How to write a Constrained Identity Function (CIF) in TypeScript

March 9th, 2021 10 min read

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In How to write a React Component in TypeScript, I typed an example React component. Here's where we left off:

const operations = {
  '+': (left: number, right: number): number => left + right,
  '-': (left: number, right: number): number => left - right,
  '*': (left: number, right: number): number => left * right,
  '/': (left: number, right: number): number => left / right,
}

type CalculatorProps = {
  left: number
  operator: keyof typeof operations
  right: number
}

function Calculator({left, operator, right}: CalculatorProps) {
  const result = operations[operator](left, right)
  return (
    <div>
      <code>
        {left} {operator} {right} = <output>{result}</output>
      </code>
    </div>
  )
}

const examples = (
  <>
    <Calculator left={1} operator="+" right={2} />
    <Calculator left={1} operator="-" right={2} />
    <Calculator left={1} operator="*" right={2} />
    <Calculator left={1} operator="/" right={2} />
  </>
)

I'm not satisfied with the operations function though. I know that every function in that object is going to have the exact same type (by necessity due to the use case):

type OperationFn = (left: number, right: number) => number

The operations object is really just a record of operation strings mapped to a function that operates on two numbers. So if we add a type annotation on our operations variable, then we don't have to type each function individually. Let's try that:

type OperationFn = (left: number, right: number) => number
const operations: Record<string, OperationFn> = {
  '+': (left, right) => left + right,
  '-': (left, right) => left - right,
  '*': (left, right) => left * right,
  '/': (left, right) => left / right,
}

type CalculatorProps = {
  left: number
  operator: keyof typeof operations
  right: number
}

Sweet, so we don't have to type every function individually, but oh no... now the typeof operations is Record<string, OperationFn> and the keyof of that is going to be string which means our CalculatorProps['operator'] type will be string. Ugh 😩

Here's what we could do to fix this:

type OperationFn = (left: number, right: number) => number
type Operator = '+' | '-' | '/' | '*'
const operations: Record<Operator, OperationFn> = {
  '+': (left, right) => left + right,
  '-': (left, right) => left - right,
  '*': (left, right) => left * right,
  '/': (left, right) => left / right,
}

type CalculatorProps = {
  left: number
  operator: keyof typeof operations
  right: number
}

But now we're back to having to add ** in two places if we decide to add the Exponentiation operator. However, in this case, TypeScript will give us a compiler error if we add it in one and not the other, so that's a step up.

This is where I left this when I first wrote this component, but then @AlekseyL13 suggested that I try a properly typed identity function.

The constrained identity function

First, let's keep in mind, we have 2 goals:

  1. Enforce that the type of each property is the same (in this simple example, it's just a number, but in our actual example, it's a function type)
  2. Ensure that keyof typeof for our object results in a finite union of the keys

With TypeScript, it's a challenge to have both of these. By default, we get the second goal. The problem is that when you try to accomplish the first goal with a type annotation like const operations: Record<string, OperationFn> = ..., you end up widening the key so keyof typeof results in string. Ugh, how annoying.

So here's where the constrained identity function comes in. By the way, "constrained" describes a situation where you have a function that accepts a narrower version of an input than it's passed.Here's a simple example:

type NamedObject = {name: string}
function getUserName<User extends NamedObject>(user: User) {
  return user.name
}

const obj = {name: 'Hannah', age: 3}
getUserName(obj)

So the object that's passed to getUserName must satisfy all the types in the NamedObject. The getUserName constrains the input to at least match that type.

And an "identity function" is a function that accepts a value and returns that value. I sometimes use these kinds of functions as the default value for callbacks:

const identity = <Type extends unknown>(item: Type) => item

type ModifyConfigFn = (config: ConfigType) => ConfigType
function buildProject(modifyConfig: ModifyConfigFn = identity) {
  const config: ConfigType = {
    /* some config */
  }
  const modifiedConfig = modifyConfig(config)
  // more stuff...
}

So with those definitions out of the way, a "constrained identity function" is a function which returns what it is given and also helps TypeScript constrain its type. This is exactly what we want to do.

We can call it a CIF (pronounced "see eye eff"). Sure, let's go with that.

Let me show you a simple example first, then I'll explain what's going on, then we can apply it more usefully to our more complicated example:

type Value = number
const createNumbers = <ObjectType extends Record<string, Value>>(
  obj: ObjectType,
) => obj

const numbers = createNumbers({one: 1, two: 2, three: 3, four: 4})

// @ts-expect-error we don't have 'five' yet
numbers['five']

So the createNumbers is the constrained identity function. It returns the obj it's given, hopefully that's clear. But how does it enforce our input and constrain the type?

Let me explain it this way. If we start with:

const numbers = {one: 1, two: 2, three: 3, four: 4}
// typeof numbers:
// {
//   one: number;
//   two: number;
//   three: number;
//   four: number;
// }

But in the future, someone could come to this code and change it like this:

const numbers = {one: 1, two: 2, three: 3, four: 4, five: '5'}
// typeof numbers:
// {
//   one: number;
//   two: number;
//   three: number;
//   four: number;
//   five: string; // 😱
// }

Yikes! Nah, we can't have that! (And, more importantly, in our Calculator example, some auto-typing on the functions is the goal here).

