Lattice declaration (#69)

* Define separate packages for orders on sets.
* Add definition of lattice and semilattice.

dedekind-matrices/src/main/java/com/github/vincentk/dedekind/linear/vector/arrays/Booleans.java

@@ -9,10 +9,10 @@
 
 import com.github.vincentk.dedekind.algebra.numbers.B;
 import com.github.vincentk.dedekind.arrays.RandomAccess;
-import com.github.vincentk.dedekind.relation.binary.SemiModule;
-import com.github.vincentk.dedekind.relation.binary.Transposed;
-import com.github.vincentk.dedekind.relation.binary.Bracket.Bra;
 import com.github.vincentk.dedekind.sets.Cardinality;
+import com.github.vincentk.dedekind.sets.relation.binary.SemiModule;
+import com.github.vincentk.dedekind.sets.relation.binary.Transposed;
+import com.github.vincentk.dedekind.sets.relation.binary.Bracket.Bra;
 
 public record Booleans
 <

dedekind-ontology/src/main/java/com/github/vincentk/dedekind/algebra/numbers/B.java

@@ -3,18 +3,19 @@
  */
 package com.github.vincentk.dedekind.algebra.numbers;
 
-import com.github.vincentk.dedekind.relation.binary.homogeneous.Ring;
 import com.github.vincentk.dedekind.sets.Cardinality;
 import com.github.vincentk.dedekind.algebra.sets.SemiRings.Booleans;
 import com.github.vincentk.dedekind.sets.Set;
+import com.github.vincentk.dedekind.sets.ordered.TotallyOrdered;
+import com.github.vincentk.dedekind.sets.relation.binary.homogeneous.Ring;
 
 /**
  * Boolean values. Roughly speaking 0 <=> false, 1 <=> true.
  */
 public interface B extends
 Number<B>, Ring<B>,
 Set.Finite<B>,
-Set.TotallyOrdered<Cardinality.Finite, B>,
+TotallyOrdered<Cardinality.Finite, B>,
 Booleans {
 
     public boolean bool();

dedekind-ontology/src/main/java/com/github/vincentk/dedekind/algebra/numbers/C.java

@@ -1,6 +1,6 @@
 package com.github.vincentk.dedekind.algebra.numbers;
 
-import com.github.vincentk.dedekind.relation.binary.homogeneous.Field;
+import com.github.vincentk.dedekind.sets.relation.binary.homogeneous.Field;
 
 /**
  * The set of complex numbers.

dedekind-ontology/src/main/java/com/github/vincentk/dedekind/algebra/numbers/Ds.java

@@ -1,6 +1,6 @@
 package com.github.vincentk.dedekind.algebra.numbers;
 
-import com.github.vincentk.dedekind.relation.binary.homogeneous.Field;
+import com.github.vincentk.dedekind.sets.relation.binary.homogeneous.Field;
 
 /**
  * The set of dual numbers.

dedekind-ontology/src/main/java/com/github/vincentk/dedekind/algebra/numbers/MetricSpace.java

@@ -3,9 +3,9 @@
  */
 package com.github.vincentk.dedekind.algebra.numbers;
 
-import com.github.vincentk.dedekind.relation.binary.homogeneous.Monoid;
 import com.github.vincentk.dedekind.algebra.sets.Fields;
 import com.github.vincentk.dedekind.sets.Set;
+import com.github.vincentk.dedekind.sets.relation.binary.homogeneous.Monoid;
 
 /**
  * @see https://en.wikipedia.org/wiki/Metric_space

dedekind-ontology/src/main/java/com/github/vincentk/dedekind/algebra/numbers/N.java

@@ -3,17 +3,18 @@
  */
 package com.github.vincentk.dedekind.algebra.numbers;
 
-import com.github.vincentk.dedekind.relation.binary.homogeneous.SemiRing;
 import com.github.vincentk.dedekind.sets.Cardinality;
 import com.github.vincentk.dedekind.sets.Set;
+import com.github.vincentk.dedekind.sets.ordered.TotallyOrdered;
+import com.github.vincentk.dedekind.sets.relation.binary.homogeneous.SemiRing;
 
