[Haskell-cafe] Explaining monads

Paul Hudak paul.hudak at yale.edu
Wed Aug 15 13:26:07 EDT 2007

I've seen the analogy with "recipes" used before, but I think that you 
need to be careful when you try to distinguish the analogy to monads 
from the analogy to functions.  The reason is that, in the one-of-many 
ways that I view monads, a monad is just a high-order /function /that 
abstracts away function composition.  In particular, if I have an action 
f, and an action g, I can think of them as recipes, because I can 
combine them via f >>= g.  It's only after I combine all of my actions 
together that I apply the result to my input (via "run").

Well, that's just like function composition.  In particular, if I have a 
function f, and a function g, I can think of them as recipes, because I 
can combine them via f . g.  It's only after I combine all of my 
functions together that I apply the result to my input.


Sebastian Sylvan wrote:
> On 14/08/07, Dan Piponi <dpiponi at gmail.com> wrote:
>> On 8/14/07, Sebastian Sylvan <sebastian.sylvan at gmail.com> wrote:
>>> Well that's easy, don't use the recipe analogy to explain code, use it
>>> for monadic values exclusively, and you avoid the confusion entirely!
>>> I don't think it's that complicated.
>> It certainly is complicated. I think I have a good grasp of monads to
>> the point where I can tease novel monads (and comonads) out from
>> algorithms that people previously didn't see as monadic. And yet I
>> still don't understand what you are saying (except with respect to one
>> specific monad, IO, where I can interpret 'action' as meaning an I/O
>> operation).
>>> Monads have a monadic type. They
>>> represent an abstract form of an "action", which can be viewed as an
>>> analogy to real-world cooking recipes.
>> All functions can be viewed as recipes. (+) is a recipe. Give me some
>> ingredients (two numbers) and I'll use (+) to give you back their sum.
> No, (+) is a function, not a "recipe". Again, you're introducing
> confusion because you use the same analogy for two *different* things.
> Use it for one of the things and you don't have that problem.
> I want to use "recipe" to mean "an abstraction for an action". It
> could litterally be a text string containing the C code required to do
> a particular IO action, for example. (+) isn't an abstraction in the
> same sense, it *is* the "action" itself. (+) is the actual value of
> the function that will add two numbers together. A monadic value is an
> abstract recipe that you can't actually use directly (you can only
> combine them, and if you're lucky you can "perform" them once you're
> done combining them, e.g. ST, but not IO).
>>> As long as you don't
>>> deliberately confuse things by using the same analogy for two
>>> different things I don't see where confusion would set in.
>> If I was one of your students and you said that monads are recipes I
>> would immediately ask you where the monads are in my factorial program
>> regardless of whether you had introduced one or two different
>> analogies for recipes.
> Why would you? I really don't see where you would get that idea? If I
> tell you that a function returns "a fruit", would you ask where the
> fruit in your factorial program is? Probably not. Why would you go off
> and take an analogy for monads and apply it to something completely
> different and still think the analogy holds?
> A function is *not* a recipe in this analogy, it's just a function
> (which you hopefully should've covered by the time you get to monads.
> Monadic values, and *only* monadic values (not functions!) are to be
> viewed as analogous to real world cooking recipes in this analogy.
> Functions shouldn't. If you start mixing things together it will get
> confused, so just don't!
> I don't think this is very difficult to understand, so if you still
> don't get it, I think you're just going to have to read it again
> because I can't explain it any better, and in my experience, newbies
> tend to understand this analogy within seconds (maybe that's the
> problem, you're not a newbie)...
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