# How to Write TypeScript Like a Haskeller

March 29th, 2022

Web apps are a mandatory part of every modern application nowadays, no matter how small or complex it is. From one-click apps that convert pictures to Photoshop, everyone wants fast and easy access to the app, and the web is one of the easiest ways to do that.

We won’t cover all the similarities or differences. We will also not say much about the differences of TypeScript’s type system vs. Haskell’s or how it works under the hood. Our main goal is to show how you can use types in TypeScript like a Haskeller.

## Why TypeScript?

Historically, any new language that allows you to write web applications translates its code to JavaScript. And there are a lot of such languages and language extensions: TypeScript, Kotlin JS, CoffeeScript, Scala JS, Babel, ClojureScript, etc. Generally, you can write web applications in almost any language.

Because we like Haskell, we could write our web applications in a functional language (or even in Haskell). There are a lot of options:

Unfortunately, these don’t give us proper flexibility in working with JS libraries (whose numbers are enormous), and when problems related to library management appear, it takes more time to fix those. Additionally, customers will be locked in when they need to maintain such applications.

Meanwhile, TypeScript, which has a vast community and provides modern technologies out of the box, is a great decision.

## Basic concepts

In this part, we will introduce you to simple built-in concepts familiar to most Haskellers that do not require any overhead when writing code. Nevertheless, we will also leave links to some more complex libraries and articles to help you investigate further.

We’ll try to explain the TypeScript syntax used, but you can also find a table in the appendix with links for each piece of syntax used in the article. In addition, there is also a table there with comparisons between the Haskell and TypeScript syntax.

### Strictness

Unlike Haskell, TypeScript does not focus on types. They are just there to help you write stricter and more understandable code, making your life easier. You can use types like any, and nobody pushes you into strict frameworks.

Nevertheless, with a bunch of compiler options, you can make TypeScript more strict in types and other things. To do that, you need to add the strict compiler option to your tsconfig.json file. It will enable all strictness-related flags for you, and if in the future something will be added to the strict options list, you will not need to add it manually.

But in case you want to specify them one-by-one, here are all the current ones: alwaysStrict, strictNullChecks, strictBindCallApply, strictFunctionTypes, strictPropertyInitialization, noImplicitAny, noImplicitThis, useUnknownInCatchVariables.

### Type aliases and newtypes

#### Type aliases

Type aliases work the same as in Haskell – you can create a new name to refer to some type:

type Email = string;


And you can also create types with properties:

type Document = {
name: string;
author?: string;
}


Symbol ? here is used as syntactic sugar for the string | undefined type.

#### Newtype

Creating a newtype is not so trivial. There is no analogue for it in TypeScript, but you can do it via tags.

type Email = string & { readonly __tag: unique symbol };
type City = string & { readonly __tag: unique symbol };


Here’s how all this magic works:

• With intersection types (via & operator), you can add a tag field to your type.
• symbol lets you declare const-named properties on types.
• unique means that the type is unique – your type is tagged with a unique symbol.

Now, with as (which does type assertion), you can cast your base type to a tagged type. And when you try to pass a value of another tagged type, the compiler says that the two unique symbols are different.

function sendMessage(email: Email);

sendMessage("message"); // Error: Argument of type 'string' is not assignable to parameter of type 'Email'.
sendMessage("St. Petersburg" as City); // Error: Argument of type 'City' is not assignable to parameter of type 'Email'.

sendMessage("email@gmail.com" as Email); // Ok


While this is the simplest solution for newtypes, it is not the best for complex systems. For a better (but more complex) one, check this comment in TypeScript’s issues.

### Algebraic data types

In Haskell, algebraic data types (ADTs) are a commonly used functionality of the language. They allow you to build your own types from small blocks. And with pattern matching, it is easy to access this data.

Unfortunately, you can’t build an ADT in TypeScript the same way as in Haskell, but we will show you what you can do with the existing type system. We will start with the easiest enums and move to more complex things after that.

#### Union types

Union types allow you to combine different types. Unions are not tagged, so they are just a set of possible types.

type Result = string | number | (() => string);


If you fail to match a type in the union, the compiler knows that it will not be present in the future.