 /**
  * The natural numbers.
  */
 public interface N
 extends
 Number<N>,
-Set.TotallyOrdered<Cardinality.Finite, N>,
+TotallyOrdered<Cardinality.Finite, N>,
 Set.Finite<N>,
 SemiRing.Natural<N>,
 MetricSpace<N, N>

dedekind-ontology/src/main/java/com/github/vincentk/dedekind/algebra/numbers/Number.java

@@ -3,8 +3,8 @@
  */
 package com.github.vincentk.dedekind.algebra.numbers;
 
-import com.github.vincentk.dedekind.relation.binary.homogeneous.SemiRing;
 import com.github.vincentk.dedekind.sets.Set;
+import com.github.vincentk.dedekind.sets.relation.binary.homogeneous.SemiRing;
 
 /**
  * In this context, a number is a member of a set with at least

dedekind-ontology/src/main/java/com/github/vincentk/dedekind/algebra/numbers/NumberLine.java

@@ -3,11 +3,11 @@
  */
 package com.github.vincentk.dedekind.algebra.numbers;
 
-import com.github.vincentk.dedekind.relation.binary.homogeneous.Ring;
-import com.github.vincentk.dedekind.relation.binary.homogeneous.SemiRing;
 import com.github.vincentk.dedekind.sets.Cardinality;
+import com.github.vincentk.dedekind.sets.ordered.TotallyOrdered;
 import com.github.vincentk.dedekind.algebra.sets.Fields;
-import com.github.vincentk.dedekind.sets.Set.TotallyOrdered;
+import com.github.vincentk.dedekind.sets.relation.binary.homogeneous.Ring;
+import com.github.vincentk.dedekind.sets.relation.binary.homogeneous.SemiRing;
 
 /**
  * A specialization of the {@link MetricSpace} to sets of {@link Number} with a total order.

dedekind-ontology/src/main/java/com/github/vincentk/dedekind/algebra/numbers/Q.java

@@ -1,8 +1,8 @@
 package com.github.vincentk.dedekind.algebra.numbers;
 
-import com.github.vincentk.dedekind.relation.binary.homogeneous.Equality;
-import com.github.vincentk.dedekind.relation.binary.homogeneous.Field;
 import com.github.vincentk.dedekind.sets.Cardinality;
+import com.github.vincentk.dedekind.sets.relation.binary.homogeneous.Equality;
+import com.github.vincentk.dedekind.sets.relation.binary.homogeneous.Field;
 
 /**
  * An implementation of rational numbers.

dedekind-ontology/src/main/java/com/github/vincentk/dedekind/algebra/numbers/R.java

@@ -1,7 +1,7 @@
 package com.github.vincentk.dedekind.algebra.numbers;
 
-import com.github.vincentk.dedekind.relation.binary.homogeneous.Field;
 import com.github.vincentk.dedekind.sets.Cardinality;
+import com.github.vincentk.dedekind.sets.relation.binary.homogeneous.Field;
 
 /**
  * The set of real numbers.

dedekind-ontology/src/main/java/com/github/vincentk/dedekind/algebra/numbers/Z.java

@@ -5,8 +5,8 @@
 
 import static java.lang.Long.compare;
 
-import com.github.vincentk.dedekind.relation.binary.homogeneous.Ring;
 import com.github.vincentk.dedekind.sets.Cardinality;
+import com.github.vincentk.dedekind.sets.relation.binary.homogeneous.Ring;
 
 /**
  * The integer numbers.

dedekind-ontology/src/main/java/com/github/vincentk/dedekind/algebra/peano/Peano.java

@@ -1,7 +1,7 @@
 package com.github.vincentk.dedekind.algebra.peano;
 
-import com.github.vincentk.dedekind.relation.binary.homogeneous.SemiRing.Natural;
 import com.github.vincentk.dedekind.sets.Cardinality;
+import com.github.vincentk.dedekind.sets.relation.binary.homogeneous.SemiRing.Natural;
 
 /**
  * Implementation of Peano Numbers / Axioms.

dedekind-ontology/src/main/java/com/github/vincentk/dedekind/bilinear/OuterProduct.java

