TypeScript Type-Level Mathematics

A library that performs arithmetic operations purely within TypeScript's type system, with calculations happening only during type checking in the TypeScript Language Server.

Current Limitations

• Range Constraints: Limited to numbers within the range of TypeScript's tuple length limit (currently 999)
• Number Types: Does not handle negative numbers or floating-point numbers

Available Operations

• Add<X, Y>
• Subtract<X, Y>
• Multiply<X, Y>
• Divide<X, Y>
• Power<X, Y>
• Mod<X, Y>
• Factorial<X>
• Min<X, Y>
• Max<X, Y>

Available Predicates

• Equal<X, Y>
• GreaterThan<X, Y>
• GreaterThanOrEqual<X, Y>
• LessThan<X, Y>
• LessThanOrEqual<X, Y>
• Zero<X>
• Even<X>
• Odd<X>
• InRange<X, RangeStart, RangeEnd>

Examples

Here's what the TypeScript compiler infers for our examples:

/**
 * OPERATIONS
 */

// Addition
type _4Plus4 = Add<Num<4>, Num<4>>; // 8
type _999Plus999 = Add<Num<999>, Num<999>>; // 1998
type _0Plus0 = Add<Num<0>, Num<0>>; // 0

// Subtraction
type _4Minus4 = Subtract<Num<4>, Num<4>>; // 0
type _8Minus3 = Subtract<Num<8>, Num<3>>; // 5

// Multiplication
type _4Times4 = Multiply<Num<4>, Num<4>>; // 16
type _5Times0 = Multiply<Num<5>, Num<0>>; // 0
type _99Times101 = Multiply<Num<99>, Num<101>>; // 9999

// Division
type _3Over0 = Divide<Num<3>, Num<0>>; // never
type _4Over4 = Divide<Num<4>, Num<4>>; // 1
type _9Over4 = Divide<Num<9>, Num<4>>; // 2
type _0Over4 = Divide<Num<0>, Num<4>>; // 0

// Power
type _0ToThe0th = Power<Num<0>, Num<0>>; // never
type _0ToThe5th = Power<Num<0>, Num<5>>; // 0
type _6ToThe0th = Power<Num<6>, Num<0>>; // 1
type _3ToThe4th = Power<Num<3>, Num<4>>; // 81

// Mod
type _1Mod0 = Mod<Num<1>, Num<0>>; // never
type _10Mod3 = Mod<Num<10>, Num<3>>; // 1
type _21Mod7 = Mod<Num<21>, Num<7>>; // 0

// Factorial
type _0Factorial = Factorial<Num<0>>; // 1
type _1Factorial = Factorial<Num<1>>; // 1
type _5Factorial = Factorial<Num<5>>; // 120

// Min
type _MinOf2And3 = Min<Num<2>, Num<3>>; // 2
type _MinOf4And3 = Min<Num<4>, Num<3>>; // 3

// Max
type _MaxOf2And3 = Max<Num<2>, Num<3>>; // 3
type _MaxOf4And3 = Max<Num<4>, Num<3>>; // 4

/**
 * PREDICATES
 */

// Equal
type _4Equals4 = Equal<Num<4>, Num<4>>; // true
type _4Equals5 = Equal<Num<4>, Num<5>>; // false

// GreaterThan
type _5GreaterThan3 = GreaterThan<Num<5>, Num<3>>; // true
type _3GreaterThan5 = GreaterThan<Num<3>, Num<5>>; // false
type _5GreaterThan5 = GreaterThan<Num<5>, Num<5>>; // false

// GreaterThanOrEqual
type _5GEQ3 = GreaterThanOrEqual<Num<5>, Num<3>>; // true
type _5GEQ5 = GreaterThanOrEqual<Num<5>, Num<5>>; // true
type _3GEQ5 = GreaterThanOrEqual<Num<3>, Num<5>>; // false

// LessThan
type _3LessThan5 = LessThan<Num<3>, Num<5>>; // true
type _5LessThan3 = LessThan<Num<5>, Num<3>>; // false
type _5LessThan5 = LessThan<Num<5>, Num<5>>; // false

// LessThanOrEqual
type _3LEQ5 = LessThanOrEqual<Num<3>, Num<5>>; // true
type _5LEQ5 = LessThanOrEqual<Num<5>, Num<5>>; // true
type _7LEQ5 = LessThanOrEqual<Num<7>, Num<5>>; // false

// Zero
type _0Zero = Zero<Num<0>>; // true
type _5Zero = Zero<Num<5>>; // false

// Even
type _0Even = Even<Num<0>>; // true
type _2Even = Even<Num<2>>; // true
type _3Even = Even<Num<3>>; // false

// Odd
type _3Odd = Odd<Num<3>>; // true
type _4Odd = Odd<Num<4>>; // false

// InRange
type _5InRange3to10 = InRange<Num<5>, Num<3>, Num<10>>; // true
type _5InRange5to10 = InRange<Num<5>, Num<5>, Num<10>>; // true
type _5InRange0to5 = InRange<Num<5>, Num<0>, Num<5>>; // true
type _5InRange10to20 = InRange<Num<5>, Num<10>, Num<20>>; // false