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Functional Reactive Programming in JavaScript","homepage":"https://github.com/timeline-monoid/timeline-monoid#readme","keywords":["monad","monads","monoid","monoidal","functional","time","FRP","reactive","observable","asynchronous","async"],"repository":{"type":"git","url":"git+https://github.com/timeline-monoid/timeline-monoid.git"},"author":{"name":"Ken OKABE"},"bugs":{"url":"https://github.com/timeline-monoid/timeline-monoid/issues"},"license":"MIT","readme":"# Timeline Monoid\n\n![](https://kenokabetech.github.io/img/timeline-logolog.png)\n\n### Super simple yet versatile Functional Reactive Programming(FRP) framework with a minimal implementation for monoidal Timeline datatype\n\n#### npm package:\n\n<https://www.npmjs.com/package/timeline-monoid>\n\n## Installation\n\n```sh\n$ npm install timeline-monoid\n```\n\n## Usage\n\n```js\n const {T, now, log, mlong} = require(\"timeline-monoid\");\n```\n\n### Equations\n\n```sh\n   b = a * 2\n   c = a + b\n\n   a = 1 or a = 5\n   a,b,c ?\n```\n\n#### code\n\n```js\n    const a = T();\n    const b = (a).sync(a => a * 2);\n    const c = (a)(b).sync(([a, b]) => a + b);\n    const abc = (a)(b)(c);\n\n    const timeline = abc.sync(log);\n\n    a[now] = 1;\n    a[now] = 5;\n```\n\n#### output\n\n```js\n[ 1, 2, 3 ]\n[ 5, 10, 15 ]\n```\n\n### Asynchronous programming\n\nAny _time functions_ which is generally called _\"events\"_ or \"_asynchronous events\"_ are encapsulated to `timeline` instance, and they are composed to another `timeline` instance.\n\n#### Basic usage\n\n```js\n      const fs = require(\"fs\");\n      const timelineA = T((timeline) => { // Event encapsulation\n        fs.readFile(\"package.json\", \"utf8\", (err, data) => {\n          timeline[now] = data;\n        });\n      });\n      const timelineB = T((timeline) => { // Event encapsulation\n        fs.readFile(\"index.js\", \"utf8\", (err, data) => {\n          timeline[now] = data;\n        });\n      });\n      const timelineAB = (timelineA)(timelineB) // Event Composition\n        .sync(([a, b]) => {\n          console.log(\"Async read: Files A and B are now ready\");\n        //console.log(a); //show file contents if needed\n        //console.log(b); //show file contents if needed\n        });\n```\n\n#### Lazy start and reusable event Timeline\n\n```js\n    const startA = T();\n    const startB = T();\n\n    const timelineA = T((timeline) => {\n\n      (startA)\n        .sync(() => fs\n          .readFile(\"package.json\", \"utf8\", (err, data) => {\n            timeline[now] = data;\n          }));\n\n    });\n\n    const timelineB = T((timeline) => {\n\n      (startB)\n        .sync(() => fs\n          .readFile(\"index.js\", \"utf8\", (err, data) => {\n            timeline[now] = data;\n          }));\n\n    });\n```\n\n#### Async read files on the reusable event Timeline\n\n```js\n          const asyncStart = T();\n          const context = asyncStart\n            .sync(() => {\n              startA[now] = true;\n              startB[now] = true;\n            });\n          const contextAB = (context)(timelineA)(timelineB)\n            .sync(([x, a, b]) => {\n              console.log(\"Async read: Files A and B are now ready\");\n            //console.log(a); //show file contents if needed\n            //console.log(b); //show file contents if needed\n            });\n\n          asyncStart[now] = true;\n```\n\n#### Sync read files on the reusable event Timeline\n\n```js\n            const syncStart = T();\n            const context = syncStart\n              .sync(() => {\n                startA[now] = true;\n              });\n            const contextA = (context)(timelineA)\n              .sync(([x, a]) => {\n                console.log(\"now A has been read\");\n                // console.log(a); //show file contents if needed\n                startB[now] = true;\n                return true;\n              });\n            const contextB = (context)(timelineB)\n              .sync(([x, b]) => {\n                console.log(\"then B has been read\");\n                // console.log(b); //show file contents if needed\n                return true;\n              });\n\n            syncStart[now] = true;\n```\n\n### Simple Mouse Draw on Canvas\n\nLive Demo\n<https://jsfiddle.net/5u9pLgme/8/>\n\n```html\n<canvas id=\"canvas1\" width=\"900\" height=\"500\"></canvas>\n```\n\n```js\n    const canvas = document.getElementById('canvas1');\n    const ctx = canvas.getContext('2d');\n    const draw = ([x0, y0], [x1, y1]) => {\n      ctx.beginPath();\n      ctx.moveTo(x0, y0);\n      ctx.lineTo(x1, y1);\n      ctx.closePath();\n      ctx.stroke();\n    };\n\n    const btnTimeline = T((timeline) => {\n      canvas.onmousedown = (e) => timeline[now] = 1;\n      canvas.onmouseup = (e) => timeline[now] = 0;\n    });\n\n    const pointTimeline = T((timeline) => {\n      canvas.onmousemove = (e) => timeline[now] = [e.clientX, e.clientY];\n    })\n\n    const pipeline = pointTimeline\n      .sync((point) => (btnTimeline[now] === 1)\n        ? draw(lastPointTimeline[now], point)\n        : true);\n\n    const lastPointTimeline = T((timeline) => {\n      pointTimeline.sync(point => {\n        timeline[now] = point;\n      });\n    });\n```\n\n## Background and Rationale\n\n[Functional Reactive Programming (FRP)](https://wiki.haskell.org/FRP) integrates **time flow** and compositional events into functional programming.\n\nThe basic idea is that **a time-varying value can be represented as a function of time**.\n\n[Structure and Interpretation of Computer Programs(SICP)](https://en.wikipedia.org/wiki/Structure_and_Interpretation_of_Computer_Programs)\n([Chapter 3.5 : Streams](https://mitpress.mit.edu/sites/default/files/sicp/full-text/book/book-Z-H-4.html))\n\n> Let's step back and review where this complexity comes from. In an attempt to model real-world phenomena, we made some apparently reasonable decisions: We modeled real-world objects with local state by computational objects with local variables. We identified time variation in the real world with time variation in the computer. We implemented the time variation of the states of the model objects in the computer with assignments to the local variables of the model objects.\n>\n> Is there another approach? Can we avoid identifying time in the computer with time in the modeled world? Must we make the model change with time in order to model phenomena in a changing world? **Think about the issue in terms of mathematical functions. We can describe the time-varying behavior of a quantity  `x`  as a function of time `x(t)`. If we concentrate on  `x` instant by instant, we think of it as a changing quantity. Yet if we concentrate on the entire time history of values, we do not emphasize change -- the function itself does not change.**\n> (Physicists sometimes adopt this view by introducing the _world lines_ of particles as a device for reasoning about motion.)\n>\n> If time is measured in discrete steps, then **we can model a time function as a (possibly infinite) sequence**. In this section, we will see **how to model change in terms of sequences that represent the time histories of the systems being modeled**. To accomplish this, we introduce new data structures called  **_streams_**. From an abstract point of view, a stream is simply a sequence. However, we will find that the straightforward implementation of streams as lists (as in section 2.2.1) doesn't fully reveal the power of stream processing. As an alternative, we introduce the technique of **_delayed evaluation_, which enables us to represent very large (even infinite) sequences as streams**.\n>\n> This is really remarkable. Even though stream-withdraw implements a well-defined mathematical function whose behavior does not change, the user's perception here is one of interacting with a system that has a changing state. **One way to resolve this paradox is to realize that it is the user's temporal existence that imposes state on the system.