"Introduction to Caml" says
Note, in Caml it is better to use Curried function definitions for multiple-argument functions, not tuples.
when comparing 'a -> 'b -> 'c calling conventions to 'a * 'b -> 'c.
When working with SML/NJ I got used to using tuple types for both input and output : ('a * 'b) -> ('c * 'd) so using tuples to express multiple inputs seems symmetric with the way I express multiple outputs.
Why is currying recommended for OCaml function declarations over tuple arguments? Is it just the greater flexibility that comes with allowing currying/partial evaluation, or is there some other benefit that derives from implementation details of the OCaml compiler?
I think a lot of it is convention -- standard library functions in OCaml are curried, whereas in Standard ML they are generally not except for some higher-order functions. However, there is one difference baked into the language: the operators (e.g. (*)) are curried in OCaml (e.g. int -> int -> int); whereas they are uncurried in Standard ML (e.g. op* can be (int * int) -> int). Because of that, built-in higher-order functions (e.g. fold) also take a function that is curried in OCaml and uncurried in Standard ML; that means for your function to work with that, you need to follow the respective convention, and it follows from there.
Yes, it is mainly the notational convenience and the flexibility to do partial application. Curried functions are idiomatic in OCaml, and the compiler is likely to optimise them somewhat better than tupled functions (whereas SML compilers typically optimise for tuples).
The pros of tupling are the argument/result symmetry you mention (which is especially useful when composing functions) and perhaps the notational familiarity (at least for people coming from the non-functional world).
Some comment about the optimisation in OCaml.
In OCaml, i noticed that tuples are always allocated when passing them as argument. Even if allocating in the primary heap is fast in ocaml, it is of course longer than doing nothing. Thus each time you pass a tuple as argument, there is some time spent to the allocation and filling of the tuple.
I expected that the ocaml compiler would be optimizing cases where it isn't needed to build the tuple. For instance, when you inline the called function, you may only use the tuple components and not the tuple itself. Thus the tuple could just be ignored. Unfortunately in this case OCaml doesn't remove the useless tuple and still perform the allocation. For this reason, it may not be a good idea to use tuples in critical sections of code.
Related
I'm pretty new to OCaml (currently taking awful classes at uni) and we recently studied recursive types. We were told that we use that to create lists but there already are lists in OCaml so I don't really understand when I should be using one over the other.
example :
(* list made with a recursive type : *)
type int_list =
| None
| Element of int * int_list
(* just a list *)
let int_list2 : int list = []
What's the difference between a recursive type and a list?
"Recursive type" describes a whole category of types whereas list is one specific recursive type. In other words: list is a recursive type, but there are recursive types other than list.
there already are lists in OCaml so I don't really understand when I should be using one over the other.
When you should use int_list over the built-in list type? Never. Your teacher showed you this definition as an example of what recursive types look like, not as something you should actually use.
You would define your own recursive types only when defining something that doesn't already exist in the standard library (except for learning exercises of course).
I was desperately looking for the last hour for a method in the OCaml Library which converts an 'a to a string:
'a -> string
Is there something in the library which I just haven't found? Or do I have to do it different (writing everything by my own)?
It is not possible to write a printing function show of type 'a -> string in OCaml.
Indeed, types are erased after compilation in OCaml. (They are in fact erased after the typechecking which is one of the early phase of the compilation pipeline).
Consequently, a function of type 'a -> _ can either:
ignore its argument:
let f _ = "<something>"
peek at the memory representation of a value
let f x = if Obj.is_block x then "<block>" else "<immediate>"
Even peeking at the memory representation of a value has limited utility since many different types will share the same memory representation.
