Kind2

Kind2 is a functional programming language and proof assistant.

It is a complete rewrite of Kind1, based on HVM, a lazy, non-garbage-collected and massively parallel virtual machine. In our benchmarks, its type-checker outperforms every alternative proof assistant by a far margin, and its programs can offer exponential speedups over Haskell's GHC. Kind2 unleashes the inherent parallelism of the Lambda Calculus to become the ultimate programming language of the next century.

Welcome to the inevitable parallel, functional future of computers!

Examples

Pure functions are defined via equations, as in Haskell:

// Applies a function to every element of a list
map <a> <b> (list: List a) (f: a -> b) : List b
map a b Nil              f = Nil
map a b (Cons head tail) f = Cons (f x) (map tail f)

Side-effective programs are written via monadic monads, resembling Rust and TypeScript:

// Prints the double of every number up to a limit
Main : IO (Result () String) {
  ask limit = IO.prompt "Enter limit:"
  for x in (List.range limit) {
    IO.print "{} * 2 = {}" x (Nat.double x)
  }
  return Ok ()
}

Theorems can be proved inductivelly, as in Agda and Idris:

// Black Friday Theorem. Proof that, for every Nat n: n * 2 / 2 == n.
black_friday_theorem (n: Nat) : Equal Nat (Nat.half (Nat.double n)) n
black_friday_theorem Nat.zero     = Equal.refl
black_friday_theorem (Nat.succ n) = Equal.apply (x => Nat.succ x) (black_friday_theorem n)

For more examples, check the Wikind.

Usage

First, install Rust first, then enter:

cargo install kind2

Then, use any of the commands below:

Command	Usage	Note
Check	kind2 check file.kind2	Checks all definitions.
Eval	kind2 eval file.kind2	Runs using the type-checker's evaluator.
Run	kind2 run file.kind2	Runs using HVM's evaluator, on Rust-mode.
To-HVM	kind2 to-hvm file.kind2	Generates a .hvm file. Can then be compiled to C.
To-KDL	kind2 to-kdl file.kind2	Generates a .kdl file. Can then be deployed to Kindelia.

Executables can be generated via HVM:

kind2 to-hvm file.kind2
hvm compile file.hvm
clang -O2 file.c -o file
./file