@@ -1,9 +1,9 @@
 package com.github.vincentk.dedekind.bilinear;
 
 import com.github.vincentk.dedekind.linear.matrix.Matrix;
-import com.github.vincentk.dedekind.relation.binary.Bracket.Bra;
-import com.github.vincentk.dedekind.relation.binary.Bracket.Ket;
-import com.github.vincentk.dedekind.relation.binary.homogeneous.SemiRing;
+import com.github.vincentk.dedekind.sets.relation.binary.Bracket.Bra;
+import com.github.vincentk.dedekind.sets.relation.binary.Bracket.Ket;
+import com.github.vincentk.dedekind.sets.relation.binary.homogeneous.SemiRing;
 
 /**
  * Outer product / tensor product implementation.

dedekind-ontology/src/main/java/com/github/vincentk/dedekind/families/Enumeration.java

@@ -2,7 +2,7 @@
 
 import java.util.Optional;
 
-import com.github.vincentk.dedekind.relation.binary.Pair;
+import com.github.vincentk.dedekind.sets.relation.binary.Pair;
 
 @FunctionalInterface
 public interface Enumeration<T, E extends Enumeration<T, E>>

dedekind-ontology/src/main/java/com/github/vincentk/dedekind/families/Net.java

@@ -4,7 +4,7 @@
 package com.github.vincentk.dedekind.families;
 
 import com.github.vincentk.dedekind.sets.Cardinality;
-import com.github.vincentk.dedekind.sets.Set;
+import com.github.vincentk.dedekind.sets.ordered.Directed;
 
 /**
  * @see https://en.wikipedia.org/wiki/Net_(mathematics)
@@ -13,7 +13,7 @@
 public interface Net<
 T,
 C extends Cardinality.Countable,
-D extends Set.Directed<C, D>
+D extends Directed<C, D>
 >
 {
     T at(D d);

dedekind-ontology/src/main/java/com/github/vincentk/dedekind/families/Sequence.java

@@ -7,6 +7,7 @@
 import com.github.vincentk.dedekind.algebra.numbers.N;
 import com.github.vincentk.dedekind.algebra.sets.SemiRings;
 import com.github.vincentk.dedekind.sets.Set;
+import com.github.vincentk.dedekind.sets.ordered.Directed;
 
 /**
  * @see https://en.wikipedia.org/wiki/Sequence
@@ -15,7 +16,7 @@
 public interface Sequence<
 T,
 C extends Cardinality.Countable,
-D extends Set.Countable<C, D> & Set.Directed<C, D> & SemiRings.Naturals
+D extends Set.Countable<C, D> & Directed<C, D> & SemiRings.Naturals
 >
 extends Net<T, C, D>
 {

dedekind-ontology/src/main/java/com/github/vincentk/dedekind/families/Tuple.java

@@ -3,15 +3,16 @@
 import java.util.List;
 import java.util.stream.Collectors;
 
-import com.github.vincentk.dedekind.relation.binary.Pair;
-import com.github.vincentk.dedekind.relation.binary.SemiModule;
-import com.github.vincentk.dedekind.relation.binary.homogeneous.SemiRing;
 import com.github.vincentk.dedekind.sets.Cardinality;
 import com.github.vincentk.dedekind.algebra.numbers.B;
 import com.github.vincentk.dedekind.algebra.numbers.N;
 import com.github.vincentk.dedekind.algebra.numbers.Number;
 import com.github.vincentk.dedekind.algebra.sets.SemiRings;
 import com.github.vincentk.dedekind.sets.Set;
+import com.github.vincentk.dedekind.sets.ordered.Directed;
+import com.github.vincentk.dedekind.sets.relation.binary.Pair;
+import com.github.vincentk.dedekind.sets.relation.binary.SemiModule;
+import com.github.vincentk.dedekind.sets.relation.binary.homogeneous.SemiRing;
 
