In this blog post, we explore how we can compute with types at compile time in TypeScript.
Note that the focus of this post is on learning how to compute with types. Therefore, we’ll use literal types a lot and the examples are less practically relevant. Future blog posts will cover realworld use cases.
Table of contents:
Consider the following two levels of TypeScript code:
The type level is a metalevel of the program level.
Level  Available at  Operands  Operations 

Program level  Runtime  Values  Functions 
Type level  Compile time  Specific types  Generic types 
What does it mean that we can compute with types? The following code is an example:
type ObjectLiteralType = {
first: 1,
second: 2,
};
// %inferredtype: "first"  "second"
type Result = keyof ObjectLiteralType; // (A)
In line A, we are taking the following steps:
ObjectLiteralType
, an object literal type.keyof
to the input. It lists the property keys of an object type.keyof
the name Result
.At the type level we can compute with the following “values”:
type ObjectLiteralType = {
prop1: string,
prop2: number,
};
interface InterfaceType {
prop1: string;
prop2: number;
}
type TupleType = [boolean, bigint];
//::::: Nullish types and literal types :::::
// Same syntax as values, but they are all types!
type UndefinedType = undefined;
type NullType = null;
type BooleanLiteralType = true;
type NumberLiteralType = 12.34;
type BigIntLiteralType = 1234n;
type StringLiteralType = 'abc';
Generic types are functions at the metalevel – for example:
type Wrap<T> = [T];
The generic type Wrap<>
has the parameter T
. Its result is T
, wrapped in a tuple type. This is how we use this metafunction:
// %inferredtype: [string]
type Wrapped = Wrap<string>;
We pass the parameter string
to Wrap<>
and give the result the alias Wrapped
. The result is a tuple type with a single component – the type string
.

) The type operator 
is used to create union types:
type A = 'a'  'b'  'c';
type B = 'b'  'c'  'd';
// %inferredtype: "a"  "b"  "c"  "d"
type Union = A  B;
If we view type A
and type B
as sets, then A  B
is the settheoretic union of these sets. Put differently: The members of the result are members of at least one of the operands.
Syntactically, we can also put a 
in front of the first component of a union type. That is convenient when a type definition spans multiple lines:
type A =
 'a'
 'b'
 'c'
;
TypeScript represents collections of metavalues as unions of literal types. We have already seen an example of that:
type Obj = {
first: 1,
second: 2,
};
// %inferredtype: "first"  "second"
type Result = keyof Obj;
We’ll soon see typelevel operations for looping over such collections.
Due to each member of a union type being a member of at least one of the component types, we can only safely access properties that are shared by all component types (line A). To access any other property, we need a type guard (line B):
type ObjectTypeA = {
propA: bigint,
sharedProp: string,
}
type ObjectTypeB = {
propB: boolean,
sharedProp: string,
}
type Union = ObjectTypeA  ObjectTypeB;
function func(arg: Union) {
// string
arg.sharedProp; // (A) OK
// @tsexpecterror: Property 'propB' does not exist on type 'Union'.
arg.propB; // error
if ('propB' in arg) { // (B) type guard
// ObjectTypeB
arg;
// boolean
arg.propB;
}
}
&
) The type operator &
is used to create intersection types:
type A = 'a'  'b'  'c';
type B = 'b'  'c'  'd';
// %inferredtype: "b"  "c"
type Intersection = A & B;
If we view type A
and type B
as sets, then A & B
is the settheoretic intersection of these sets. Put differently: The members of the result are members of both operands.
The intersection of two object types has the properties of both types:
type Obj1 = { prop1: boolean };
type Obj2 = { prop2: number };
type Both = {
prop1: boolean,
prop2: number,
};
// Type Obj1 & Obj2 is assignable to type Both
// %inferredtype: true
type IntersectionHasBothProperties = IsAssignableTo<Obj1 & Obj2, Both>;
(The generic type IsAssignableTo<>
is explained later.)
If we are mixin in an object type Named
into another type Obj
, then we need an intersection type (line A):
interface Named {
name: string;
}
function addName<Obj extends object>(obj: Obj, name: string)
: Obj & Named // (A)
{
const namedObj = obj as (Obj & Named);
namedObj.name = name;
return namedObj;
}
const obj = {
last: 'Doe',
};
// %inferredtype: { last: string; } & Named
const namedObj = addName(obj, 'Jane');
A conditional type has the following syntax:
«Type2» extends «Type1» ? «ThenType» : «ElseType»
If Type2
is assignable to Type1
, then the result of this type expression is ThenType
. Otherwise, it is ElseType
.
