What a Monad is not | Hacker News Reader

What a Monad is not

haskell.org

49 pointsfogus24 comments

Also, a Monad is not a "thing", it's a property of a thing. "Monad" is a typeclass, not a type.

What follows is that Monads are not containers; you don't store a value in your Monad, you store it in your List. The List just happens to be a monad. (Similarly, you can't store a ball inside your "Red", but you can store it in a "Red Box". The fact that the box is red has nothing to do with its ability to be a container. If you paint a piece of paper red, it does not suddenly become a container.)

(Side note: it happens that Monads are Functors, and Functors are logically containers... but remember, the Monad or Functor instance is not what makes something a container; something is a container because of its underlying type. "Monad" is a property possessed by certain containers, just as "Red" is a property possessed by certain other containers. Oh, and please don't make me insert a joke about Red/Black trees here...)

Put simply; Monad = adjective, not Monad = noun. It took me like two years to come to terms with this, but now that I have, Haskell is one of the easiest-to-use programming languages I know.

"Also, a Monad is not a 'thing', it's a property of a thing. "Monad" is a typeclass, not a type. What follows is that Monads are not containers;"

Thanks for this observation, however you (in your comment) and everyone else uses the word "monad" as a noun. Hence much confusion.

"The List just happens to be a monad. "

Why not say "The List just happens to be monadic", rather than saying it is a monad?

Thanks for this observation, however you (in your comment) and everyone else uses the word "monad" as a noun. Hence much confusion.

I agree with you here 100%. I was confused for years for this exact reason.

I tried avoiding the noun form for a while, but the problem is that while it's technically correct, nobody "in the know" quite understands what you are talking about. "Why didn't he just call it a Monad?"

Why not say "The List just happens to be monadic", rather than saying it is a monad?

I should have.

Doesn't predication usually work this way? "Socrates is a mortal" makes just as much sense as "Socrates is mortal". The former is extensional, the latter intensional.

I haven't worked much with Haskell, but at first blush, monads to me seem almost like a perverse functional converse to Greenspun's 10th Law. Haskell is purely functional, which imposes programing constraints, but of course it's turing-complete so it can still do anything a procedural language can. In the limit case, it can use denotational semantics to describe an emulation of a state-based program. And that's what a monad is (or at least, that's what they look like to me): a DSL for denotational semantics.

Altogether, that's probably for the better. If people are going to use denotational semantics to emulate a state-capabale environment, it's better if the method for doing so is standardized, well-specified, and optimized.

If people are going to use denotational semantics to emulate a state-capabale environment, it's better if the method for doing so is standardized, well-specified, and optimized.

I am not following you here. State is nothing special, except that it is something made special by most popular programming languages. (Where it causes lots of fun problems.)

I am also not sure that "Monads" are optimized any more than any other function application. Monadic state-passing is syntax sugar more than anything else. (With other languages, state is "something else"; lexical environments, dynamic environments, and so on.)

It's not about state, it's about denotational semantics. A pure functional language can use denotational semantics to embed non-pure languages/programs/concepts, because the denotational semantics of non-pure concepts are still pure. State is the most common example of a non-pure concept that many programmers miss in Haskell, but it's not the only one. So it's not a question of state being useful or awesome or even a good idea, but rather a question of how Monads are how Haskell escapes its own constraints to express 'foreign' ideas.

My point was that, in practice, if pure functional langues ruled the world and did not include built-in Monads, many applications would re-invent them anyways because of their expressivity, in much the same way that C applications are said to re-invent LISP.

State is nothing special, except that it is something made special by most popular programming languages. (Where it causes lots of fun problems.)

With very elementary design decisions, mutable state is very much manageable in the most popular languages.

Hiding state maintenance through a monad solves very little, while throwing performance out of the window. Yeah, you can get performance out of a lazy functional language, but the hoops you have to jump through are not worth it.

Ocaml is eager functional, and IMHO is a very nice compromise between expressibility and purity. Now if only its type system was as capable as haskell, and only if it had multi processor support :(

"Now if only its type system was as capable as haskell"

One of the reasons is precisely the "impurity" of the language. I am referring to the value restriction, which inserts `'_a` (which means "because of possible side effects, this value won't have a polymorphic type, sorry") sometimes when you do partial applications (even ones without any side effect). It bit me once when I tried to do FRP (Yampa-style) in Ocaml. I couldn't define some of the operators (time) in a modular way (in terms of integral) without losing polymorphism.

Another reason has to do with the fact that Ocaml is strict. I tried to define a mini "batteries" module with purely functional lazy lists instead of destructive streams (the enumeration). There is simply no way to define map or filter in terms of fold without losing laziness, or seriously polluting the type of fold, map, and filter. This can still be regarded as a type system issue : if strict and lazy types were compatible, as they are in Haskell, it wouldn't have been such a problem.

Monads handle much more than state -- they're an elegant alternative to exception handling, IO, and anything sequential. There's no performance penalty involved in using a monad, and very little penalty for using lazy evaluation. I've written Haskell code which is on even ground performance-wise with C, and no hoops were involved.

