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

Vanessa McHale vanessa.mchale at iohk.io
Mon Jul 16 12:13:51 UTC 2018


On 07/16/2018 02:56 AM, PY wrote:
> 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
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