 /**
  * Tuple ~ a finite sequence of number-like things.
@@ -22,7 +23,7 @@
  */
 public interface Tuple<
 T extends Number<T>,
-D extends Set.Finite<D> & Set.Directed<Cardinality.Finite, D> & SemiRings.Naturals,
+D extends Set.Finite<D> & Directed<Cardinality.Finite, D> & SemiRings.Naturals,
 I extends Tuple<T, D, I>
 >
 extends
@@ -33,7 +34,7 @@ public interface Tuple<
 
     public interface Tuple2<
     T extends Number<T>,
-    D extends Set.Finite<D>  & Set.Directed<Cardinality.Finite, D> & SemiRings.Booleans
+    D extends Set.Finite<D>  & Directed<Cardinality.Finite, D> & SemiRings.Booleans
     >
     extends
     Tuple<T, D, Tuple2<T, D>>,

dedekind-ontology/src/main/java/com/github/vincentk/dedekind/linear/Basis.java

@@ -3,9 +3,9 @@
  */
 package com.github.vincentk.dedekind.linear;
 
-import com.github.vincentk.dedekind.relation.binary.Vector;
-import com.github.vincentk.dedekind.relation.binary.homogeneous.Field;
 import com.github.vincentk.dedekind.sets.Cardinality;
+import com.github.vincentk.dedekind.sets.relation.binary.Vector;
+import com.github.vincentk.dedekind.sets.relation.binary.homogeneous.Field;
 
 /**
  * An appropriate way to model the notion of a basis would appear to

dedekind-ontology/src/main/java/com/github/vincentk/dedekind/linear/FunctionSpace.java

@@ -3,9 +3,9 @@
  */
 package com.github.vincentk.dedekind.linear;
 
-import com.github.vincentk.dedekind.relation.binary.Vector;
-import com.github.vincentk.dedekind.relation.binary.homogeneous.Field;
 import com.github.vincentk.dedekind.sets.Cardinality;
+import com.github.vincentk.dedekind.sets.relation.binary.Vector;
+import com.github.vincentk.dedekind.sets.relation.binary.homogeneous.Field;
 
 /**
  * @https://en.wikipedia.org/wiki/Vector_space#Function_spaces

dedekind-ontology/src/main/java/com/github/vincentk/dedekind/linear/LinearMap.java

@@ -2,9 +2,9 @@
 
 import java.util.function.Function;
 
-import com.github.vincentk.dedekind.relation.binary.SemiModule;
-import com.github.vincentk.dedekind.relation.binary.Bracket.Ket;
-import com.github.vincentk.dedekind.relation.binary.homogeneous.SemiRing;
+import com.github.vincentk.dedekind.sets.relation.binary.SemiModule;
+import com.github.vincentk.dedekind.sets.relation.binary.Bracket.Ket;
+import com.github.vincentk.dedekind.sets.relation.binary.homogeneous.SemiRing;
 
 /**
  * @see https://en.wikipedia.org/wiki/Linear_map

dedekind-ontology/src/main/java/com/github/vincentk/dedekind/linear/finite/One.java

@@ -2,10 +2,10 @@
 
 import com.github.vincentk.dedekind.algebra.peano.Peano.Succ;
 import com.github.vincentk.dedekind.algebra.peano.Peano.Zero;
-import com.github.vincentk.dedekind.relation.binary.Module;
-import com.github.vincentk.dedekind.relation.binary.Transposed;
-import com.github.vincentk.dedekind.relation.binary.Bracket.Bra;
-import com.github.vincentk.dedekind.relation.binary.homogeneous.Ring;
+import com.github.vincentk.dedekind.sets.relation.binary.Module;
+import com.github.vincentk.dedekind.sets.relation.binary.Transposed;
+import com.github.vincentk.dedekind.sets.relation.binary.Bracket.Bra;
+import com.github.vincentk.dedekind.sets.relation.binary.homogeneous.Ring;
 
 /**
  * Vector with just one element.

dedekind-ontology/src/main/java/com/github/vincentk/dedekind/linear/finite/Two.java

