In OCaml, is there a way to refer to the cons operator by itself?
For example, I can use (+) and ( * ) as int -> int -> int functions, but I cannot use (::) as a 'a -> 'a list -> 'a list function, as the following example show:
# (+) 3 5;;
- : int = 8
# ( * ) 4 6;;
- : int = 24
# (::) 1 [2;3;4];;
Error: Syntax error: operator expected.
Is there a way to produce a result like (::) other than with fun x y -> x::y? And does anyone know why (::) wasn't implemented in OCaml?
Adding to the answer of #seanmcl,
Actually OCaml supports a prefix form of (::):
# (::)(1, []);;
- : int list = [1]
This is in the uncurried form, corresponding with the fact that all the OCaml variant constructors are not curried and cannot be partially applied. This is handled by a special parsing rule just for (::), which is why you got a rather strange error message Error: Syntax error: operator expected..
Update:
Upcoming OCaml 4.02 removes this parsing rule, therefore this is no longer available.
No. Cons (::) is a constructor, constructors can not be infix operators. The allowed infix symbols are here:
http://caml.inria.fr/pub/docs/manual-caml-light/node4.9.html
Some workarounds are (as you mention) the verbose
(fun x l -> x :: l)
and defining your own nontraditional infix cons
let (+:) x l = x :: l
As of Ocaml 4.03, you can now use cons (in the List module). That is, cons x xs is the same as x :: xs.
It's also possible to just define your own cons function:
let cons = fun a list -> a :: list
Related
I meet an error about subtyping.
For this code, List.map (fun ((String goal_feat):> Basic.t) -> goal_feat) (goal_feats_json:> Basic.t list).
I meet the following error in vscode:
This expression cannot be coerced to type
Yojson.Basic.t =
[ Assoc of (string * Yojson.Basic.t) list
| Bool of bool
| Float of float
| Int of int
| List of Yojson.Basic.t list
| Null
| String of string ];
it has type [< String of 'a ] -> 'b but is here used with type
[< Yojson.Basic.t ].
While compiling, I meet the following error.
Error: Syntax error: ')' expected.
If I change the code to List.map (fun ((String goal_feat): Basic.t) -> goal_feat) (goal_feats_json:> Basic.t list), which useq explicit type cast instead of subtyping, then the error disappeared. I can not understand what is the problem with my code when i use subtyping. Much appreciation to anyone who could give me some help.
First of all, most likely the answer that you're looking for is
let to_strings xs =
List.map (function `String x -> x | _ -> assert false) (xs :> t list)
The compiler is telling you that your function is handling only one case and you're passing it a list that may contain many other things, so there is a possibility for runtime error. So it is better to indicate to the compiler that you know that only the variants tagged with String are expected. This is what we did in the example above. Now our function has type [> Yojson.Basic.t].
Now back to your direct question. The syntax for coercion is (expr : typeexpr), however in the fun ((String goal_feat):> Basic.t) -> goal_feat snippet, String goal_feat is a pattern, and you cannot coerce a pattern, so we shall use parenthesized pattern here it to give it the right, more general, type1, e.g.,
let exp xs =
List.map (fun (`String x : t) -> x ) (xs :> t list)
This will tell the compiler that the parameter of your function shall belong to a wider type and immediately turn the error into warning 8,
Warning 8: this pattern-matching is not exhaustive.
Here is an example of a case that is not matched:
(`Bool _|`Null|`Assoc _|`List _|`Float _|`Int _)
which says what I was saying in the first part of the post. It is usually a bad idea to leave warning 8 unattended, so I would suggest you to use the first solution, or, otherwise, find a way to prove to the compiler that your list doesn't have any other variants, e.g., you can use List.filter_map for that:
let collect_strings : t list -> [`String of string] list = fun xs ->
List.filter_map (function
| `String s -> Some (`String s)
| _ -> None) xs
And a more natural solution would be to return untagged strings (unless you really need the to be tagged, e.g., when you need to pass this list to a function that is polymorphic over [> t] (Besides, I am using t for Yojson.Basic.t to make the post shorter, but you should use the right name in your code). So here is the solution that will extract strings and make everyone happy (it will throw away values with other tags),
let collect_strings : t list -> string list = fun xs ->
List.filter_map (function
| `String s -> Some s
| _ -> None) xs
Note, that there is no need for type annotations here, and we can easily remove them to get the most general polymoprhic type:
let collect_strings xs =
List.filter_map (function
| `String s -> Some s
| _ -> None) xs
It will get the type
[> `String a] list -> 'a list
which means, a list of polymorphic variants with any tags, returning a list of objects that were tagged with the String tag.