Look at the code below. In the first if, we pass typeof result === "number", so we know that it may be only function or string. And we can run length.toString() on this value (even if number doesn’t have such a property) since both function and string have the property length. But we can’t call this value because string is not callable. We can do it only after we fail to match string.

const resultInterpreter = (result: Result): string | undefined => {
if (typeof result === "number") {
return result.toFixed();
}

// Okay: return result.lenght.toString();
// Error: return result();

if (typeof result === "string") {
return result.toLocaleUpperCase();
}

return result();
};


However, if your type consists of two callable parts, you are able to call it, and the resulting type will be just a union of function result types. You are also able to combine these checks using || to expand restrictions.

#### Unit types

The next feature is unit types. Unit types are a subtype of primitive types that contain precisely one primitive value. With unions, you can use them like enums by setting unique string values or even values with different types.

type Result = true | "error" | 5;


You can pass the Result type to a function and match it by its type.

const resultInterpreter = (result: Result): string => {
if (result === true) {
return "true";
}
if (result === "error") {
return result;
}
return "five";
};


#### Discriminated unions (analogue of data types)

By storing a unique property in each member of a union that we can switch on, we can make an analogue of Haskell data types. Unions like these are called discriminated unions.

type Result =
| {type: "error"; message: string}
| {type: "result"; value: number}

