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

*Guards
#mathjax

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

The full syntax of a rule is: ( Head :- [Guard | ] Body )
**Rules with a Guard [#x7373323]

Guard must be a multiset of type constraints of the form: p($p1,...,$pn). The same abbreviation scheme as defined for atoms applies to type constraints when a process context name $pi occurs exactly two times in the rule. Guards specify applicability conditions of rewrite rules. The syntax of a rule with a guard is: >$$\textit{Head}\ \texttt{:-}\ \textit{Guard}\ \texttt{|}\ \textit{Body}$$ Type constraints put constraints on the shapes of processes with which the process contexts specified in the arguments can match. The type constraint name p specifies the content of the constraints. where $$\textit{Guard}$$ is a multiset of ''type constraints'' of the form $$c(\texttt{\}p_1, \dots, \texttt{\}p_n)$$. For example, the following type constraints can be used in Guard: 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. -int($p) specifies that $p must be an integer atom. -$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.
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).

In reality, 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 of its input arguments are all determined.
***Examples [#oc28c486]

**Typed Process Contexts
Here is an example rule with guard:

A process context name $p constrained in Guard is said to be typed in that rule. As a syntactic sugar, typed process context names can be written as link names as follows: waitint(X),$p[X] :- int($p) | ok. ( Res = gen(N) :- N > 0 | Res = [N|gen(N-1)] ), p(gen(10)) This can be abbreviated to **Guard Library Currently, the following type constraints can be used in the gua rd. waitint($p) :- int($p) | ok. '='(+Unary,-Unary) - equivalence '='(-Unary,+Unary) - equivalence '=='(+Unary,+Unary) - equivalence unary(+Unary) int(+Int) float(+Float) int(+Float,-Int) - cast float(+Int,-Float) - cast 345(-Int) - for every integer, not only with 345 '-3.14'(-Float) - for every floating, not only with -3.14 '<'(+Int,+Int) - integer comparison, as well as: > =< >= =:= =\= '+'(+Int,+Int,-Int) - integer operation, as well as: - * / mod '<.'(+Float,+Float) - floating comparison, as well as: >. =<. >=. =:=. =\=. '+.'(+Float,+Float,-Float) - floating operation, as well as: -. *. /. and can be thought of representing the following infinite number of rules: waitint(0) :- ok. waitint(1) :- ok. waitint(-1) :- ok. waitint(2) :- ok. waitint(-2) :- ok. ... The following are examples of some type constraints that can be written in '''Guard''': -&color(#8B4513){int($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 [#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

// **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.

**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

***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};, ..., $'''p'''&size(10){'''n'''}; before. As a special case of '''n'''=0, ''uniq'' succeeds if the rule in question has not been used before. The ''uniq''() test is a general tool for avoiding infinite application of rules whose right-hand side is a super(multi)set of the left-hand side. //***Others [#i37c8a7c] :uniq(+$g1,...,+$gn)|uniqueness constraint; checks if the rule has not been applied to the tuple$g1[X1], ..., \$gn[Xn] (n>=0).