[phizy]

>Not all aspects of programming can be described by math.

This is completely untrue. You may not be familiar with the math, but that doesn't mean it doesn't exist. If you can model something well enough to understand it, then you can model it mathematically. There really isn't any domain of knowledge that math is unsuitable for, excepting if you don't know any relevant math to do.

[nendroid]

Technically everything in the universe can be modelled by math. If it isn't modelled yet we can make something up to model it. Math is just axioms and theorems so yeah, you're not wrong.

I'm speaking in less technical terms. For example in general mathematical equations or axioms represent immutable concepts. In programming, variables mutate and change... very different from what math traditionally represents. Haskell is an attempt to segregate the immutability (the math part) away from the less "mathy" part (the mutations/IO).

Maybe math is too broad of a term. I probably meant to say "algebra" can't model all of programming, or whatever more suitable word that may or may not exist.

[phizy]

Mathematicians have no trouble modeling change. There are many ways to do so. Some are algebraic, some are not. There is nothing wrong with modelling mutability using immutable structures: that is how you probably think about history, after all.

Either way, it is unclear what you're actually trying to say. Haskell has methods for modelling change of state through pure objects, but you're talking about that as though it were an inherently flawed or invalid approach, rather than one of many equally valid approaches to modelling state transformations.