const resultInterpreter = (result: Result): string => {
switch (result.type) {
case "error":
return result.message;
case "result":
.with({ type: 'ok', data: { type: 'img', src: select() } }, (src) => <img src=${src} />) .exhaustive();  ### Immutability #### const and readonly TypeScript has two base primitives to work with immutability: const and readonly. The first one is used to prevent variable reference change. const a = 1; a = 2; // Error: Cannot assign to 'a' because it is a constant.  And the second one is used to make properties immutable. type A = { readonly x: number; } const a: A = { x: 1 }; a.x = 12; // Error: Cannot assign to 'x' because it is a read-only property.  Nevertheless, there are some problems here. const and readonly only block reference changes but do nothing about values. With const a = [1, 2, 3] or readonly x: number[], you can still change the contents of an array. Also, you need to be careful when passing an object with read-only fields to a function because it may be changed inside the function. This happens because of information loss. The type of an object with readonly is a subtype of the type without it, and when you pass it to a function with a more general type, the function does not have access to information about its subtype. For this reason, you should always write proper types of arguments. const a: { readonly x: number } = { x: 1 }; const changeA = (arg: { x: number }): void => { const argC = arg; argC.x = 2; } changeA(a); a.x; // 2  #### Readonly type With the Readonly type, you can mark all properties as readonly. type A = { x: number; y: number; }; type ImmutableA = Readonly<A>; const a: ImmutableA = { x: 1, y: 2 }; a.x = 2; // Error: Cannot assign to 'x' because it is a read-only property. a.y = 1; // Error: Cannot assign to 'y' because it is a read-only property.  With ReadonlyArray, you can make all array elements readonly. const arr: ReadonlyArray<number> = [1, 2, 3]; arr[0] = 4; // Error: Index signature in type 'readonly number[]' only permits reading.  You can also make a readonly dictionary, for example: type A = { readonly [x: string]: number; } const a: A = { x: 1, y: 2 }; a.x = 2; // Error: Index signature in type 'A' only permits reading. a.y = 1; // Error: Index signature in type 'A' only permits reading.  #### Working with immutable objects Although you can now make immutable objects, usually you don’t need them as they are. You want to do some actions on them and make new immutable objects. To do that, you can construct new objects by hand or use the Writable utility type, but it is not that simple. Fortunately, there are libraries that can help you deal with this issue. The most powerful is immer, which is used for immutable state flow. Immutable data there is not copied but shared in memory. In other words, immer gives you the ability to work with a draft copy of your data and not worry about mutability. After all the changes are done, it will produce an actually immutable state. It also has helpers for React. Here’s an example of its use: type A = Immutable< { text: string; valid: boolean; }[] >; const a: A = [ { text: "valid text", valid: true, }, { text: "invalid text", valid: false, }, ]; const nextA = produce(a, (draft) => { draft[1].valid = false; // set valid = false for the second element draft.push({ text: "some text", valid: false }); // add new element to array });  In the code example above, produce is a base primitive for working with immer. It takes your current state and a function, which takes a draft and applies changes. And in the end, it creates a new nextA state without any changes in a. There are also three interesting optics libraries that can help you work with immutable data structures: ### Higher-order functions and currying Many languages support higher-order functions, and TypeScript is not an exception. You can use functions as an argument and also return them. const filterArray = (fn: (elem: string) => boolean, arr: string[]): string[] => { const newArray: string[] = []; for (let i = 0; i < arr.length; i++) { if (fn(arr[i])) { newArray.push(arr[i]); } } return newArray; // or just simply return arr.filter(fn); }; const f = (x: string): ((s: number) => boolean) => { return (s: number) => { return s.toString() === x; }; }; f("5")(5) // true;  As you may see in the last example, we can call the function f and return a function that takes another argument. It’s definitely possible to implement some kind of currying through this. You can split the type signature of the function from its implementation. Unfortunately, unnamed parameters are not supported, but you can set them as _. type addT = (_: number) => (_: number) => number; const add: addT = (l) => (r) => l + r; type foldArrT = (_: (_: number) => (_: number) => number) => (_: number) => (_: number[]) => number; const foldArr: foldArrT = (f) => (z) => (arr) => { let m = z; arr.forEach((elem) => { m = f(m)(elem); }); return m; }; foldArr(add)(0)([1, 2, 3, 4, 5]) // 15;  The syntax is weird since you always need to use named parameters. But it is still possible, and you can use it in your code quite easily. ### Polymorphism There are different kinds of polymorphisms, but we will cover only three of them: parametric, ad-hoc, and row polymorphism. Let’s start with the first one. #### Parametric polymorphism Parametric polymorphism allows us to write abstract functions that, for instance, don’t depend on concrete types of particular arguments and types that can abstract out parts of themselves as type parameters. In TypeScript, we call those generics. const arrLength: <T>(_: T[]) => number = (arr) => arr.length; arrLength([1, 2, 3]); // 3 arrLength<string>(["1", "2"]); // 2 arrLength<number>(["1", "2", "3"]); // Error: Type 'string' is not assignable to type 'number'. type NonEmpty<T> = { head: T; tail: T[]; };  #### Ad-hoc polymorphism Ad-hoc polymorphism allows you to implement abstract functions, the logic of which will be different with different types. Let’s define an Eq interface: interface Eq<T> { equal: (f: T, s: T) => boolean; }  And now we will create two implementations of it: IntEq for numbers and IntArrEq for arrays of numbers. The first one will simply compare two numbers, and the second one will return equality if the first array contains all the elements from the second array. class IntEq implements Eq<number> { equal(f: number, s: number) { return f === s; } } class IntArrEq implements Eq<number[]> { equal(f: number[], s: number[]) { return f.filter(item => s.indexOf(item) < 0).length === 0; } }  Now let’s implement a lookup function, which for an array of key-value pairs and a specific key will return the value associated with this key or undefined. We can make it polymorphic by passing a comparator class that implements Eq for the key type. const lookup = <T, K extends Eq<T>, V>(cmp: K, k: T, mp: [T, V][]): V | undefined => { let result: V | undefined; mp.forEach(([kk, v]) => { if (cmp.equal(k, kk)) { result = v; } }); return result; }; lookup(new IntEq(), 1, [[1, "2"], [2, "1"]]); // "2" lookup(new IntArrEq(), [1, 2, 3], [[[1, 3], "1"], [[3, 2], "2"], [[2, 1, 3], "3"]]); // "3"  #### Row polymorphism The last kind of polymorphism is row polymorphism. It allows you to ensure that a record contains at least the given set of fields. Unfortunately, TypeScript’s type compatibility is based on structural subtyping, so what we have available is not exactly row polymorphism. Despite this, we can use intersection types to emulate this. But you should be careful with that since you can lose information during assignments. Therefore, you must be cautious about propagating the full type-level information when you need it. type fnT = <T>(v: T & { x: number }) => T & { x: number } // You should fully describe all types to not lose information. // Look at example below type A = {}; type B = A & {x: number}; let a: A = {}; const b: B = {x: 1}; a = b; a.x; // Error: Property 'x' does not exist on type 'A'.  ### Mapped types, conditional types, and type families Mapped and conditional types are a rather practical part of TypeScript. They give us the flexibility to modify existing types or create new types out of them. #### Mapped types Mapped types allow you to create new types based on old types by transforming them in some way. The syntax looks like this: [set of field names]: type;. For example, you can add an optional modifier or a readonly modifier to each field with type Partial<T> = { [P in keyof T]?: T[P] } and type Readonly<T> = { readonly [P in keyof T]: T[P] }, respectively. type Partial<T> = { [P in keyof T]?: T[P] }; type A = { x: number; y: number }; type PartialA = Partial<A>; const a: A = { x: 1 }; // Error: Property 'y' is missing in type '{ x: number; }' but required in type 'A'. const a: PartialA = { x: 1 }; // Ok  In the code above: • Partial type adds the ? modifier for each property. • The keyof operator in the code above produces a union of property names. • Square brackets indicate the computed names. • And the in operator goes over all the field keys. It is also possible to remove such modifiers using -? and -readonly. Let’s try to do that. type NoModifiers<T> = { -readonly [P in keyof T]-?: T[P] }; type A = { readonly x?: number; readonly y?: number }; type NoModifiersA = NoModifiers<A>; const a: A = { x: 1 }; // Ok a.x = 1; // Error: Cannot assign to 'x' because it is a read-only property. const a: NoModifiersA = { x: 1 }; // Error: Property 'y' is missing in type '{ x: number; }' but required in type 'NoModifiers<A>' const a: NoModifiersA = { x: 1, y: 2 }; // Ok a.x = 2; // Ok  Now, let’s look at some more complex examples of mapped types. First, let’s define a Point type with some string and numerical properties. type Point = { x: number; y: number; 0: string; }  Now, using mapped types, we can create a type that will pick a subset of the properties of a type. Here,K is a generic type that is constrained by keyof T, which is a union of all T’s properties. For each of the properties in K, we pick them out of T. type Pick<T, K extends keyof T> = { [P in K]: T[P]; };  Then, by applying Pick to Point and "x" | 0, we can map a type from Point to a type with only the properties listed. type PointValues = Pick<Point, "x" | 0> // type PointValues = { x: number; 0: number }  The next example will be more complex. We will try to create a type that produces a type with getters for all string properties. To implement it, let’s first define a Getter helper type (Capitalize<T> is a built-in type that can be applied to the string type.). type Getter<T extends string> = get${Capitalize<T>};


