Bagl checks every matrix operation at compile time, and its compiler writes derivatives for you. It is written in OCaml, and it also runs in the browser.
// Gradient descent on XOR, in your browser.
// The compiler writes the gradient of the loss,
// and it checks the shape of every step.
// The exact solution is [1, 1, -2].
let x = [[0.0, 0.0, 0.0],
[0.0, 1.0, 0.0],
[1.0, 0.0, 0.0],
[1.0, 1.0, 1.0]] in
let y = [0.0, 1.0, 1.0, 0.0] in
let dloss = grad (fn w: tensor<float>[3] ->
let e = dot(x, w) - y in
dot(e, e)) in
letrec train = fn n ->
if n < 0.5 then [0.0, 0.0, 0.0] else
let w = train (n - 1.0) in
w - 0.1 * dloss w
in train 200.0Output: = [0.999987, 0.999987, -1.99996] : tensor<float>[3]
RunThe size of each dimension is part of a tensor's type, so a product of a 2x3 and a 2x2 matrix doesn't compile.
let a = [[1.0, 2.0, 3.0],
[4.0, 5.0, 6.0]] in
let b = [[1.0, 2.0],
[3.0, 4.0]] in
dot(a, b)Output: error: Dimension mismatch: 3 vs 2
Rungrad turns a function into its derivative. Over tensors it uses reverse mode, which gives every partial derivative in one pass.
let x = [[1.0, 2.0], [3.0, 4.0]] in
let y = [1.0, 2.0] in
grad (fn w: tensor<float>[2] ->
let e = dot(x, w) - y in
dot(e, e)) [0.0, 0.0]Output: = [-14, -20] : tensor<float>[2]
RunHindley-Milner inference, as in ML and OCaml, finds every type. You annotate only to fix a tensor's rank or to ask for floats.
let id = fn x -> x in
if id true then id 1 else id 2Output: = 1 : int
Run$ git clone https://github.com/aibrahm/bagl $ cd bagl && dune build && dune install $ baglc examples/train_xor.bagl