From 3b053fed3bd58fa20be233715ba1212e0ef1c6ef Mon Sep 17 00:00:00 2001
From: Daniel Gronau <daniel.gronau@datameer.com>
Date: Tue, 19 Dec 2017 17:35:54 +0100
Subject: [PATCH 1/2] #76 invective and isomorphic type classes - initial
 commit

---
 .../highj/typeclass2/injective/Injective.java | 29 +++++++++++
 .../typeclass2/injective/Injective1.java      | 39 +++++++++++++++
 .../typeclass2/injective/Isomorphic.java      | 35 +++++++++++++
 .../typeclass2/injective/Isomorphic1.java     | 50 +++++++++++++++++++
 4 files changed, 153 insertions(+)
 create mode 100644 src/main/java/org/highj/typeclass2/injective/Injective.java
 create mode 100644 src/main/java/org/highj/typeclass2/injective/Injective1.java
 create mode 100644 src/main/java/org/highj/typeclass2/injective/Isomorphic.java
 create mode 100644 src/main/java/org/highj/typeclass2/injective/Isomorphic1.java

diff --git a/src/main/java/org/highj/typeclass2/injective/Injective.java b/src/main/java/org/highj/typeclass2/injective/Injective.java
new file mode 100644
index 0000000..345a8c9
--- /dev/null
+++ b/src/main/java/org/highj/typeclass2/injective/Injective.java
@@ -0,0 +1,29 @@
+package org.highj.typeclass2.injective;
+
+import java.util.function.Function;
+
+/**
+ * An injective relationship.
+ *
+ * Law:
+ * if x != y then injective.to(x) != injective.to(y)
+ *
+ * @param <A> source type
+ * @param <B> target type
+ */
+public interface Injective<A, B> extends Function<A, B> {
+
+    B to(A input);
+
+    default B apply(A input) {
+       return to(input);
+    }
+
+    static <A,B> Injective<A,B> of(Function<A,B> f) {
+        return f::apply;
+    }
+
+    static <A> Injective<A,A> identity() {
+        return a -> a;
+    }
+}
diff --git a/src/main/java/org/highj/typeclass2/injective/Injective1.java b/src/main/java/org/highj/typeclass2/injective/Injective1.java
new file mode 100644
index 0000000..8682daf
--- /dev/null
+++ b/src/main/java/org/highj/typeclass2/injective/Injective1.java
@@ -0,0 +1,39 @@
+package org.highj.typeclass2.injective;
+
+import org.derive4j.hkt.__;
+
+/**
+ * An injective relationship of type constructors.
+ *
+ * Law:
+ * if x != y then injective1.to(x) != injective1.to(y)
+ *
+ * @param <F> the source type constructor
+ * @param <G> the target type constructor
+ */
+public interface Injective1<F, G> {
+
+    <A> __<G, A> to(__<F, A> input);
+
+    default <A> Injective<__<F,A>, __<G,A>> to() {
+        return this::to;
+    }
+
+    default <H> Injective1<F, H> andThen(Injective1<G, H> that) {
+         return new Injective1<F, H>() {
+             @Override
+             public <A> __<H, A> to(__<F, A> input) {
+                 return that.to(Injective1.this.to(input));
+             }
+         };
+    }
+
+    static <M> Injective1<M, M> identity() {
+        return new Injective1<M, M>() {
+            @Override
+            public <A> __<M, A> to(__<M, A> input) {