So, for each T that extends string, we can produce a getter-specific name.

After that, we can implement the Getters type by using the Extract type, which will construct a type by extracting from type K all union members that are assignable to string.

type Getters<T> = {
[K in keyof T as Getter<Extract<K, string>>]: () => T[K];
}


So for each property name K in T that is assignable to string, we create a getter with the property name and type () => T[K].

type PointGetters = Getters<Point> // type PointGetters = { getX: () => number; getY: () => number; }


#### Conditional types

Another great feature of TypeScript is conditional types. They allow you to choose the type based on some condition expressed as another type.

Here is a basic example of a conditional type:

type A = { x: number };
type B = { x: number; y: number };
type C = { y: number };

type Condition<T, V> = T extends V ? number : string;

type N = Condition<B, A>; // type N = number
type E = Condition<C, A>; // type E = string


With the extends keyword, you can make a condition: T extends U ? X : Y. In the example, type B extends A but type C doesn’t. So the Condition type will be number with Condition<B,A> and string with Condition<C,A>.

You can also choose from more than two types: T extends U ? X : T extends W ? Y : Z.

With such functionality, you can implement things that resemble type families, although they are not quite like them. In conjunction with mapped types, it’s a great feature to manage your types.

Conditional types together with union types are called distributive conditional types. How they work might be a little bit confusing, but we’ll give an example.

Take a look at this:

type Exclude<T, U> = T extends U ? never : T;


The Exclude type may look strange, but what if we will pass union types to it? It will simply exclude such types in union T which exist in union U by setting never type, where the never type describes the type of values that will never occur.