@@ -2,11 +2,11 @@
 
 import com.github.vincentk.dedekind.algebra.peano.Peano.Succ;
 import com.github.vincentk.dedekind.algebra.peano.Peano.Zero;
-import com.github.vincentk.dedekind.relation.binary.Bracket.Bra;
-import com.github.vincentk.dedekind.relation.binary.Module;
-import com.github.vincentk.dedekind.relation.binary.Pair;
-import com.github.vincentk.dedekind.relation.binary.Transposed;
-import com.github.vincentk.dedekind.relation.binary.homogeneous.Ring;
+import com.github.vincentk.dedekind.sets.relation.binary.Module;
+import com.github.vincentk.dedekind.sets.relation.binary.Pair;
+import com.github.vincentk.dedekind.sets.relation.binary.Transposed;
+import com.github.vincentk.dedekind.sets.relation.binary.Bracket.Bra;
+import com.github.vincentk.dedekind.sets.relation.binary.homogeneous.Ring;
 
 /**
  * Vector with exactly two elements.

dedekind-ontology/src/main/java/com/github/vincentk/dedekind/linear/matrix/Matrix.java

@@ -3,10 +3,10 @@
 import java.util.function.Function;
 
 import com.github.vincentk.dedekind.linear.LinearMap;
-import com.github.vincentk.dedekind.relation.binary.Dual;
-import com.github.vincentk.dedekind.relation.binary.Bracket.Bra;
-import com.github.vincentk.dedekind.relation.binary.Bracket.Ket;
-import com.github.vincentk.dedekind.relation.binary.homogeneous.SemiRing;
+import com.github.vincentk.dedekind.sets.relation.binary.Dual;
+import com.github.vincentk.dedekind.sets.relation.binary.Bracket.Bra;
+import com.github.vincentk.dedekind.sets.relation.binary.Bracket.Ket;
+import com.github.vincentk.dedekind.sets.relation.binary.homogeneous.SemiRing;
 
 /**
  * @see https://en.wikipedia.org/wiki/Matrix_(mathematics)

dedekind-ontology/src/main/java/com/github/vincentk/dedekind/linear/matrix/MatrixAddition.java

@@ -1,7 +1,7 @@
 package com.github.vincentk.dedekind.linear.matrix;
 
-import com.github.vincentk.dedekind.relation.binary.Bracket.Ket;
-import com.github.vincentk.dedekind.relation.binary.homogeneous.SemiRing;
+import com.github.vincentk.dedekind.sets.relation.binary.Bracket.Ket;
+import com.github.vincentk.dedekind.sets.relation.binary.homogeneous.SemiRing;
 
 /**
  * A lazy / symbolic implementation of matrix addition.

dedekind-ontology/src/main/java/com/github/vincentk/dedekind/linear/matrix/MatrixMultiplication.java

@@ -1,7 +1,7 @@
 package com.github.vincentk.dedekind.linear.matrix;
 
-import com.github.vincentk.dedekind.relation.binary.Bracket.Ket;
-import com.github.vincentk.dedekind.relation.binary.homogeneous.SemiRing;
+import com.github.vincentk.dedekind.sets.relation.binary.Bracket.Ket;
+import com.github.vincentk.dedekind.sets.relation.binary.homogeneous.SemiRing;
 
 /**
  * A lazy / symbolic implementation of matrix multiplication.

dedekind-ontology/src/main/java/com/github/vincentk/dedekind/linear/matrix/OneByOne.java

@@ -1,8 +1,8 @@
 package com.github.vincentk.dedekind.linear.matrix;
 
 import com.github.vincentk.dedekind.linear.finite.One;
-import com.github.vincentk.dedekind.relation.binary.Transposed;
-import com.github.vincentk.dedekind.relation.binary.homogeneous.Ring;
+import com.github.vincentk.dedekind.sets.relation.binary.Transposed;
+import com.github.vincentk.dedekind.sets.relation.binary.homogeneous.Ring;
 
 /**
  * 1 x 1 matrix.

dedekind-ontology/src/main/java/com/github/vincentk/dedekind/linear/matrix/Square.java

@@ -3,8 +3,8 @@
  */
 package com.github.vincentk.dedekind.linear.matrix;
 
-import com.github.vincentk.dedekind.relation.binary.Bracket.Ket;
-import com.github.vincentk.dedekind.relation.binary.homogeneous.SemiRing;
+import com.github.vincentk.dedekind.sets.relation.binary.Bracket.Ket;
+import com.github.vincentk.dedekind.sets.relation.binary.homogeneous.SemiRing;
 
 /**
  * A square matrix domain and range are essentially the same.