+                return input;
+            }
+        };
+    }
+}
diff --git a/src/main/java/org/highj/typeclass2/injective/Isomorphic.java b/src/main/java/org/highj/typeclass2/injective/Isomorphic.java
new file mode 100644
index 0000000..d62fe9d
--- /dev/null
+++ b/src/main/java/org/highj/typeclass2/injective/Isomorphic.java
@@ -0,0 +1,35 @@
+package org.highj.typeclass2.injective;
+
+import java.util.function.Function;
+
+/**
+ * The class of isomorphic types, i.e. those which can be cast to each other without loss of information.
+ * @param <A> source type
+ * @param <B> target type
+ */
+public interface Isomorphic<A, B> extends Injective<A, B> {
+
+    A from(B input);
+
+    static <A, B> Isomorphic<A, B> of(Function<A, B> fnTo, Function<B, A> fnFrom) {
+        return new Isomorphic<A, B>() {
+            @Override
+            public A from(B input) {
+                return fnFrom.apply(input);
+            }
+
+            @Override
+            public B to(A input) {
+                return fnTo.apply(input);
+            }
+        };
+    }
+
+    static <A> Isomorphic<A, A> identity() {
+        return Isomorphic.of(a -> a, a -> a);
+    }
+
+    default Isomorphic<B, A> inverse() {
+        return Isomorphic.of(Isomorphic.this::from, Isomorphic.this::to);
+    }
+}
diff --git a/src/main/java/org/highj/typeclass2/injective/Isomorphic1.java b/src/main/java/org/highj/typeclass2/injective/Isomorphic1.java
new file mode 100644
index 0000000..5944b98
--- /dev/null
+++ b/src/main/java/org/highj/typeclass2/injective/Isomorphic1.java
@@ -0,0 +1,50 @@
+package org.highj.typeclass2.injective;
+
+import org.derive4j.hkt.__;
+
+/**
+ * The class of isomorphic type constructors, i.e. those which can be cast to each other without loss of information.
+ * @param <F>
+ * @param <G>
+ */
+public interface Isomorphic1<F,G> extends Injective1<F,G> {
+
+    <A> __<F, A> from(__<G, A> input);
+
+    default <A> Injective<__<G,A>, __<F,A>> from() {
+        return this::from;
+    }
+
+    default <A> Isomorphic<__<F,A>, __<G,A>> isomorphic() {
+        return Isomorphic.of(f -> Isomorphic1.this.to(f), g -> Isomorphic1.this.from(g));
+    }
+
+    default Isomorphic1<G,F> inverse() {
+        return new Isomorphic1<G, F>() {
+            @Override
+            public <A> __<G, A> from(__<F, A> input) {
+                return Isomorphic1.this.to(input);
+            }
+
+            @Override
+            public <A> __<F, A> to(__<G, A> input) {
+                return Isomorphic1.this.from(input);
+            }
+        };
+    }
+
+    static <F> Isomorphic1<F,F> identity() {
+        return new Isomorphic1<F, F>() {
+            @Override
+            public <A> __<F, A> from(__<F, A> input) {
+                return input;
+            }
+
+            @Override
+            public <A> __<F, A> to(__<F, A> input) {
+                return input;
+            }
+        };
+    }
+
+}