You may think about it as two nested cycles. For each type in T and each type in U, if T extends U, set never. Otherwise, set T.

type A = "a" | "b" | "c";
type B = Exclude<A, "a" | "b">; // type B = "c"
type C = Exclude<A, "a" | "b" | "c">; // type C = never
type D = Exclude<A, "z">; // type D = "a" | "b" | "c"


With distributed conditional types, we can write an Omit type, which will remove properties from a type. When taking properties of T via keyof T, we exclude properties whose names are written in K, and then simply pick the remaining ones using Pick.

type Omit<T, K> = Pick<T, Exclude<keyof T, K>>;

type Point = {
x: number;
y: number;
z: number;
}

type PointX = Omit<Point, "y" | "z">; // type PointX = { x: number }


TypeScript contains a lot of predefined conditional and mapped types that you can use out of the box.

## Going further

Built-in concepts are good. But, as you can see, TypeScript’s type system is not really a weak one. By adding our knowledge from Haskell and type theory, we can get more from this type system. This part will show very brief descriptions of different approaches. We have also added links to references and other articles to help you understand them more deeply, if necessary.

### HKTs

As we said before, TypeScript’s type system is not as bad as one may think. But it has one significant limitation: the absence of kinds. Higher-kinded types let us to write types that have their own type constructors as parameters. So, with them, we can create another level of abstraction. For example, imagine that your generic type is not just a specific type, but a type constructor like Map or Array that is waiting for its own generic type to be specified.

Let’s take a look at an example of a theoretical implementation, which, unfortunately, TypeScript’s type system doesn’t allow.

type Collection<F> = {
create: <A>() => F<A>; // Error: Type 'F' is not generic.
insert: <A>(v: A) => (c: F<A>) => F<A>; // Error: Type 'F' is not generic.
};

const collectionArray: Collection<Array> = {
create: () => [],
insert: (v) => (c: number[]) => [...c, v]
};


Fortunately, we can simulate kinds by using defunctionalization, which allows us to translate higher-order programs into a first-order language. The main idea is to map type constructor names to their implementations. With it, we can create a type called Kind which works with * -> * constructors, Kind2 for * -> * -> *, and so on.

Let’s define two types: URItoKind and URItoKind2. They will be our identifiers for types with arities 1 and 2. And URIS with URIS2 will be present for all such types.

type URItoKind<A> = {
'Array': Array<A>;
'Set': Set<A>;
}

type URItoKind2<A, B> = {
'Map': Map<A, B>;
}

type URIS = keyof URItoKind<unknown>;
type URIS2 = keyof URItoKind2<unknown, unknown>;


Above, unknown is a more type-safe representation of any that forces us to do some checks before doing actions with values of this type.

Our kinds take an identifier property as the first type parameter, and the rest of parameters are type parameters of this identifier.

type Kind<F extends URIS, A> = URItoKind<A>[F];
type Kind2<F extends URIS2, A, B> = URItoKind2<A, B>[F];


And now we can return to our theoretical Collection above and implement it using kinds. The three dots ... operator here is the array/object spread operator. Here, in array, we simply copy the array c and add value v to it. And in object, you are able to copy all property values from the old object and change some of them by specifying only the ones you need.

type Collection<F extends URIS> = {
create: <A>() => Kind<F, A>;
insert: <A>(v: A, c: Kind<F, A>) => Kind<F, A>;
}

const collectionArray: Collection<"Array"> = {
create: () => [],
insert: (v, c) => [...c, v]
};


And this is how type classes look in TypeScript. We represent them as a dictionary of related methods carried in a mere type. Our Collection is effectively a type class that works with 1-arity constructors that we defined in URItoKind. And collectionArray is an instance of this type class for "Array" which is Array<A> in URItoKind.

Let’s see how it works in practice.

We implement a new Collection instance for Set and then write a generic function f over Collection. The last thing we need to do is to pass the implementation as a function argument like a type class function context.

const collectionSet: Collection<"Set"> = {
create: () => new Set(),
};

const f = <F extends URIS, A>(C: Collection<F>, v1: A, v2: A): Kind<F, A> => {
const newCollection = C.create<A>();
return C.insert(v2, C.insert(v1, newCollection));
};

f(collectionArray, 1, 2); // [ 1, 2 ]
f(collectionSet, 2, 2); // Set(1) { 2 }


Of course, this is a tiny subset of what you can do with kinds. Most of this part is inspired by the fp-ts library and Yuriy Bogomolov’s blog. fp-ts contains a ton of things that you may know from Haskell, and in the blog, you can find excellent explanations of how the library works.

