Printing a list of items to the console is inherently imperative. On top of that,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.
<! language lang-ml -->
let rate = 0.2
let threshold = 2.0
let inline output a b weightA weightB = if threshold > a * weightA + b * weightB then 0.0 else 1.0
let inline display output real = printfn <| 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 > 0 then
loop n 0 weightA weightB
and loop n i weightA weightB =
if i < 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:
<! language lang-ml -->
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.