[Haskell-cafe] Monads because of I/O?

[PY]

Hello, Olaf! It's very good point. I'll read more about it. May be I'm 
wrong, but I don't remember any monads in CT, so my suggestion was that 
they were introduced in pure functional languages research (Hope, 
Haskell), not math itself. May be I'm not right. Thanks a lot!


15.07.2018 23:06, Olaf Klinke wrote:
> Paul,
>
> monads were not invented because I/O could not be presented in another 
> way in Haskell. Monads are way older than Haskell. It is a concept of 
> category theory which was developed in the 1950s. Actually some 
> concepts of algebra that are even older turn out to be monads. Take 
> Galois theory for example. Once you know the pattern, you find a monad 
> under every stone you turn around. It's one of the luckiest things 
> that people like Moggi and Wadler realized that monads can be applied 
> to structure programs. And don't blame them that monads are not 
> composable - it is simply a mathematical fact. Some monads do compose 
> with any other monad, and those are the monad transformers.
>
> If you like Prolog's relational programming model so much, then you 
> should play with those programs that have "no business value". Because 
> Haskell's type inference algorithm, together with multi-parameter type 
> classes and maybe type level natural numbers together give rise to 
> Prolog-like capabilities. All the work is done by the compiler this way.
>
> What you say about FSM is certainly true to some extent - they are 
> well understood, can be generated automatically, and there is decent 
> theory to reason about them. That is why this model is used in 
> safety-sensitive environments such as aviation. I once applied for a 
> position in verification in the automotive industry, and the interview 
> partner told me that they struggle mightily with the vast state spaces 
> of the FSMs they are checking.
> All this speaks in favour of Haskell. The semantics is simple and 
> beautiful, because it is a single-paradigm language. And because of 
> that, clever people can leverage theorem provers to mathematically 
> prove correctness of Haskell code. I don't know of many languages 
> where that is possible. (But then, I'm not an expert on verification.)
>
> Olaf