There are also a lot of other libraries based on fp-ts:

### Peano numbers

Moving further, we can look into type-level programming and, more concretely, computations on types. The basic primitive that can guide us is Peano numbers. Let’s see how those would look in TypeScript.

type Zero = "zero";

type Nat = Zero | { n: Nat };


Now we are able to define Succ, which adds one to our Nat.

type Succ<N extends Nat> = { n: N };


With a simple Nat definition, we can make something useful.

#### Type-safe vector

Let’s create a type-safe vector that will store its length in type.

An empty vector will simply be a "nil".

type Nil = "nil";


Type Cons will add a value to the vector and increase its type-level length.

type Cons<A, N extends Nat> = {a: A, v: Vec<A, N>};


And the main type, Vec, combines them by using a conditional type.

type Vec<A, N extends Nat> = N extends Succ<infer R> ? Cons<A, R> : Nil;


Using infer, we are able to infer a new type variable R from N. So, when N is a Succ, we can infer a nested R from it and return Cons<A, R>. Otherwise, it is Nil.

And here are examples of Vec’s usage. We define two helper functions that build Vec values. And, as you can see, we can use it safely.

const emptyVec: <A>() => Vec<A, Zero> = () => "nil";

const pushVec: <A, N extends Nat>(a: A, v: Vec<A, N>) => Vec<A, Succ<N>> = (a, v) => {
return {a, v}
};

let empty: Vec<number, Zero> = emptyVec(); // Ok
let oneElem: Vec<number, Succ<Zero>> = pushVec(1, empty); // Ok
let twoElems: Vec<number, Succ<Succ<Zero>>> = pushVec(2, oneElem); // Ok
let twoElemsInvalid: Vec<number, Succ<Zero>> = pushVec(2, oneElem); // Error
oneElem = twoElems; // Error


This was a simple example of what we can do with type-level programming. Using such primitives, we can implement different operations on types and even type-level Fibonacci, for example.

type Fibonacci<N, F0 = Zero, F1 = One> = {
acc: F0
n: N extends Succ<infer _> ? Fibonacci<Decrement<N>, F1, Add<F0, F1>> : never
}[IfElse<Equals<Zero, N>, "acc", "n">]


#### Generalized algebraic data types

Generalized algebraic data types (GADTs) in Haskell give us the ability to manually write types of constructors. With a data type D a with the type value a, we can create constructors like C :: Int -> D Int.

The great feature of this approach is that we can make a nice eDSL. TypeScript will not provide you with such a good eDSL as Haskell would, but it doesn’t mean that we can’t do it.

Let’s show on example how it will look like and work. We will use fp-ts here and below since it has a lot of useful built-in types and functions.

import { identity } from "fp-ts/lib/function";


Haskell can infer the equality of types a and Int. TypeScript, on the other hand, doesn’t have equality inference. Nevertheless, we can manually provide such equality to it as a value. To provide equality as a value, we use Leibniz equality.

Interface Equality is a hybrid type, which gives an object the ability to act as a function.

interface Equality<A, B> {
(a: A): B;
}


Then in ArithExpr, we simplify Equality<A, B> into an identity (a: A) => A, which gives us proof representation as a value.

type ArithExpr<A> =
| { type: "Num"; v: number; proof: Equality<number, A> }
| { type: "Plus"; l: ArithExpr<number>; r: ArithExpr<number>; proof: Equality<number, A> }
| { type: "Gt"; l: ArithExpr<number>; r: ArithExpr<number>; proof: Equality<boolean, A> }
| { type: "And"; l: ArithExpr<boolean>; r: ArithExpr<boolean>; proof: Equality<boolean, A> };


Now let’s define our helper functions which will help us to build expressions and use identity<A>(a: A): A as a proof.