So, let's enforce our value types with a type annotation:

// @ts-expect-error HA! We gotcha! No strings in this object!
const numbers: Record<string, number> = {
  one: 1,
  two: 2,
  three: 3,
  four: 4,
  five: '5',
}

But now by typing our values explicitly, we've told TypeScript that our key can be a string. Unfortunately, there's no way to tell TypeScript: "This thing has the keys it has, but the values are this specific type." IMO, this is a missing feature of TypeScript. Our createNumbers constrained identity function (er... "CIF") is a workaround.

So here's what that workaround is:

Constrained identity functions allow us to not explicitly annotate our variable while still getting to enforce the values.

So we create the object, get the best type that TypeScript can offer us (which includes the narrow keys and wide values), then we pass it to a function which accepts wide keys and narrow values. TypeScript combines that to give us a Record with a key and value which are both narrow!

Alrighty, so let's apply a CIF to our original situation:

type OperationFn = (left: number, right: number) => number
const createOperations = <OperationsType extends Record<string, OperationFn>>(
  operations: OperationsType,
) => operations

const operations = createOperations({
  '+': (left, right) => left + right,
  '-': (left, right) => left - right,
  '*': (left, right) => left * right,
  '/': (left, right) => left / right,
})

type CalculatorProps = {
  left: number
  operator: keyof typeof operations
  right: number
}

// @ts-expect-error we haven't added support
// for the exponentiation operator yet
operations['**'](1, 2)

Wahoo! So with this solution we don't have to explicitly type all the operation functions the exact same way and we can still get a union type of all available operations.

A generic CIF?

You may have noticed that we had two CIFs in the previous section:

type Value = number
const createNumbers = <ObjectType extends Record<string, Value>>(
  obj: ObjectType,
) => obj

type OperationFn = (left: number, right: number) => number
const createOperations = <OperationsType extends Record<string, OperationFn>>(
  operations: OperationsType,
) => operations

Wouldn't it be neat if we could combine those? Sure would. But you're not going to like it... Here's what I tried first:

const constrain = <Given, Inferred extends Given>(item: Inferred) => item

// @ts-expect-error Expected 2 type arguments, but got 1.(2558)
const numbers = constrain<Record<string, number>>({one: 1 /* etc. */})

Sad day. Unfortunately this is just not possible with TypeScript today. But here's a workaround:

const constrain =
  <Given extends unknown>() =>
  <Inferred extends Given>(item: Inferred) =>
    item

const numbers = constrain<Record<string, number>>()({one: 1 /* etc. */})

... yeah, I told you you wouldn't like it. It's marginally better like this:

const createNumbers = constrain<Record<string, number>>()
const numbers = createNumbers({one: 1 /* etc. */})

But like, huh. Bummer.

Luckily, I don't find myself making CIFs very often anyway and they aren't difficult to write so I don't need an abstraction for them. Thought it'd be interesting to share with you though 😄

Conclusion

Here's the final version of our calculator component with everything typed with our CIF:

type OperationFn = (left: number, right: number) => number
const createOperations = <OperationsType extends Record<string, OperationFn>>(
  opts: OperationsType,
) => opts

const operations = createOperations({
  '+': (left, right) => left + right,
  '-': (left, right) => left - right,
  '*': (left, right) => left * right,
  '/': (left, right) => left / right,
})

type CalculatorProps = {
  left: number
  operator: keyof typeof operations
  right: number
}
function Calculator({left, operator, right}: CalculatorProps) {
  const result = operations[operator](left, right)
  return (
    <div>
      <code>
        {left} {operator} {right} = <output>{result}</output>
      </code>
    </div>
  )
}

const examples = (
  <>
    <Calculator left={1} operator="+" right={2} />
    <Calculator left={1} operator="-" right={2} />
    <Calculator left={1} operator="*" right={2} />
    <Calculator left={1} operator="/" right={2} />
  </>
)

Yup, this entire blog post was written just to explain those 3 lines of code to you. So yeah, there you go.

Some folks may finish reading this post and scoff, saying things like: "Why would you ever want to use TypeScript if it requires you to do weird things like this?"

First, I'd say that just because a tool like TypeScript requires workarounds for some stuff like this doesn't mean it's not worthwhile. The cost here is minimal and the benefit is significant. I'm not here to convince you to use TypeScript. I can't do as good a job convincing you as your runtime bugs do I'm sure 😜 Secondly, this is definitely something that could improve with TypeScript in the future. In fact, this may be a nice step to improving things. Finally, like I said, this isn't something that we're doing all the time. Most of my time with TypeScript is delightful.

Take care!

Kent C. Dodds
Written by Kent C. Dodds

Kent C. Dodds is a JavaScript software engineer and teacher. He's taught hundreds of thousands of people how to make the world a better place with quality software development tools and practices. He lives with his wife and four kids in Utah.

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