Monads are also not a feature of Haskell -- they can be used in any language which supports closures. I've used them in Python to great effect, though the lack of syntax support is annoying.

The problem with Haskell monad tutorials is that they focus on one thing that monads can do--in your case state. Monads can do more than that, though; nondeterministic computation comes to mind, as does simple error handling through the Maybe monad, and you can do continuations through a monad. It's a very abstract concept, and because of that people have a lot of trouble with it.

Monads can do more than that, though; nondeterministic computation comes to mind, as does simple error handling through the Maybe monad, and you can do continuations through a monad.

Please correct me if I am wrong, but all the examples you cite are about hiding mutable state using monads.

1. Non deterministic computation -> remembering last value of m and n. I assume you are talikng pseudo random generators here.

2. error handling with Maybe -> remembering last value or Nothing. Almost like passing along a single error code variable.

3. continuations -> Remember what state your computation variable and PC were last at.

If I am seeing this wrong, then I will be happy to take a second look at monads :)

It is about state not necessarily mutable state. Monads are rather abstract and not really worth all the attention they get. A monad is simply: a type constructor, a function that puts a value into the type constructor, and a function that pulls the value from the type constructor and pass it on to the next function(often referred to as return and bind respectively). Then depending on how you define the type constructor and functions to push and pull you get different Monads. Monads are no different than Objects or design patterns, they are a code organization technique that happens to fit functional programming well.

There's no "remembering" the last value or Nothing; it immediately short-circuits, and not because Haskell is lazy, but because that's how monads are defined.

If you don't understand why "monads are programmable semi-colons", take that second look. See also the list monad; the key is not the "storing in a list" but the way it does "nondeterministic computations".

That is how maybe is defined not all monads.

No, I'm talking about the definition of Monad themselves. They don't work the way most people think they do, especially most of the critics. Monads have that function application step, and at every point that function can be applied one, zero, or many times. There is no "remembering" of a Nothing; the Monad definition is such that it calls the next application function zero times and immediately returns Nothing, which short-circuits the remainder of the monadic computation. That is, it doesn't "keep running" anyhow the way you might expect an imperative language would (or might, anyhow).

This is why I also point out the list monad; fully understanding that is necessary to be sure you understand monads. I have seen numerous "monad" implementations in $YOUR_FAVORITE_LANGUAGE that can't do the list monad correctly because they can do 0 and 1 applications of a function, but can't correctly do arbitrarily many, because the people implementing the Monad interface didn't actually understand the interface. (In fact when I see such an implementation the first thing I look for now is the list monad, and so far of the four or five I've seen only one has gotten it right.)

They're no more about hiding mutable state than imperative languages are about hiding the purely-functional representation of state transfer semantics :)

All you've done is listed alternative ways of implementing things, which is obviously possible in a range of paradigms (albeit with semantics that are usually harder to reason about in an imperative setting).

Well, it runs on a CPU with mutable state. So you could claim that everything is all about mutation of state. But that's not a very useful position to take, because reasoning about, reading and writing code at that low level is too concrete.

When I say nondeterministic computation I do not mean PRNGs. I mean "give me all possible solutions to the N-queens problem". I mean "solve this sudoku puzzle with no explicit loop". Constraint solvers. Some classes of search algorithm. Proof systems. That kind of nondeterministic computation.

You'll probably respond claiming all this is state. Sure, fine, whatever makes you happy. Everything in programming is state. Everything is also lambda calls. Everything is Horn clauses. You can think about these in some very low level dungeon but that doesn't mean you ought to.

That's a pretty good way of thinking about it (if still a bit state-ist), but the reality in Haskell is not quite optimal. Since Monads aren't really built-in, there's no semantics-checking -- the compiler can't confirm that your 'monads' actually follow the Monad Laws.

If you can confirm that your monads follow the Monad Laws, you've solved the halting problem.

That's demonstrably false (Coq will do this for you handily), but furthermore you're missing the point entirely!

Any worthwhile type-checking algorithm (like Haskell's) would have to Scoop the Loop Snooper to accept every valid formula and deny all invalid or undecidable ones. Of course they don't actually do that, instead accepting incompleteness -- that there will be valid code that they reject.

I agree, but that's not too practical. I mean, give me a system that will show [] to satisfy monad laws. You won't, because the definition of >>= for [] involves concat and map... both functions are recursive, and you know your system is going to reject that because it's not part of your strongly normalizing language, consequently rejecting [] as a monad.

Yes, it will work if you redefine the list constructors as functions...

  (:) x xs = \f z -> f x (xs f z)
  []       = \f z -> z

... and then we can define fold in a non-recursive way... but can this work in Haskell?

Seriously, no. You are wrong. By a large margin. Monad laws are fairly straight forward.

While I grant that the ML family of languages implements some truly brilliant ideas, ...

... blog posts like this remind me why I love Tcl/Tk and shell scripting.

It is embarrassing, but I always prefer the raccoon to the panda bear.

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