const num: (v: number) => ArithExpr<number> = (v) => {
return { type: "Num", v, proof: identity };
};

const plus: (l: ArithExpr<number>, r: ArithExpr<number>) => ArithExpr<number> = (l, r) => {
return { type: "Plus", l, r, proof: identity };
};

const gt: (l: ArithExpr<number>, r: ArithExpr<number>) => ArithExpr<boolean> = (l, r) => {
return { type: "Gt", l, r, proof: identity };
};

const and: (l: ArithExpr<boolean>, r: ArithExpr<boolean>) => ArithExpr<boolean> = (l, r) => {
return { type: "And", l, r, proof: identity };
};


The last step will be just the implementation of interpret. With a switch statement on expr.type, we construct our result by running interpret on nested expressions and proving the resulting types with the proof from this expr.

const interpret: <A>(expr: ArithExpr<A>) => A = (expr) => {
switch (expr.type) {
case "Num":
return expr.proof(expr.v);
case "Plus":
return expr.proof(interpret(expr.l) + interpret(expr.r));
case "Gt":
return expr.proof(interpret(expr.l) > interpret(expr.r));
case "And":
return expr.proof(interpret(expr.l) && interpret(expr.r));
default:
return expr;
}
};

const testExpr = and(gt(plus(num(23), num(12)), num(170)), gt(num(35), num(47)));
interpret(testExpr); // false

const wrongExpr = and(num(23), num(12)); // Error: Argument of type 'ArithExpr<number>' is not assignable to parameter of type 'ArithExpr<boolean>'.


For a deeper understanding of this, you can check the original PureScript article and also Giulio Canti’s example (on which this part is based on) of its implementation in TypeScript.

#### Tagless final eDSL

Another way to implement an eDSL is tagless final. We can move from data type to type classes with the same logic. Here the type class will describe possible actions, and by using instances, we will be able to write interpreters.

Let’s start by defining our type class. To do this, we need the already-mentioned URIS(which is a union of all 1-arity defined in URItoKind) and the already-mentioned Kind.

import { Kind, URIS } from "fp-ts/HKT";

type ArithExpr<Expr extends URIS> = {
num: (v: number) => Kind<Expr, number>;
plus: (l: Kind<Expr, number>, r: Kind<Expr, number>) => Kind<Expr, number>;
gt: (l: Kind<Expr, number>, r: Kind<Expr, number>) => Kind<Expr, boolean>;
and: (l: Kind<Expr, boolean>, r: Kind<Expr, boolean>) => Kind<Expr, boolean>;
};


Here are the types for which we will create ArithExpr instances:

• Interpreter<A>, which defines how the algebra should behave.
• ToS<A>, which will create a string representation of the expression.

We need to somehow add them to the fp-ts URItoKind interface to be able to use them in ArithExpr since it takes Expr extends URIS, where URIS is just keyof URItoKind<unknown>.

Here we need the TypeScript’s module augmentation feature, which allows us to patch existing objects by importing and then updating them. So, we simply add Interpreter and ToS to URItoKind.

type Interpreter<A> = {
interpret: A;
};

type ToS<A> = {
toString: string;
};

declare module "fp-ts/lib/HKT" {
interface URItoKind<A> {
}
}


After all the preparations, we are ready to create instances.

const arithInterpreter: ArithExpr<"Interpreter"> = {
num: (v: number) => {
return { interpret: v };
},
plus: (l: Interpreter<number>, r: Interpreter<number>) => {
return { interpret: l.interpret + r.interpret };
},
gt: (l: Interpreter<number>, r: Interpreter<number>) => {
return { interpret: l.interpret > r.interpret };
},
and: (l: Interpreter<boolean>, r: Interpreter<boolean>) => {
return { interpret: l.interpret && r.interpret };
},
};

const arithToS: ArithExpr<"ToS"> = {
num: (v: number) => {
return { toString: v.toString() };
},
plus: (l: ToS<number>, r: ToS<number>) => {
return { toString: (${l.toString} +${r.toString}) };
},
gt: (l: ToS<number>, r: ToS<number>) => {
return { toString: (${l.toString} >${r.toString}) };
},
and: (l: ToS<boolean>, r: ToS<boolean>) => {
return { toString: (${l.toString} &&${r.toString}) };
},
};


And finally, let’s create a test expression and run it with different instances.

const testExpr: <Expr extends URIS>(E: ArithExpr<Expr>) => Kind<Expr, boolean> = (E) =>
E.and(E.gt(E.plus(E.num(23), E.num(12)), E.num(170)), E.gt(E.num(35), E.num(47)));

testExpr(arithInterpreter).interpret; // false
testExpr(arithToS).toString; // (((23 + 12) > 170) && (35 > 47))


You can also see more complex examples in Yuriy Bogomolov’s eDSL workshop.

