Remove unlawful alternative

package.json

@@ -42,6 +42,7 @@
     "@types/node": "7.0.4",
     "docs-ts": "^0.3.4",
     "fp-ts": "^2.4.3",
+    "fp-ts-laws": "^0.2.1",
     "import-path-rewrite": "github:gcanti/import-path-rewrite",
     "jest": "^24.8.0",
     "mocha": "^5.2.0",

src/Observable.ts

@@ -1,7 +1,6 @@
 /**
  * @since 0.6.0
  */
-import { Alternative1 } from 'fp-ts/lib/Alternative'
 import * as E from 'fp-ts/lib/Either'
 import { Filterable1 } from 'fp-ts/lib/Filterable'
 import { identity, Predicate } from 'fp-ts/lib/function'
@@ -14,6 +13,8 @@ import { map as rxMap, mergeMap } from 'rxjs/operators'
 import { IO } from 'fp-ts/lib/IO'
 import { Task } from 'fp-ts/lib/Task'
 import { MonadObservable1 } from './MonadObservable'
+import { Alt1 } from 'fp-ts/lib/Alt'
+import { Plus1 } from './Plus'
 
 declare module 'fp-ts/lib/HKT' {
   interface URItoKind<A> {
@@ -79,7 +80,7 @@ export function toTask<A>(o: Observable<A>): Task<A> {
 /**
  * @since 0.6.0
  */
-export const observable: Monad1<URI> & Alternative1<URI> & Filterable1<URI> & MonadObservable1<URI> = {
+export const observable: Monad1<URI> & Alt1<URI> & Plus1<URI> & Filterable1<URI> & MonadObservable1<URI> = {
   URI,
   map: (fa, f) => fa.pipe(rxMap(f)),
   of,

src/Plus.ts

@@ -0,0 +1,20 @@
+import { Kind, URIS } from 'fp-ts/lib/HKT'
+import { Alt1 } from 'fp-ts/lib/Alt'
+
+/**
+ * The `Plus` type class extends the `Alt` type class with a value that should be the left and right identity for `alt`.
+ *
+ * It is similar to `Monoid`, except that it applies to types of kind `* -> *`, like `Array` or `Option`, rather than
+ * concrete types like `string` or `number`.
+ *
+ * `Plus` instances should satisfy the following laws:
+ *
+ * 1. Left identity: `A.alt(zero, fa) == fa`
+ * 2. Right identity: `A.alt(fa, zero) == fa`
+ * 3. Annihilation: `A.map(zero, f) == zero`
+ *
+ * @since 0.7.0
+ */
+export interface Plus1<F extends URIS> extends Alt1<F> {
+  readonly zero: <A>() => Kind<F, A>
+}

test/Observable.ts

@@ -1,14 +1,147 @@
 import * as assert from 'assert'
-import { from } from 'rxjs'
-import { bufferTime } from 'rxjs/operators'
+import { from, Observable } from 'rxjs'
+import { bufferTime, subscribeOn } from 'rxjs/operators'
 import * as O from 'fp-ts/lib/Option'
 import * as E from 'fp-ts/lib/Either'
 import * as T from 'fp-ts/lib/Task'
 import { identity } from 'fp-ts/lib/function'
+import * as laws from 'fp-ts-laws'
 
 import { observable as R } from '../src'
+import { TestScheduler } from 'rxjs/testing'
+import { Eq, eqNumber, eqString } from 'fp-ts/lib/Eq'
+import { getEq } from 'fp-ts/lib/Array'
+
+const liftE = <A>(E: Eq<A>): Eq<Observable<A>> => {
+  const arrayE = getEq(E)
+  return {
+    equals: (x, y) => {
+      const scheduler = new TestScheduler(assert.deepStrictEqual)
+      const xas: Array<A> = []
+      x.pipe(subscribeOn(scheduler)).subscribe(a => xas.push(a))
+      const yas: Array<A> = []
+      y.pipe(subscribeOn(scheduler)).subscribe(a => yas.push(a))
+      scheduler.flush()
+      assert.deepStrictEqual(xas, yas)
+      return arrayE.equals(xas, yas)
+    }
+  }
+}
 
