[Haskell-cafe] Join and it's relation to >>= and return

Benjamin Franksen benjamin.franksen at bessy.de
Thu Jun 10 09:01:43 EDT 2004

On Wednesday 09 June 2004 17:20, Ron de Bruijn wrote:
> --- "Iavor S. Diatchki" <diatchki at cse.ogi.edu> wrote:
> Only I still find it weird that join is called a
> multiplication, because according to the definition of
> multiplication, there should be an inverse. I think,
> thus that multiplication is only defined on a group.
> And now still remains: why do they call it a
> multiplication, while by definition it's not. Or
> should I understand it as: there's a concept called
> multiplication and for different structures there's a
> definition? I think, now I think over it, that it
> would seem logical.
> It could be possible that the definition is incorrect,
> though. Does anyone knows of a definition that is more
> general (and not absolute nonsens ;))?

The term "multiplication" as it stands (i.e. without context) is not a 
defined mathematical concept. I.e. there is no (generally accepted) 

Of course multiplication of numbers, vectors, matrices, functions etc... 
are all well defined. Multiplication isn't even constrained to the 
operation on a semi-group as the example of multiplication of scalars 
to vectors shows.

You probably would not use the term "multiplication" for anything that 
is not at least a function f: A, B -> C where A, B, and C are sets (or 
at least classes). If A=B, then you would probably assume 
associativity, though there migth be "counter-examples" even for this 


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