## Conclusion

In this article, we have shown how your knowledge from Haskell may help you write type-safe code in TypeScript. We started from basic concepts such as type aliases and data types and moved towards more complex and TypeScript-specific topics like mapped and conditional types. In the last part, we learned how to implement simple eDSLs with TypeScript’s type system.

Hopefully, you can use things you’ve learned here, develop your own solutions based on them, and dive into the extraordinary world of TypeScript.

## Appendix

After all these descriptions of the possibilities of TypeScript, we want to present a summary of all the syntax and TypeScript features that were discussed here. Below the summary, you can find a comparison between Haskell and TypeScript syntax.

### Syntax cheat sheet

Syntax Name & link to docs
type Point = {
y: number;
x?: number;
};


Optional parameters

type PointWithZ = Point & { z: number };


Intersection types

const x = (s as string).length;


Type assertions

const s: unique symbol;


Symbols

const s = "hello";
const n: typeof s;


Typeof types

const a = "Hello";
type A = "Hello";

const b = ${a} world!; type B = ${A} world!;

type Point = {
y: number;
x?: number;
};

type P = keyof Point;


Keyof types

const a: never;


Never type

const arr = [1, 2, 3];
const newArr = [...arr, 4, 5];


const a: unknown;


Unknown type

type A<T> = T extends Array<infer B> ? B : T;


Inferring

declare module "someModule" {
interface I<A> {
arr: Array<A>;
}
}


Module augmentation

### Comparison between Haskell and TypeScript

#### Type aliases

type Email = String


TypeScript

type Email = string;


#### Newtypes

newtype Email = Email String


TypeScript

type Email = string & { readonly __tag: unique symbol };


#### Unit types

data Result = Error | Success


TypeScript

type Result = "Error" | "Success";


#### Discriminated unions

data Result = Error String | Success Int


TypeScript

type Result =
| { type: "Error"; message: string }
| { type: "Success"; n: number };


#### Immutability

On by default.

TypeScript

const a = 1;
type A = { readonly x: number };
const arr: ReadonlyArray<number> = [1, 2, 3];
type A = { readonly [x: string]: number };


#### Currying

On by default.

TypeScript

type addT = (_: number) => (_: number) => number;


#### Parametric polymorphism

length :: [a] -> Int


TypeScript

type length = <T>(_: T[]) => number;


lookup :: Eq a => a -> [(a,b)] -> Maybe b;


TypeScript

type lookup = <T, K extends Eq<T>, V>(cmp: K, k: T, mp: [T, V][]) => V | undefined;


#### Row polymorphism

On by default.

TypeScript

type fnT = <T>(v: T & { x: number }) => T & { x: number };


#### Conditional types

type family G a where
G Int = Bool
G a = Char

type family H a where
G Int = Bool
G String = [Int]


TypeScript

type G<A> = A extends number ? boolean : string;

type H<A extends number | string> = A extends number ? boolean : number[];


#### Mapped types

Mapped types don’t realy have an analogue in Haskell.

TypeScript

type Partial<T> = { [P in keyof T]?: T[P] };


#### HKTs

class Collection (t :: * -> *) where
create :: t a

withCollection :: Collection t => t a


TypeScript

type URItoKind<A> = { Array: Array<A> };
type URIS = keyof URItoKind<unknown>;
type Kind<F extends URIS, A> = URItoKind<A>[F];

type Collection<F extends URIS> = { create: <A>() => Kind<F, A> };

type withCollection = <F extends URIS, A>(C: Collection<F>) => Kind<F, A>;


#### Peano numbers

data Peano = Zero | Succ Peano

type Zero = "zero";