If you want to print a type, you need to create a printer for this type. You can either do this by hand using the Fmt library (or the Format module in the standard library)
type tree = Leaf of int | Node of { left:tree; right: tree }
let pp ppf tree = match tree with
| Leaf d -> Fmt.fp ppf "Leaf %d" d
| Node n -> Fmt.fp ppf "Node { left:%a; right:%a}" pp n.left pp n.right
or by using a ppx (a small preprocessing extension for OCaml) like https://github.com/ocaml-ppx/ppx_deriving.
type tree = Leaf of int | Node of { left:tree; right: tree } [##deriving show]
If you just want a quick hacky solution, you can use dump from theBatteries library. It doesn't work for all cases, but it does work for primitives, lists, etc. It accesses the underlying raw memory representation, hence is able to overcome (to some extent) the difficulties mentioned in the other answers.
You can use it like this (after installing it via opam install batteries):
# #require "batteries";;
# Batteries.dump 1;;
- : string = "1"
# Batteries.dump 1.2;;
- : string = "1.2"
# Batteries.dump [1;2;3];;
- : string = "[1; 2; 3]"
If you want a more "proper" solution, use ppx_deriving as recommended by #octachron. It is much more reliable/maintainable/customizable.
What you are looking for is a meaningful function of type 'a. 'a -> string, with parametric polymorphism (i.e. a single function that can operate the same for all possible types 'a, even those that didn’t exist when the function was created). This is not possible in OCaml. Here are explications depending on your programming background.
Coming from Haskell
If you were expecting such a function because you are familiar with the Haskell function show, then notice that its type is actually show :: Show a => a -> String. It uses an instance of the typeclass Show a, which is implicitly inserted by the compiler at call sites. This is not parametric polymorphism, this is ad-hoc polymorphism (show is overloaded, if you want). There is no such feature in OCaml (yet? there are projects for the future of the language, look for “modular implicits” or “modular explicits”).
Coming from OOP
If you were expecting such a function because you are familiar with OO languages in which every value is an object with a method toString, then this is not the case of OCaml. OCaml does not use the object model pervasively, and run-time representation of OCaml values retains no (or very few) notion of type. I refer you to #octachron’s answer.
Again, toString in OOP is not parametric polymorphism but overloading: there is not a single method toString which is defined for all possible types. Instead there are multiple — possibly very different — implementations of a method of the same name. In some OO languages, programmers try to follow the discipline of implementing a method by that name for every class they define, but it is only a coding practice. One could very well create objects that do not have such a method.
[ Actually, the notions involved in both worlds are pretty similar: Haskell requires an instance of a typeclass Show a providing a function show; OOP requires an object of a class Stringifiable (for instance) providing a method toString. Or, of course, an instance/object of a descendent typeclass/class. ]
Another possibility is to use https://github.com/ocaml-ppx/ppx_deriving with will create the function of Path.To.My.Super.Type.t -> string you can then use with your value. However you still need to track the path of the type by hand but it is better than nothing.
Another project provide feature similar to Batterie https://github.com/reasonml/reason-native/blob/master/src/console/README.md (I haven't tested Batterie so can't give opinion) They have the same limitation: they introspect the runtime encoding so can't get something really useable. I think it was done with windows/browser in mind so if cross plat is required I will test this one before (unless batterie is already pulled). and even if the code source is in reason you can use with same API in OCaml.
I have read some of this post Meaning of Alternative (it's long)
What lead me to that post was learning about Alternative in general. The post gives a good answer to why it is implemented the way it is for List.
My question is:
Why is Alternative implemented for List at all?
Is there perhaps an algorithm that uses Alternative and a List might be passed to it so define it to hold generality?
I thought because Alternative by default defines some and many, that may be part of it but What are some and many useful for contains the comment:
To clarify, the definitions of some and many for the most basic types such as [] and Maybe just loop. So although the definition of some and many for them is valid, it has no meaning.
In the "What are some and many useful for" link above, Will gives an answer to the OP that may contain the answer to my question, but at this point in my Haskelling, the forest is a bit thick to see the trees.
Thanks
There's something of a convention in the Haskell library ecology that if a thing can be an instance of a class, then it should be an instance of the class. I suspect the honest answer to "why is [] an Alternative?" is "because it can be".