** If the user could step back from the interaction and think in terms of streams of balances rather than individual transactions, the system would appear stateless.\n> (**Similarly in physics, when we observe a moving particle, we say that the position (state) of the particle is changing. However, from the perspective of the particle's _world line in space-time_ there is no change involved.**)\n>\n> We began this chapter with the goal of building computational models whose structure matches our perception of the real world we are trying to model. We can model the world as a collection of separate, time-bound, interacting objects with state, or **we can model the world as a single, timeless, stateless unity**. Each view has powerful advantages, but neither view alone is completely satisfactory. A grand unification has yet to emerge.\n\nOur world is modeled as an immutable, timeless, stateless unity from the perspective of physics\n\n![](https://upload.wikimedia.org/wikipedia/commons/6/6f/CMB_Timeline300_no_WMAP.jpg)\n\nFrozen Block Universe and Human Consciousness\n\n![](https://github.com/kenokabe/00img/wiki/block-universe.jpg)\n\n[Conal Elliott(a developer who has contributed to early FRP) explaines](https://stackoverflow.com/questions/1028250/what-is-functional-reactive-programming)\n\n> FRP is about \"datatypes that represent a value **over time** \".\n> Conventional imperative programming captures these dynamic values only indirectly, through state and mutations. The complete history (past, present, future) has no first class representation. Moreover, only _discretely evolving_ values can be (indirectly) captured, since the imperative paradigm is temporally discrete.\n> In contrast, FRP captures these evolving values _directly_ and has no difficulty with _continuously_ evolving values.\n> Dynamic/evolving values (i.e., values \"over time\") are first class values in themselves. You can define them and combine them, pass them into & out of functions.\n\n## `timeline` as a datatype that represents a first-class value over time /  a stream (infinite sequence) in JavaScript\n\n `timeline` : a datatype that represents **a first class value over time** in JavaScript /  a stream (infinite sequence) / time function as a stream / _world line in space-time_.\n\n### T() : `timeline` instance\n\n`T()` is a `timeline` instance:\n\n```js\n    const a = T();\n```\n\n### timeline [now]\n\n As `timeline` is an infinite stream of time, `timeline` has a (a user's perspective) current value: `timeline[now]`, and can be easily get/set as below:\n\n```js\n    a[now] = 1;\n    console.log(a[now]);\n```\n\n```sh\n1\n```\n\n## `timeline` as a functor\n\n`timeline`datatype is a [functor](https://en.wikipedia.org/wiki/Functor) (a datatype that methods/functions always return the identical datatype, such as [`Array.map`](https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Array/map)).\n\n`timeline` has only one method/function,  `sync`.\n\n### timeline.sync()\n\n`timeline.sync()` returns a new `timeline` instance that a given function applied to on every update of `timeline[now]` [in reactive manner](https://en.wikipedia.org/wiki/Reactive_programming)\n\n`timeline.sync()`  corresponds to `Array.map`, but on TimeLine.\n\n```js\n    const a = T();\n    const timeline = a.sync(log);\n\n    a[now] = 1;\n    a[now] = 5;\n```\n\n```sh\n1\n5\n```\n\nAs `timeline.sync` is functor:\n\n```js\n    const a = T();\n    const tl = a\n      .sync(log)\n      .sync(log);\n\n    a[now] = 9;\n```\n\n```sh\n9\n9\n```\n\n```js\n    const a = T();\n    const b = (a).sync(a => a * 2);\n    const c = (a)(b).sync(([a, b]) => a + b);\n    const abc = (a)(b)(c);\n\n    const timeline = abc.sync(log);\n\n    a[now] = 1;\n    a[now] = 5;\n```\n\n```sh\n[ 1, 2, 3 ]\n[ 5, 10, 15 ]\n```\n\nNow, the values `a` and `b` are guaranteed to synchronize with satisfying the equation.