[Haskell-beginners] Question about example in 'using do notation with Writer' section of LYH

[Olumide]

On 27/01/2017 08:34, Theodore Lief Gannon wrote:
> Fully expanding your program might help. One of the great things about
> Haskell is equational reasoning: if two things have been declared equal,
> you can substitute one for the other.
>
> First, let's desugar that do notation to the equivalent bind chain:
>
>     multWithLog =
>       logNumber 3 >>= \a ->
>         logNumber 5 >>= \b ->
>           return (a*b)
>
>
> Evaluate the logNumber and return calls to normal form from their
> definitions, also considering the monoid definitions of (++) and mempty
> for lists:
>
>     multWithLog =
>       Writer (3, ["Got number: 3"]) >>= \a ->
>         Writer (5, ["Got number: 5"]) >>= \b ->
>           Writer (a*b, [])
>
>
> Now, refer to the definition of (>>=) for Writer (as shown in LYAH):
>
>     (Writer (x, v)) >>= f = let (Writer (y, v')) = f x in Writer (y, v
>     `mappend` v')
>

Thank you for your explanation. The substitutions helped a lot even 
though I wasn't able to follow the equational reasoning. The expansion 
gave me enough starting information to figure out what's going on by 
starting from the innermost bind.

BTW, I thought the definition of (>>=) was supposed to come from 
Control.Monad.Writer.

Regards,

- Olumide