Add wrapper and instances for Sequence

kategory/src/main/kotlin/kategory/data/SequenceKW.kt

@@ -0,0 +1,84 @@
+package kategory
+
+fun <A> SequenceKWKind<A>.toList(): List<A> = this.ev().sequence.toList()
+
+@higherkind
+@deriving(Monad::class, Traverse::class, MonoidK::class)
+data class SequenceKW<out A> constructor(val sequence: Sequence<A>) : SequenceKWKind<A>, Sequence<A> by sequence {
+
+    fun <B> flatMap(f: (A) -> SequenceKWKind<B>): SequenceKW<B> = this.ev().sequence.flatMap { f(it).ev().sequence }.k()
+
+    fun <B> map(f: (A) -> B): SequenceKW<B> = this.ev().sequence.map(f).k()
+
+    fun <B> foldL(b: B, f: (B, A) -> B): B = this.ev().fold(b, f)
+
+    fun <B> foldR(lb: Eval<B>, f: (A, Eval<B>) -> Eval<B>): Eval<B> {
+        fun loop(fa_p: SequenceKW<A>): Eval<B> = when {
+            fa_p.sequence.none() -> lb
+            else -> f(fa_p.first(), Eval.defer { loop(fa_p.drop(1).k()) })
+        }
+        return Eval.defer { loop(this.ev()) }
+    }
+
+    fun <G, B> traverse(f: (A) -> HK<G, B>, GA: Applicative<G>): HK<G, SequenceKW<B>> =
+            foldR(Eval.always { GA.pure(emptySequence<B>().k()) }) { a, eval ->
+                GA.map2Eval(f(a), eval) { (sequenceOf(it.a) + it.b).k() }
+            }.value()
+
+    fun <B, Z> map2(fb: SequenceKWKind<B>, f: (Tuple2<A, B>) -> Z): SequenceKW<Z> =
+            this.ev().flatMap { a ->
+                fb.ev().map { b ->
+                    f(Tuple2(a, b))
+                }
+            }.ev()
+
+    companion object {
+
+        fun <A> pure(a: A): SequenceKW<A> = sequenceOf(a).k()
+
+        fun <A> empty(): SequenceKW<A> = emptySequence<A>().k()
+
+        fun <A, B> tailRecM(a: A, f: (A) -> HK<SequenceKWHK, Either<A, B>>): SequenceKW<B> {
+            tailrec fun <A, B> go(
+                    buf: MutableList<B>,
+                    f: (A) -> HK<SequenceKWHK, Either<A, B>>,
+                    v: SequenceKW<Either<A, B>>) {
+                if (!v.isEmpty()) {
+                    val head: Either<A, B> = v.first()
+                    when (head) {
+                        is Either.Right<A, B> -> {
+                            buf += head.b
+                            go(buf, f, v.drop(1).k())
+                        }
+                        is Either.Left<A, B> -> {
+                            if (v.count() == 1)
+                                go(buf, f, (f(head.a).ev()).k())
+                            else
+                                go(buf, f, (f(head.a).ev() + v.drop(1)).k())
+                        }
+                    }
+                }
+            }
+
+            val buf = mutableListOf<B>()
+            go(buf, f, f(a).ev())
+            return SequenceKW(buf.asSequence())
+        }
+
+        fun functor(): SequenceKWHKMonadInstance = SequenceKW.monad()
+
+        fun applicative(): SequenceKWHKMonadInstance = SequenceKW.monad()
+
+        fun <A> semigroup(): SequenceKWMonoid<A> = object : SequenceKWMonoid<A> {}
+
+        fun semigroupK(): SequenceKWHKMonoidKInstance = SequenceKW.monoidK()
+
+        fun <A> monoid(): SequenceKWMonoid<A> = object : SequenceKWMonoid<A> {}
+
+        fun foldable(): SequenceKWHKTraverseInstance = SequenceKW.traverse()
+    }
+}
+
+fun <A> SequenceKW<A>.combineK(y: SequenceKWKind<A>): SequenceKW<A> = (this.sequence + y.ev().sequence).k()
+
+fun <A> Sequence<A>.k(): SequenceKW<A> = SequenceKW(this)

kategory/src/main/kotlin/kategory/instances/SequenceKWMonoid.kt

@@ -0,0 +1,7 @@
+package kategory
+
+interface SequenceKWMonoid<A> : Monoid<SequenceKW<A>> {
+    override fun combine(a: SequenceKW<A>, b: SequenceKW<A>): SequenceKW<A> = (a + b).k()
+
+    override fun empty(): SequenceKW<A> = emptySequence<A>().k()
+}

kategory/src/test/kotlin/kategory/data/SequenceKWTest.kt

@@ -0,0 +1,21 @@
+package kategory.data
+
+import io.kotlintest.KTestJUnitRunner
+import kategory.*
+import org.junit.runner.RunWith
+
+@RunWith(KTestJUnitRunner::class)
+class SequenceKWTest : UnitSpec() {
+    val applicative = SequenceKW.applicative()
+
+    init {
+        val eq: Eq<HK<SequenceKWHK, Int>> = object : Eq<HK<SequenceKWHK, Int>> {
+            override fun eqv(a: HK<SequenceKWHK, Int>, b: HK<SequenceKWHK, Int>): Boolean =
+                    a.toList() == b.toList()
+        }
+
+        testLaws(MonadLaws.laws(SequenceKW.monad(), eq))
+        testLaws(MonoidKLaws.laws(SequenceKW.monoidK(), applicative, eq))
+        testLaws(TraverseLaws.laws(SequenceKW.traverse(), applicative, { n: Int -> SequenceKW(sequenceOf(n)) }, eq))
+    }
+}