Jip J. Dekker
fad1b07018
git-subtree-dir: software/minizinc git-subtree-split: 4f10c82056ffcb1041d7ffef29d77a7eef92cf76
84 lines
4.7 KiB
MiniZinc
84 lines
4.7 KiB
MiniZinc
/***
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@groupdef stdlib.logic Logical operations
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Logical operations are the standard operators of Boolean logic.
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*/
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/** @group stdlib.logic Return truth value of \a x ∧ \a y */
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function bool: '/\'( bool: x, bool: y);
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/** @group stdlib.logic Return truth value of \a x ∧ \a y with identity <> = True*/
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function bool: '/\'(opt bool: x, opt bool: y) = (absent(x) \/ deopt(x)) /\ (absent(y) \/ deopt(y));
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/** @group stdlib.logic Return truth value of \a x ∧ \a y */
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function var bool: '/\'(var bool: x, var bool: y);
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/** @group stdlib.logic Return truth value of \a x ∧ \a y with identity <> = True*/
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function var bool: '/\'(var opt bool: x, var opt bool: y) = (absent(x) \/ deopt(x)) /\ (absent(y) \/ deopt(y));
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/** @group stdlib.logic Return truth value of \a x ∨ \a y */
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function bool: '\/'( bool: x, bool: y);
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/** @group stdlib.logic Return truth value of \a x ∨ \a y with identity <> = False*/
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function bool: '\/'(opt bool: x, opt bool: y) = (occurs(x) /\ deopt(x)) \/ (occurs(y) /\ deopt(y));
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/** @group stdlib.logic Return truth value of \a x ∨ \a y */
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function var bool: '\/'(var bool: x, var bool: y);
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/** @group stdlib.logic Return truth value of \a x ∨ \a y with identity <> = False*/
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function var bool: '\/'(var opt bool: x, var opt bool: y) = (occurs(x) /\ deopt(x)) \/ (occurs(y) /\ deopt(y));
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/** @group stdlib.logic Return truth value of \a x implies \a y */
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function bool: '->'( bool: x, bool: y);
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/** @group stdlib.logic Return truth value of \a x implies \a y */
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function var bool: '->'(var bool: x, var bool: y);
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/** @group stdlib.logic Return truth value of \a y implies \a x */
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function bool: '<-'( bool: x, bool: y);
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/** @group stdlib.logic Return truth value of \a y implies \a x */
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function var bool: '<-'(var bool: x, var bool: y);
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/** @group stdlib.logic Return truth value of \a x if-and-only-if \a y */
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function bool: '<->'( bool: x, bool: y);
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/** @group stdlib.logic Return truth value of \a x if-and-only-if \a y */
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function var bool: '<->'(var bool: x, var bool: y);
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/** @group stdlib.logic Return truth value of \a x xor \a y */
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function bool: 'xor'( bool: x, bool: y);
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/** @group stdlib.logic Return truth value of \a x xor \a y */
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function var bool: 'xor'(var bool: x, var bool: y);
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/** @group stdlib.logic Return truth value of the negation of \a x */
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function bool: 'not'( bool: x);
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/** @group stdlib.logic Negation of \a x if it occurs, otherwise absent */
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function opt bool: 'not'(opt bool: x) = if absent(x) then <> else not deopt(x) endif;
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/** @group stdlib.logic Return truth value of the negation of \a x */
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function var bool: 'not'(var bool: x);
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/** @group stdlib.logic Negation of \a x if it occurs, otherwise absent */
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function var opt bool: 'not'(var opt bool: x) = if absent(x) then <> else not deopt(x) endif;
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/** @group stdlib.logic Return truth value of \(\bigwedge_i \a x[i]\) */
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function bool: forall(array[$T] of bool: x);
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/** @group stdlib.logic Return truth value of \(\bigwedge_i \a x[i]\) */
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function var bool: forall(array[$T] of var bool: x);
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/** @group stdlib.logic True iff for any \p i, \a x[i] is absent or true */
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predicate forall (array[int] of var opt bool: x) =
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forall ([absent(x[i]) \/ deopt(x[i]) | i in index_set(x)]);
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/** @group stdlib.logic Return truth value of \(\bigvee_i \a x[i]\) */
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function bool: exists(array[$T] of bool: x);
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/** @group stdlib.logic Return truth value of \(\bigvee_i \a x[i]\) */
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function var bool: exists(array[$T] of var bool: x);
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/** @group stdlib.logic True iff for at least one \p i, \a x[i] occurs and is true */
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predicate exists (array[int] of var opt bool: x) =
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exists ([occurs(x[i]) /\ deopt(x[i]) | i in index_set(x)]);
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/** @group stdlib.logic Return truth value of \(\oplus_i \a x[i]\) */
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function bool: xorall(array[$T] of bool: x);
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/** @group stdlib.logic Return truth value of \(\oplus_i \a x[i]\) */
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function var bool: xorall(array[$T] of var bool: x) =
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array_bool_xor(array1d(x));
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/** @group stdlib.logic Return truth value of \(\text{true}\oplus (\oplus_i \a x[i])\) */
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function bool: iffall(array[$T] of bool: x);
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/** @group stdlib.logic Return truth value of \(\text{true}\oplus (\oplus_i \a x[i])\) */
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function var bool: iffall(array[$T] of var bool: x) =
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array_bool_xor(array1d(x)++[true]);
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/** @group stdlib.logic Return truth value of \((\bigvee_i \a x[i]) \lor (\bigvee_j \lnot \a y[j])\) */
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function var bool: clause(array[$T] of var bool: x, array[$T] of var bool: y);
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/** @group stdlib.logic Return truth value of \((\bigvee_i \a x[i]) \lor (\bigvee_j \lnot \a y[j])\) */
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function var bool: clause(array[$T] of bool: x, array[$T] of bool: y);
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/** @group stdlib.logic Return negation of \a b */
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function var bool: bool_not(var bool: b);
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