.length
In the following example, Wrap<>
only wraps types in oneelement tuples if they have the property .length
whose values are numbers:
type Wrap<T> = T extends { length: number } ? [T] : T;
// %inferredtype: [string]
type A = Wrap<string>;
// %inferredtype: RegExp
type B = Wrap<RegExp>;
We can use a conditional type to implement an assignability check:
type IsAssignableTo<A, B> = A extends B ? true : false;
// Type `123` is assignable to type `number`
// %inferredtype: true
type Result1 = IsAssignableTo<123, number>;
// Type `number` is not assignable to type `123`
// %inferredtype: false
type Result2 = IsAssignableTo<number, 123>;
For more information on the type relationship assignability, see the blog post “What is a type in TypeScript? Two perspectives”.
Conditional types are distributive: Applying a conditional type C
to a union type U
is the same as the union of applying C
to each component of U
. This is an example:
type Wrap<T> = T extends { length: number } ? [T] : T;
// %inferredtype: boolean  [string]  [number[]]
type C1 = Wrap<boolean  string  number[]>;
// Equivalent:
type C2 = Wrap<boolean>  Wrap<string>  Wrap<number[]>;
In other words, distributivity enables us to “loop” over the components of a union type.
This is another example of distributivity:
type AlwaysWrap<T> = T extends any ? [T] : [T];
// %inferredtype: ["a"]  ["d"]  [{ a: 1; } & { b: 2; }]
type Result = AlwaysWrap<'a'  ({ a: 1 } & { b: 2 })  'd'>;
never
to ignore things Interpreted as a set, type never
is empty. Therefore, if it appears in a union type, it is ignored:
// %inferredtype: "a"  "b"
type Result = 'a'  'b'  never;
That means we can use never
to ignore components of a union type:
type DropNumbers<T> = T extends number ? never : T;
// %inferredtype: "a"  "b"
type Result1 = DropNumbers<1  'a'  2  'b'>;
This is what happens if we swap the type expressions of the thenbranch and the elsebranch:
type KeepNumbers<T> = T extends number ? T : never;
// %inferredtype: 1  2
type Result2 = KeepNumbers<1  'a'  2  'b'>;
Exclude<T, U>
Excluding types from a union is such a common operation that TypeScript provides the builtin utility type Exclude<T, U>
:
/**
* Exclude from T those types that are assignable to U
*/
type Exclude<T, U> = T extends U ? never : T;
// %inferredtype: "a"  "b"
type Result1 = Exclude<1  'a'  2  'b', number>;
// %inferredtype: "a"  2
type Result2 = Exclude<1  'a'  2  'b', 1  'b'  'c'>;
Extract<T, U>
The inverse of Exclude<T, U>
is Extract<T, U>
:
/**
* Extract from T those types that are assignable to U
*/
type Extract<T, U> = T extends U ? T : never;
// %inferredtype: 1  2
type Result1 = Extract<1  'a'  2  'b', number>;
// %inferredtype: 1  "b"
type Result2 = Extract<1  'a'  2  'b', 1  'b'  'c'>;
Similarly to JavaScript’s ternary operator, we can also chain TypeScript’s conditional type operator:
type LiteralTypeName<T> =
T extends undefined ? "undefined" :
T extends null ? "null" :
T extends boolean ? "boolean" :
T extends number ? "number" :
T extends bigint ? "bigint" :
T extends string ? "string" :
never;
// %inferredtype: "bigint"
type Result1 = LiteralTypeName<123n>;
// %inferredtype: "string"  "number"  "boolean"
type Result2 = LiteralTypeName<true  1  'a'>;
A mapped type produces an object by looping over a collection of keys – for example:
// %inferredtype: { a: number; b: number; c: number; }
type Result = {
[K in 'a'  'b'  'c']: number
};
The operator in
is a crucial part of a mapped type: It specifies where the keys for the new object literal type come from.
