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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: >'''Head''' :- '''Guard''' | '''Body''' >\( \textit{Head}\ \texttt{:-}\ \textit{Guard}\ \texttt{|}\ \textit{Body} \) 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($p) | ok, is preferred // because, unlike link names, typed process context names has no constraints // on the number of their occurrences. **Avoiding Infinite Rule Application **Guard Library [#udf848a7] A constraint of the form ''uniq''($'''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};, ..., $'''p'''&size(10){'''n'''}; before. As a special case of '''n'''=0, ''uniq'' succeeds if the rule in question has not been used before. The ''uniq''() test is a general tool for avoiding infinite application of rules whose right-hand side is a super(multi)set of the left-hand side. **Guard Library The following type constraints can be used in guards. The + (input) sign preceding a process context name means that the name should appear in the head, while the - (output) sign means that the name should not appear in the head. ***Type checking ***Type checking [#l78e805c] :int(+$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 $g[X1,...,Xn] (n>0) is a connected graph whose free links are exactly X1,...,Xn. Note that ''unary'' is a subtype of ''ground''. ***Comparison ***Comparison [#r7825264] :'='(+$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,+$int)|integer comparison; also: ''&color(#8B4513){'>'};'', ''&color(#8B4513){'=<'};'', ''&color(#8B4513){'>='};'', ''&color(#8B4513){'=:='};'', ''&color(#8B4513){'=\='};''. ***Assignment ***Assignment [#ne364170] :'='(+$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,-$float)|float operation; also: ''&color(#8B4513){'-.'};'', ''&color(#8B4513){'*.'};'', ''&color(#8B4513){'/.'};''. ***Others **Avoiding Infinite Rule Application [#w149d3ab] A constraint of the form ''uniq''($'''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).