From 6851719ae8940d7d4111279153e65a8901bac8b8 Mon Sep 17 00:00:00 2001
From: DanielGronau <Daniel.Gronau@gmx.de>
Date: Wed, 20 Dec 2017 00:00:15 +0100
Subject: [PATCH 2/2] injective and isomorphic laws, and an Isomorphic1 example

---
 .../maybe/MaybeEitherIsomorphic1.java         | 20 ++++++++++
 .../typeclass2/injective/InjectiveLaw.java    | 37 ++++++++++++++++++
 .../typeclass2/injective/IsomorphicLaw.java   | 39 +++++++++++++++++++
 3 files changed, 96 insertions(+)
 create mode 100644 src/main/java/org/highj/data/instance/maybe/MaybeEitherIsomorphic1.java
 create mode 100644 src/test/java/org/highj/typeclass2/injective/InjectiveLaw.java
 create mode 100644 src/test/java/org/highj/typeclass2/injective/IsomorphicLaw.java

diff --git a/src/main/java/org/highj/data/instance/maybe/MaybeEitherIsomorphic1.java b/src/main/java/org/highj/data/instance/maybe/MaybeEitherIsomorphic1.java
new file mode 100644
index 0000000..d8ae1c4
--- /dev/null
+++ b/src/main/java/org/highj/data/instance/maybe/MaybeEitherIsomorphic1.java
@@ -0,0 +1,20 @@
+package org.highj.data.instance.maybe;
+
+import org.derive4j.hkt.__;
+import org.highj.Hkt;
+import org.highj.data.Either;
+import org.highj.data.Maybe;
+import org.highj.data.tuple.T0;
+import org.highj.typeclass2.injective.Isomorphic1;
+
+public interface MaybeEitherIsomorphic1 extends Isomorphic1<Maybe.µ, __<Either.µ, T0>> {
+    @Override
+    default <A> Maybe<A> from(__<__<Either.µ, T0>, A> input) {
+        return Hkt.asEither(input).either(u -> Maybe.Nothing(), Maybe::Just);
+    }
+
+    @Override
+    default <A> Either<T0, A> to(__<Maybe.µ, A> input) {
+        return Hkt.asMaybe(input).cata(Either.Left(T0.unit), Either::<T0, A>Right);
+    }
+}
diff --git a/src/test/java/org/highj/typeclass2/injective/InjectiveLaw.java b/src/test/java/org/highj/typeclass2/injective/InjectiveLaw.java
new file mode 100644
index 0000000..7271d53
--- /dev/null
+++ b/src/test/java/org/highj/typeclass2/injective/InjectiveLaw.java
@@ -0,0 +1,37 @@
+package org.highj.typeclass2.injective;
+
+import org.highj.data.eq.Eq;
+import org.highj.util.Gen;
+import org.highj.util.Law;
+
+import static org.assertj.core.api.Assertions.assertThat;
+
+public class InjectiveLaw<A,B> implements Law {
+
+    private final Injective<A,B> injective;
+    protected final Gen<A> genA;
+    protected final Eq<A> eqA;
+    protected final Eq<B> eqB;
+
+    public InjectiveLaw(Injective<A, B> injective, Gen<A> genA, Eq<A> eqA, Eq<B> eqB) {
+        this.injective = injective;
+        this.genA = genA;
+        this.eqA = eqA;
+        this.eqB = eqB;
+    }
+
+    public void injectivity(){
+        for(A a1 : genA.get(10)) {
+            B b1 = injective.to(a1);
+           for(A a2 : genA.get(10)) {
+               B b2 = injective.to(a2);
+               assertThat(eqA.eq(a1, a2) == eqB.eq(b1, b2)).isTrue();
+           }
+        }
+    }
+
+    @Override
+    public void test() {
+        injectivity();
+    }
+}
diff --git a/src/test/java/org/highj/typeclass2/injective/IsomorphicLaw.java b/src/test/java/org/highj/typeclass2/injective/IsomorphicLaw.java
new file mode 100644
index 0000000..d68cd3c
--- /dev/null
+++ b/src/test/java/org/highj/typeclass2/injective/IsomorphicLaw.java
@@ -0,0 +1,39 @@
+package org.highj.typeclass2.injective;
+
+import org.highj.data.eq.Eq;
+import org.highj.util.Gen;
+
+import static org.assertj.core.api.Assertions.assertThat;
+
+public class IsomorphicLaw<A,B> extends InjectiveLaw<A,B> {
+
+    private final Isomorphic<A,B> isomorphic;
+    protected final Gen<B> genB;
+
+    public IsomorphicLaw(Isomorphic<A,B> isomorphic, Gen<A> genA, Gen<B> genB, Eq<A> eqA, Eq<B> eqB) {
+        super(isomorphic, genA, eqA, eqB);
+        this.isomorphic = isomorphic;
+        this.genB = genB;
+    }
+
+    public void isomorphism() {
+        for(A a : genA.get(20)) {
+            assertThat(eqA.eq(a, isomorphic.from(isomorphic.to(a)))).isTrue();
+        }
+        for(B b : genB.get(20)) {
+            assertThat(eqB.eq(b, isomorphic.to(isomorphic.from(b)))).isTrue();
+        }
+    }
+
+    public void inverseInjectivity() {
+        new InjectiveLaw<>(isomorphic.inverse(), genB, eqB, eqA).test();
+    }
+
+    @Override
+    public void test() {
+        isomorphism();
+        inverseInjectivity();
+        super.test();
+    }
+
+}