...okay, but why does that convention exist? The short answer there is that instances are sort of the one part of Haskell that succumbs only to whole-program analysis. They are global, and if there are two parts of the program that both try to make a particular class/type pairing, that conflict prevents the program from working right. To deal with that, there's a rule of thumb that any instance you write should live in the same module either as the class it's associated with or as the type it's associated with.
Since instances are expected to live in specific modules, it's polite to define those instances whenever you can -- since it's not really reasonable for another library to try to fix up the fact that you haven't provided the instance.
Alternative is useful when viewing [] as the nondeterminism-monad. In that case, <|> represents a choice between two programs and empty represents "no valid choice". This is the same interpretation as for e.g. parsers.
some and many does indeed not make sense for lists, since they try iterating through all possible lists of elements from the given options greedily, starting from the infinite list of just the first option. The list monad isn't lazy enough to do even that, since it might always need to abort if it was given an empty list. There is however one case when both terminates: When given an empty list.
Prelude Control.Applicative> many []
[[]]
Prelude Control.Applicative> some []
[]
If some and many were defined as lazy (in the regex sense), meaning they prefer short lists, you would get out results, but not very useful, since it starts by generating all the infinite number of lists with just the first option:
Prelude Control.Applicative> some' v = liftA2 (:) v (many' v); many' v = pure [] <|> some' v
Prelude Control.Applicative> take 100 . show $ (some' [1,2])
"[[1],[1,1],[1,1,1],[1,1,1,1],[1,1,1,1,1],[1,1,1,1,1,1],[1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1],[1,1,1,1,1,"
Edit: I believe the some and many functions corresponds to a star-semiring while <|> and empty corresponds to plus and zero in a semiring. So mathematically (I think), it would make sense to split those operations out into a separate typeclass, but it would also be kind of silly, since they can be implemented in terms of the other operators in Alternative.
Consider a function like this:
fallback :: Alternative f => a -> (a -> f b) -> (a -> f e) -> f (Either e b)
fallback x f g = (Right <$> f x) <|> (Left <$> g x)
Not spectacularly meaningful, but you can imagine it being used in, say, a parser: try one thing, falling back to another if that doesn't work.
Does this function have a meaning when f ~ []? Sure, why not. If you think of a list's "effects" as being a search through some space, this function seems to represent some kind of biased choice, where you prefer the first option to the second, and while you're willing to try either, you also tag which way you went.
Could a function like this be part of some algorithm which is polymorphic in the Alternative it computes in? Again I don't see why not. It doesn't seem unreasonable for [] to have an Alternative instance, since there is an implementation that satisfies the Alternative laws.
As to the answer linked to by Will Ness that you pointed out: it covers that some and many don't "just loop" for lists. They loop for non-empty lists. For empty lists, they immediately return a value. How useful is this? Probably not very, I must admit. But that functionality comes along with (<|>) and empty, which can be useful.
In chapter 2 of "A gentle introduction to Haskell", user-defined types are explained and then the notion that built-in types are, apart from a special syntax, no more different than user-defined ones:
Earlier we introduced several "built-in" types such as lists, tuples, integers, and characters. We have also shown how new user-defined types can be defined. Aside from special syntax, are the built-in types in any way more special than the user-defined ones? The answer is no. (The special syntax is for convenience and for consistency with historical convention, but has no semantic consequences.)
So you could define a tuple like to the following:
data (a,b) = (a,b)
data (a,b,c) = (a,b,c)
data (a,b,c,d) = (a,b,c,d)
Which sure you cannot because that would require an infinite number of declarations. So how are these types actually implemented? Especially regarding the fact that only against a type declaration you can pattern-match?
Since GHC is open source, we can just look at it:
The tuples are a lot less magical than you think:
From https://github.com/ghc/ghc/blob/master/libraries/ghc-prim/GHC/Tuple.hs
data (a,b) = (a,b)
data (a,b,c) = (a,b,c)
data (a,b,c,d) = (a,b,c,d)
data (a,b,c,d,e) = (a,b,c,d,e)
data (a,b,c,d,e,f) = (a,b,c,d,e,f)
data (a,b,c,d,e,f,g) = (a,b,c,d,e,f,g)
-- and so on...
