)}; ... specifies that$p must be an integer atom.
-&color(#8B4513){4($p)}; ... specifies that$p must be a unary integer atom of value 4 (i.e., 4(X)).
-&color(#8B4513){$p <$q}; ... specifies that $p and$q are integer atoms
such that the value of $p is less than that of$q.
-&color(#8B4513){$r =$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 $r. ***Notes ***Notes [#z6515d94] Each type constraint name (such as int or <) has its own mode of usage that specifies which of its arguments are input arguments. The effect of the constraint specified by a type constraint is enabled only after the shapes (or values) of its input arguments are all determined. For example,$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
$'''p'''&size(10){'''k'''}; occurs exactly twice in the rule. For example, p($n) :- $n>$z, 0($z) | ok can be abbreviated to p($n) :- $n>0 | ok. For example, p($n) :- $n>$z, 0($z) | ok can be abbreviated to: p($n) :- $n>0 | ok **Typed Process Contexts // **Typed Process Contexts [#z5d7f69f] A process context constrained in '''Guard''' is said to be a ''typed process context''. // As a syntactic sugar, // typed process context names can be written as link names. // For inscance, the above example can be written as: // waitint(X) :- int(X) | ok. // // ( Res = gen(N) :- N > 0 | Res = [N|gen(N-1)] ), p(gen(10)) // However, the original form, waitint($p) :- int($p) | ok, is preferred // because, unlike link names, typed process context names has no constraints // on the number of their occurrences. **Avoiding Infinite Rule Application **Guard Library [#udf848a7] The following type constraints can be used in guards. The + (input) sign preceding a process context name means that the name should appear in the head, while the - (output) sign means that the name should not appear in the head. ***Type checking [#l78e805c] :int(+$i)|check if $i[X] is an integer. :float(+$f)|check if $f[X] is a floating-point number. :unary(+$u)|check if $u[X] is a unary atom. Note that ''int'' and ''float'' are subtypes of ''unary''. :ground(+$g)|check if $g[X1,...,Xn] (n>0) is a connected graph whose free links are exactly X1,...,Xn. Note that ''unary'' is a subtype of ''ground''. ***Comparison [#r7825264] :'='(+$u,+$v)|check if$u[X1,...,Xn] and $v[Y1,...,Yn] are connected graphs with the same structure. :'\='(+$u,+$v)|check if$u[X1,...,Xn] and $v[Y1,...,Ym] are connected graphs with different structures. :'=='(+$u,+$v)|check if$u[X] and $v[Y] are unary atoms with the same name. :'\=='(+$u,+$v)|check if$u[X] and $v[Y] are unary atoms with different names (if either of them are not unary, the check fails.) :'<.'(+$float,+$float)|float comparison; also: ''&color(#8B4513){'>.'};'', ''&color(#8B4513){'=<.'};'', ''&color(#8B4513){'>=.'};'', ''&color(#8B4513){'=:=.'};'', ''&color(#8B4513){'=\=.'};''. :'<'(+$int,+$int)|integer comparison; also: ''&color(#8B4513){'>'};'', ''&color(#8B4513){'=<'};'', ''&color(#8B4513){'>='};'', ''&color(#8B4513){'=:='};'', ''&color(#8B4513){'=\='};''. ***Assignment [#ne364170] :'='(+$u,-$v)|make sure that$u[X] and $v[Y] are unary atoms with the same name. :'='(-$u,+$v)|same as above. :int(+$float,-$int)|cast to int. :float(+$int,-$float)|cast to float. :345(-$int)|defined for every integer (not only with 345).
:'-3.14'(-$float)|defined for every float. :'+'(+$int,+$int,-$int)|integer operation;  also: ''&color(#8B4513){'-'};'', ''&color(#8B4513){'*'};'', ''&color(#8B4513){'/'};'', ''&color(#8B4513){mod};''.
:'+.'(+$float,+$float,-$float)|float operation; also: ''&color(#8B4513){'-.'};'', ''&color(#8B4513){'*.'};'', ''&color(#8B4513){'/.'};''. **Avoiding Infinite Rule Application [#w149d3ab] A constraint of the form ''uniq''($'''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'''};
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.

**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

:'='(+$u,-$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.
:'\=='(+$u,+$v)|check if $u[X] and$v[Y] are unary atoms with different names
(if either of them are not unary, the check fails.)
: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 floating-point number.
: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: ''&color(#8B4513){'>'};'', ''&color(#8B4513){'=<'};'', ''&color(#8B4513){'>='};'', ''&color(#8B4513){'=:='};'', ''&color(#8B4513){'=\='};''.
:'+'(+$int,+$int,-$int)|integer operation; also: ''&color(#8B4513){'-'};'', ''&color(#8B4513){'*'};'', ''&color(#8B4513){'/'};'', ''&color(#8B4513){mod};''. :'<.'(+$float,+$float)|float comparison; also: ''&color(#8B4513){'>.'};'', ''&color(#8B4513){'=<.'};'', ''&color(#8B4513){'>=.'};'', ''&color(#8B4513){'=:=.'};'', ''&color(#8B4513){'=\=.'};''. :'+.'(+$float,+$float,-$float)|float operation;    also: ''&color(#8B4513){'-.'};'', ''&color(#8B4513){'*.'};'', ''&color(#8B4513){'/.'};''.
//***Others [#i37c8a7c]
:uniq(+$g1,...,+$gn)|uniqueness constraint; checks if the rule has not been applied to the tuple $g1[X1], ...,$gn[Xn] (n>=0).