 describe('Observable', () => {
+  describe('laws', () => {
+    const f = (n: number): string => `map(${n})`
+    const a = R.observable.of(1)
+    const b = R.observable.of(2)
+    const c = R.observable.of(3)
+    it('Monad', () => {
+      laws.monad(R.observable)(liftE)
+    })
+    describe('Alt', () => {
+      it('associativity', () => {
+        const left = R.observable.alt(
+          R.observable.alt(a, () => b),
+          () => c
+        )
+        const right = R.observable.alt(a, () => R.observable.alt(b, () => c))
+        assert.ok(liftE(eqNumber).equals(left, right))
+      })
+      it('distributivity', () => {
+        const left = R.observable.map(
+          R.observable.alt(a, () => b),
+          f
+        )
+        const right = R.observable.alt(R.observable.map(a, f), () => R.observable.map(b, f))
+        assert.ok(liftE(eqString).equals(left, right))
+      })
+    })
+    describe('Plus', () => {
+      it('right identity', () => {
+        const left = R.observable.alt(a, () => R.observable.zero())
+        assert.ok(liftE(eqNumber).equals(left, a))
+      })
+      it('left identity', () => {
+        const left = R.observable.alt(R.observable.zero<number>(), () => a)
+        assert.ok(liftE(eqNumber).equals(left, a))
+      })
+      it('annihilation', () => {
+        const left = R.observable.map(R.observable.zero<number>(), f)
+        const right = R.observable.zero<string>()
+        assert.ok(liftE(eqString).equals(left, right))
+      })
+    })
+    describe('Observable is not an Alternative', () => {
+      describe('no distributivity', () => {
+        const a = 1
+        const f = (n: number) => n + 1
+        const g = (n: number) => n / 2
+        const result = { b: f(a), c: g(a) }
+        const success = {
+          fa: '                             ------------a----------------|',
+          fab: '                            ---f-------------------------|',
+          gac: '                            ----------------g------------|',
+
+          'LEFT SIDE': '',
+          'alt(fab, gac)': '                ---f------------g------------|',
+          'ap(alt(fab, gac), fa)': '        ------------b---c------------|',
+
+          'RIGHT SIDE': '',
+          'ap(fab, fa)': '                  ------------b----------------|',
+          'ap(gac, fa)': '                  ----------------c------------|',
+          'alt(ap(fab, fa), ap(gac, fa))': '------------b---c------------|'
+        }
+        const failure = {
+          fa: '                             ------------a----------------|',
+          fab: '                            ---f-------------------------|',
+          gac: '                            --------g--------------------|',
+
+          'LEFT SIDE': '',
+          'alt(fab, gac)': '                ---f----g--------------------|',
+          'ap(alt(fab, gac), fa)': '        ------------c----------------|',
+
+          'RIGHT SIDE': '',
+          'ap(fab, fa)': '                  ------------b----------------|',
+          'ap(gac, fa)': '                  ----------------c------------|',
+          'alt(ap(fab, fa), ap(gac, fa))': '------------b---c------------|'
+        }
+        it('left sides are not equal but they should be', () => {
+          assert.notDeepStrictEqual(success['ap(alt(fab, gac), fa)'], failure['ap(alt(fab, gac), fa)'])
+        })
+        it('right sides should be equal', () => {
+          assert.deepStrictEqual(success['alt(ap(fab, fa), ap(gac, fa))'], failure['alt(ap(fab, fa), ap(gac, fa))'])
+        })
+        it('success', () => {
+          new TestScheduler(assert.deepStrictEqual).run(({ cold, expectObservable }) => {
+            const fa = cold(success.fa, { a })
+            const fab = cold(success.fab, { f })
+            const gac = cold(success.gac, { g })
+            const left = R.observable.ap(
+              R.observable.alt(fab, () => gac),
+              fa
+            )
+            const right = R.observable.alt(R.observable.ap(fab, fa), () => R.observable.ap(gac, fa))
+            expectObservable(left).toBe(success['ap(alt(fab, gac), fa)'], result)
+            expectObservable(right).toBe(success['alt(ap(fab, fa), ap(gac, fa))'], result)
+          })
+        })
+        it('failure', () => {
+          // use assert.notDeepStrictEqual as assert
+          new TestScheduler(assert.notDeepStrictEqual).run(({ cold, expectObservable }) => {
+            const fa = cold(failure.fa, { a })
+            const fab = cold(failure.fab, { f })
+            const gac = cold(failure.gac, { g })
+            const left = R.observable.ap(
+              R.observable.alt(fab, () => gac),
+              fa
+            )
+            const right = R.observable.alt(R.observable.ap(fab, fa), () => R.observable.ap(gac, fa))
+            expectObservable(left).toBe(success['ap(alt(fab, gac), fa)'], result)
+            expectObservable(right).toBe(success['alt(ap(fab, fa), ap(gac, fa))'], result)
+          })
+        })
+      })
+    })
+  })
   it('of', () => {
     const fa = R.observable.of(1)
     return fa