\n\n## `timeline` as a monoid\n\nA [monoid](https://en.wikipedia.org/wiki/Monoid) is an [algebraic structure](https://en.wikipedia.org/wiki/Algebraic_structure \"Algebraic structure\") with a single [associative](https://en.wikipedia.org/wiki/Associative \"Associative\")  [binary operation](https://en.wikipedia.org/wiki/Binary_operation \"Binary operation\") and an [identity element](https://en.wikipedia.org/wiki/Identity_element \"Identity element\").\n\nIn algebra,\n\n`0` is an identiy element in +(addition) operation,\n\n```sh\n    a + 0 = a  //right identity\n    0 + a = a  //left identity\n```\n\n`1` is an identity element in \\*(multiplication) operation,\n\n```sh\n    a ∗ 1 = a  //right identity\n    1 ∗ a = a  //left identity\n```\n\nAssociative property\n\n```sh\n   1 + 2 + 3 = 1 + 2 + 3\n   (1+2) + 3 = 1 + (2+3)\n       3 + 3 = 1 + 5\n           6 = 6\n```\n\nA string is also a monoid\n\n`string + string => string`\n\n```sh\n    \"Hello\" + \" \" + \"world\"\n    = \"Hello \" + \"world\"\n    = \"Hello\" + \" world\"\n```\n\nappears to be associative, and identity element is `\"\"`.\n\n### identiy of `timeline`\n\n`timeline` is a monoid, and the identity element of `timeline` is `T` or `(T)`:\n\n```sh\nT(a) = a = a(T)\n\n(T)(a) = (a) = (a)(T)\n```\n\nThe nature of left identity: `T(a) = a`   is especially important because we should intuitively be aware of that an instance of `timeline` for a given `timeline` instance is identical.\n\n### `timeline` composition\n\n`timeline` is a monoid, and composable:\n\n```js\nconst a = T();\nconst b = T();\nconst ab = (a)(b); // ab is another `timeline` composed of a and b\n\nconst c = T();\nconst abc = (ab)(c); //  == (a)(b)(c)\n```\n\n### associative of `timeline`\n\n`timeline` is a monoid, and satisfies associative law:\n\n```sh\n(a)(b)(c)\n= ((a)(b))(c)\n= (a)((b)(c))\n```\n\n## Timeline composition\n\nHere we can compose `timeline`s.\n\nNow we have 2 equations:\n\n```sh\n   b = a * 2\n   c = a + b\n```\n\nThese equations can be easily implemented to a `timeline` code:\n\n```js\n    const a = T();\n    const b = a\n      .sync(a => a * 2);\n    const c = (a)(b)\n      .sync(([a, b]) => a + b);\n\n    const timeline = c.sync(log);\n\n    a[now] = 1;\n```\n\n```sh\n3\n```\n\nIf we need a synchronized update of all of `a`,`b`,`c` which is an atomic update of `[a,b,c]`,\n\n```js\n    const a = T();\n    const b = a.sync(a => a * 2);\n    const c = (a)(b).sync(([a, b]) => a + b);\n\n    const abc = (a)(b)(c);\n    const tl = abc.sync(log);\n\n    a[now] = 1;\n    a[now] = 5;\n```\n\n```sh\n[ 1, 2, 3 ]\n[ 5, 10, 15 ]\n```\n\nThe values of `a`,`b`,`c` are now guaranteed to synchronize with satisfying the equation.\n\nIn a practical program, in this manner, we can define dependencies of events, IO, etc., and `timeline` is a complete alternative of [State Monad](https://en.wikibooks.org/wiki/Haskell/Understanding_monads/State) or Continuation Monad such as [Promise](https://developer.mozilla.org/en-US/docs/Web/JavaScript/Guide/Using_promises) simply because there is \"no state\"  as discussed earlier.\n\n## Event encapsulation\n\nWhen we define a `timeline` with an empty argument:\n\n```js\n    const a = T();\n```\n\nis it really an empty `timeline`?\n\nThe fact is it is not empty because actually, we occasionally \"manually\" update the `timeline` value as\n\n```js\n    a[now] = 1;\n```\n\nThe argument of `timeline` in empty, Nevertheless, various inputs would happen to the `timeline`. In a sense, implicitly, our real-world events or time function of the world: `f(t)` are encapsulated to it.\n\n```js\n    const a = T(realWorldTimeFunction);\n```\n\nHaving said that. any event functions can be encapsulated to `timeline` instances.\n\nThey can be IO inputs or simply a timer event,\n\n```js\n    const start1 = T((timeline) => {\n      setTimeout(() => (timeline[now] = true), 1000);\n    });\n    const start2 = T((timeline) => {\n      setTimeout(() => (timeline[now] = true), 2000);\n    });\n```\n\nObviously, the \"custom\" `timelilne` can be composed.