So, tuples with different arities are just different data types, and tuples with very big number of arities is not supported.
Lists are also around there:
From https://github.com/ghc/ghc/blob/master/libraries/ghc-prim/GHC/Types.hs#L101
data [] a = [] | a : [a]
But there is a little bit of magic (special syntax) for lists.
Note: I know that GitHub is not where GHC is developed, but searching "ghc source code" on Google did not yield the correct page, and GitHub was the easiest.
You defined three tuple types there, not one hence your argument with the infinite number of declarations doesn't cut. A standard confoming Haskell needs to support only a finite number of tuple types. Hence finitely many declarations.
In fact, you can define:
data Pair a b = Pair a b
and this is isomorphic to an ordinary 2-tuple.
I'm not sure I even know how to ask this question .. In implementing a compiler I would like to allow the client to specify, say, folds on tuples. I have provided a way to curry and uncurry a function, but only because I wrote a binary operator in Ocaml and folded it over the term and type representations. The user could not write this function.
In the macro processor, the user can write this function because tuples are lists.
For curried functions, the user can easily write transformers, because the term is binary in both the target language and the Ocaml representation of the term and the typing.
But they can't do this for tuples. Here's another example: the user easily defines serial functional composition operator. But the user cannot define parallel composition: the binary version:
f1: D1 -> C1, f2: D2-> C2 --> f1 * f2: D1 * D2 -> C1 * C2
is easily written, but cannot be extended to 3 terms: here a fold would compute
f1 * (f2 * f3)
instead of
f1 * f2 * f3
[isomorphic but not equal]
The generalisation of this question is "How do I implement a polyadic programming language" which is a bit too much to ask here. What I tried to do was provide a builtin transformer:
curry: T1 * T2 * T3 ... --> T1 -> T2 -> ...
uncurry: T1 -> T2 -> .. T1 * T2 * T3
so then the user could just do folds with a binary operator:
uncurry (fold user_op (uncurry term))
but this is neither general enough nor works so well.. :)
I guess an equivalent question for Haskell would be: since Haskell has no n-ary products, the n-ary tuple constructors is simulated in the library with n functions, where each one has to be written out by hand. This clearly sucks. How would this be fixed?
[I mean, it is trivial to write a Python script to generate those n functions up to some limit n, so why is it so hard to do this in a well typed way inside the language?]
There are two components that collaborate to cause this issue:
Tuples are not auto-flattened - the parentheses in type expressions do more than group, they create distinct types that are joined by further tuples. This leads to your observation that a * (b * c) is isomorphic but not equivalent to a * b * c.
The type system does not provide a means to express algebra on tuple types. By this I mean that the type system does not have a cons operator or any equivalent for tuples; there is no way to express that a type has more or fewer tupled elements than another type.
The result is that there is no way to express the type of a function that operates on tuples of arbitrary length.
So, the short summary is that the OCaml type system lacks mechanisms to express the type of the function you are trying to write, and therefore you cannot write the function (setting aside nasty games with Obj; you could write the function, but you could not express its type to use it in a type-safe fashion).
There are basically two options.
You can make your language untyped or weakly typed. In C for example, tuples (of integers, say) can be represented as int*. Something would need to keep track of the tuples' lengths but the type system won't. I assume you do not want to go that way.
For a type-safe language, you need a very expressive type system. Namely, you need types that depend on values. The members of which are functions that return types. For example the tuple type constructor (not to be confused with the tuple constructor) could have type tuple : int -> Type -> Type.
An operation that extends a tuple could have type forall n:int. forall T:Type. tuple n T -> T -> tuple (n+1) T. Such type systems come at a cost: Typically, type inference is not recursive and type checking is only decidable if you are willing to annotate all kinds of subexpressions with their type (The annotations in the forall parts above are only a hint of what that would entail.).
This options seems to be overkill if all you want to achieve is polyadicity, though.
Disclaimer: My knowledge on type theory is a bit dated.