Recently, after reading two different articles online, I've had the idea seeing what I could build if I used just the TypeScript type system as my programming language. No Javascript allowed! Since the type system is Turing Complete it means we should be able to program anything we'd like in it.
About a year ago I read a lovely little book called The Little Schemer. One of the goals of the book is to teach the reader to think recursively and one of the earlier exercises in the book is about building recursive functions that do addition and subtraction. You are given two functions add1(x) and sub1(x) that, respectively, add and subtract 1 from a single arguement. Using these functions you can then build add(x, y) and subtract(x, y).
If you squint you can see how the TypeScript type system looks an awful lot like the functional programming parts of JavaScript which in turn look a lot like Scheme. After figuring out how to create AddOne and SubtractOne in the type system it was possible to implement Add and Subtract from The Little Schemer.
| Concept | JavaScript | TypeScript type system |
|---|---|---|
| Named Values | const result = [primative] |
type Result = [primative] |
| Functions | const func = (a, b) => a |
type Func<A, B> = A |
| Equality | a === b |
A extends B |
| Conditional Branching | a === b ? a : b |
A extends B ? A : B |
| Recursion | const func = (a, b) => func(a, b) |
type Func<A, B> = Func<B, A> |