\n\n      (start1)(start2)\n         .sync(doSomethingFunction);\n\n## Tiny library in around 100 lines\n\n**Timeline Monoid** is a minimal library and the code is in around 100 lines\n\nbased on my other library `free-monoid`\n\n<https://www.npmjs.com/package/free-monoid>\n\nThe latest code of  `free-monoid` is hard-coded and included in the same module file of `timeline-monoid`.\n\n### SourceCode :\n\n```js\n(() => {\n  \"use strict\";\n  const freeMonoid = (operator) => (() => {\n  const flattenDeep = (arr1) => arr1\n    .reduce((acc, val) => Array.isArray(val)\n      ? acc.concat(flattenDeep(val))\n      : acc.concat(val), []);\n  const M = (() => { //(M)(a)(b)\n    const toList = arr => arr.reduce((a, b) => (a)(b), (M));\n    const m = (a) => (Array.isArray(a))\n      ? toList(flattenDeep(a))\n      : (!!a && !!a.M)\n        ? (a)\n        : (() => {\n          const ma = b => (b === m) // right id\n            ? (ma)\n            : !b.M\n              ? (ma)(M(b))\n              : (() => {\n                const mab = M();\n                mab.units = ma.units.concat(b.units);\n                mab.val = mab.units.map(unit => unit.val[0]);\n                return mab; // (m)(a)(b)\n              })();\n          ma.M = m;\n          ma.val = [a];\n          ma.units = [ma];\n          operator(ma);\n          return ma;\n        })();\n    m.M = m;\n    m.val = [m]; //[\"__IDENTITY__\"];\n    m.units = [m];\n    operator(m);\n    return (m);\n  })();\n  return M;\n})();\n  //Timeline monoid based on freeMonoid =============\n  const now = \"now\";\n  const log = (m) => {\n    console.log(m);\n    return m;\n  };\n  const mlog = (msg) => (m) => {\n    console.log(msg + \": \" + m);\n    return m;\n  };\n  const _T = () => freeMonoid(operator);\n  const operator = (timeline) => {\n    const T = timeline.M;\n    Object.defineProperties(timeline, //detect TL update\n      {\n        now: { //timeline[now]\n          get() {\n            return timeline.value[0];\n          },\n          set(tUpdate) {\n            return (() => {\n              timeline.value = [tUpdate];\n              timeline._wrapF.map(f => f(tUpdate));\n            })();\n          }\n        }\n      });\n    timeline.value = [];\n    timeline.sync = f => {\n      const syncTL = T();\n      timeline._eval()._wrap(val => (syncTL[now] = f(val)));\n      return syncTL;\n    };\n    timeline._wrapF = [];\n    timeline._wrap = f => {\n      timeline._wrapF[timeline._wrapF.length] = f;\n      return timeline;\n    };\n    timeline._eval = () => (timeline.evaluated)\n    || (timeline.units.length === 1)\n      ? timeline\n      : (() => {\n        timeline.evaluated = true;\n        const reset = () => timeline.units\n          .map((t, i) => updates[i][now] = 0);\n        const update = () => timeline[now] = timeline.units\n          .map((t) => t[now]);\n        const check = () => (timeline.units\n          .map((t, i) => updates[i][now])\n          .reduce((a, b) => (a * b)) === 1) //all updated\n          ? update()\n          : true;\n        const updates = timeline.units\n          .map((t) => T()._wrap(check));\n        const dummy0 = timeline.units\n          .map((t, i) => t._wrap(() => updates[i][now] = 1));\n        const dummy1 = timeline._wrap(reset);\n        timeline[now] = null; //initial reset\n        return timeline;\n      })();\n    //------------------\n    timeline._timeF = () => (typeof timeline.val[0]\n    === \"function\") //_wrapped eventF\n      ? timeline.val[0](timeline)\n      : true;\n    //non-lazy evaluate on the creation of timeF TL\n    timeline._timeF();\n  }; //-------operator\n  const T = _T();\n  //------------------\n  const timeline = {\n    T: T,\n    now: now,\n    log: log,\n    mlog: mlog\n  };\n  //------------------\n  const exporting = (typeof module === \"object\"\n  && typeof module.exports === \"object\")\n    ? module.exports = timeline\n    : self.timeline = timeline;\n//============================\n})();\n```\n\n## MIT License\n","readmeFilename":"README.md"}