Basic neural network
Printing a list of items to the console is inherently imperative. But keeping track of lots of state between iterations using higher-order functions is often inelegant. Regardless, there are some things you can do to clean this up and (if you're compelled) get rid of mutables. Most notably, you can use tuples instead of arrays/lists with an assumed width.

I'm not familiar with this algorithm, so I've merely translated what you have. You can implement it using a pair of mutually recursive functions. This allows you to "persist" the weight values between iterations.



let rate = 0.2
let threshold = 2.0

let inline output a b weightA weightB = if threshold &gt; a * weightA + b * weightB then 0.0 else 1.0
let inline display output real = printfn &lt;| if output = real then "yes" else "no"
let inline computeWeight weight c out = weight + rate * (c - out)

let matrix = 
  [|
    0.0, 0.0, 0.0
    0.0, 1.0, 1.0
    1.0, 0.0, 1.0
    1.0, 1.0, 1.0
  |]

let rec iter n weightA weightB = 
  if n &gt; 0 then
    loop n 0 weightA weightB
and loop n i weightA weightB =
  if i &lt; matrix.Length then
    let a, b, c = matrix.[i]
    let out = output a b weightA weightB
    let weightA = computeWeight weightA c out
    display out c
    let out = output a b weightA weightB
    let weightB = computeWeight weightB c out
    display out c
    loop n (i + 1) weightA weightB
  else iter (n - 1) weightA weightB


Usage:



let initialWeightA = 0.4
let initialWeightB = 0.6
iter 100 initialWeightA initialWeightB


loop could be implemented as a fold, but fold is not typically used with side-effects.