Pick<T, K>
The following builtin utility type lets us create a new object by specifying which properties of an existing object type we want to keep:
/**
* From T, pick a set of properties whose keys are in the union K
*/
type Pick<T, K extends keyof T> = {
[P in K]: T[P];
};
It is used as follows:
type ObjectLiteralType = {
eeny: 1,
meeny: 2,
miny: 3,
moe: 4,
};
// %inferredtype: { eeny: 1; miny: 3; }
type Result = Pick<ObjectLiteralType, 'eeny'  'miny'>;
Omit<T, K>
The following builtin utility type lets us create a new object type by specifying which properties of an existing object type we want to omit:
/**
* Construct a type with the properties of T except for those in type K.
*/
type Omit<T, K extends keyof any> = Pick<T, Exclude<keyof T, K>>;
Explanations:
K extends keyof any
means that K
must be a subtype of the type of all property keys:
// %inferredtype: string  number  symbol
type Result = keyof any;
Exclude<keyof T, K>>
means: take the keys of T
and remove all “values” mentioned in K
.
Omit<>
is used as follows:
type ObjectLiteralType = {
eeny: 1,
meeny: 2,
miny: 3,
moe: 4,
};
// %inferredtype: { meeny: 2; moe: 4; }
type Result = Omit<ObjectLiteralType, 'eeny'  'miny'>;
keyof
We have already encountered the type operator keyof
. It lists the property keys of an object type:
type Obj = {
0: 'a',
1: 'b',
prop0: 'c',
prop1: 'd',
};
// %inferredtype: 0  1  "prop0"  "prop1"
type Result = keyof Obj;
Applying keyof
to a tuple type has a result that may be somewhat unexpected:
// number  "0"  "1"  "2"  "length"  "pop"  "push"  ···
type Result = keyof ['a', 'b', 'c'];
The result includes:
"0"  "1"  "2"
number
of index property keys.length
Array
methods: "pop"  "push"  ···
The property keys of an empty object literal type are the empty set never
:
// %inferredtype: never
type Result = keyof {};
This is how keyof
handles intersection types and union types:
type A = { a: number, shared: string };
type B = { b: number, shared: string };
// %inferredtype: "a"  "b"  "shared"
type Result1 = keyof (A & B);
// %inferredtype: "shared"
type Result2 = keyof (A  B);
This makes sense if we remember that A & B
has the properties of both type A
and type B
. A
and B
only have property .shared
in common, which explains Result2
.
T[K]
The indexed access operator T[K]
returns the types of all properties of T
whose keys are assignable to type K
. T[K]
is also called a lookup type.
These are examples of the operator being used:
type Obj = {
0: 'a',
1: 'b',
prop0: 'c',
prop1: 'd',
};
// %inferredtype: "a"  "b"
type Result1 = Obj[0  1];
// %inferredtype: "c"  "d"
type Result2 = Obj['prop0'  'prop1'];
// %inferredtype: "a"  "b"  "c"  "d"
type Result3 = Obj[keyof Obj];
The type in brackets must be assignable to the type of all property keys (as computed by keyof
). That’s why Obj[number]
and Obj[string]
are not allowed. However, we can use number
and string
as index types if the indexed type has an index signature (line A):
type Obj = {
[key: string]: RegExp, // (A)
};
// %inferredtype: string  number
type KeysOfObj = keyof Obj;
// %inferredtype: RegExp
type ValuesOfObj = Obj[string];
KeysOfObj
includes the type number
because number keys are a subset of string keys in JavaScript (and therefore in TypeScript).
Tuple types also support indexed access:
type Tuple = ['a', 'b', 'c', 'd'];
// %inferredtype: "a"  "b"
type Elements = Tuple[0  1];
The bracket operator is also distributive:
type MyType = { prop: 1 }  { prop: 2 }  { prop: 3 };
// %inferredtype: 1  2  3
type Result1 = MyType['prop'];
// Equivalent:
type Result2 =
 { prop: 1 }['prop']
 { prop: 2 }['prop']
 { prop: 3 }['prop']
;
typeof
The type operator typeof
converts a (JavaScript) value to its (TypeScript) type. Its operand must be an identifier or a sequence of dotseparated identifiers:
const str = 'abc';
// %inferredtype: "abc"
type Result = typeof str;
The first 'abc'
is a value, while the second "abc"
is its type, a string literal type.
This is another example of using typeof
:
const func = (x: number) => x + x;
// %inferredtype: (x: number) => number
type Result = typeof func;
Sect. “Adding a symbol to a type” in another blog post describes an interesting use case for typeof
.