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.

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 head) (Map tail f)

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

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

For more examples, check the Kindex.

First, install Rust first, then enter:

cargo +nightly install kind2

Then, use any of the commands below:

The rust crate can be generated via HVM:

kind2 to-hvm file.kind2 > file.hvm
hvm compile file.hvm

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