1)It is not a limitation that coercion doesn't work on patterns, moreover it wouldn't make any sense to coerce a pattern. The coercion takes an expression with an existing type and upcasts (weakens) it to a supertype. A function parameter is not an expression, so there is nothing here to coerce. You can just annotate it with the type, e.g., fun (x : #t) -> x will say that our function expects values of type [< t] which is less general than the unannotated type 'a. To summarize, coercion is needed when you have a function that accepts an value that have a object or polymorphic variant type, and in you would like at some expressions to use it with a weakened (upcasted type) for example
type a = [`A]
type b = [`B]
type t = [a | b]
let f : t -> unit = fun _ -> ()
let example : a -> unit = fun x -> f (x :> t)
Here we have type t with two subtypes a and b. Our function f is accepting the base type t, but example is specific to a. In order to be able to use f on an object of type a we need an explicit type coercion to weaken (we lose the type information here) its type to t. Notice that, we do not change the type of x per se, so the following example still type checks:
let rec example : a -> unit = fun x -> f (x :> t); example x
I.e., we weakened the type of the argument to f but the variable x is still having the stronger type a, so we can still use it as a value of type a.
If I want a function that subtracts an int argument from the number 2, I can do
let two_minus = (-) 2
But what if I want a function that subtracts 2 from an int argument?
In Haskell, I can do
let minus2 = flip (-) 2
But in Ocaml 4.02, flip is not part of the standard library.
For now, I've settled on
let minus2 = (+) ~-2
which adds negative 2 to an int argument. I find it looks cleaner than
let minus2 = fun x -> x-2
... or at least it takes less characters.
Is there a better, more idiomatic way?
In Haskell, you can do what you want with operator sections, which is much cleaner than flip imo:
Prelude> :t (2 -)
(2 -) :: Num a => a -> a
Prelude> :t ((-) 2)
((-) 2) :: Num a => a -> a
OCaml does not support this nicety (afaik). However, if you like flip, it is trivial to define your own:
let flip f x y = f y x;;
Or you can use a standard library that has it defined already, like Core and Batteries. E.g.,
# open Core
utop # Fn.flip;;
- : ('a -> 'b -> 'c) -> 'b -> 'a -> 'c = <fun>
fwiw, in the absence of operator sections, I find fun x -> x-2 much clearer than either of the two alternatives you propose. It may not look as nice, but it is immediately clear what it means.
Favoring clear and very explicit expressions over clever and concise ones is very idiomatic OCaml.
OCaml is a programming language. You are free to define whatever you feel convenient:
let flip f x y = f y x
List.map is of type
- : ('a -> 'b) -> 'a list -> 'b list = <fun>
It's easy for me to understand the following code:
List.map (fun x -> x+1) [1;2;3;4];;
which adds 1 to each element of the list so it returns the following list :
- : int list = [2;3;4;5]
Now this is in an exercise where I'm asked to indicate the type of this :
List.map (fun p -> p 7) [ (fun n m -> n + m) ];;
I don't understand at all what it means to be honest.
What does p 7 mean ?
Why is there a function in the list ?
The type is
- : (int -> int) list = [<fun>]
But I can't understand why.
What does it mean when fun is between brackets ?
Thank you.
What does p 7 mean?
It means the application of function p to argument 7 .... You might spend some time reading the wikipage on λ-calculus (at least to learn about functional abstraction)
Read also about currying.
Why is there a function in the list ?
In Ocaml, functions are values, so you can have list of functions. If it was not a list of functions, you'll get a typing error. If you think more, you can understand what kind of functions are allowed.
What does it mean when fun is between brackets ?
The toplevel is not able to print functional values (implemented as closures). It shows them as <fun>. For a simpler example, pass fun x -> x+1;; (then try also fun y -> y;;) to your REPL.
(the rest of the exercise is left to the reader)
when trying to write a simple program for solving a toy SAT problem, I came across the following problem I cannot get my head around.
I have a type variable which is defined as follows:
type prefix =
| Not
| None
type variable =
| Fixed of (prefix * bool)
| Free of (prefix * string)
from which I can build a clause of type variable list and a formula of type clause list. Essentially this boils down to having a formula in
either CNF or DNF (this has less to do with the problem).
When now trying to simplify a clause I do the following:
Filter all Fixed variables from the clause which gives a list
Simplify the variables (Fixed(Not, true) => Fixed(None, false))
Now I have a list containing just Fixed variables which I now want to combine to a single Fixed value by doing something like this
let combine l =
match l with
| [] -> []
| [x] -> [x]
| (* Get the first two variables, OR/AND them
and recurse on the rest of the list *)
How would I achieve my desired behavior in a functional language? My experience in OCaml is not that big, I am rather a beginner.
I tried doing x::xs::rest -> x <||> xs <||> combine rest but this does not work. Where <||> is just a custom operator to OR the variables.
Thanks for your help.
How about using the neat higher order functions already there?
let combine = function
| x::xs -> List.fold_left (<||>) x xs
| [] -> failwith "darn, what do I do if the list is empty?"
For clarification:
List.fold_left : ('a -> 'b -> 'a) -> 'a -> 'b list -> 'a
takes a function that gets the running aggregate and the next element of the list; it returns the new aggregate; then we need an initial value and the list of items to fold over.
The use of your infix operator <||> in brackets makes it a prefix function so we can give it to List.fold_left just like that -- instead of writing (fun a b -> a <||> b).
If you have a neutral element of your <||> operator, lets call it one, we could write it even more concise:
let combine = List.fold_left (<||>) one
As List.fold_left requires three arguments and we only gave it two, combine here is a function of variable list -> variable as the previous one. If you wonder why this works, check out the concept of currying.
Here's my attempt:
let rec combine l =
match l with
| [] -> []
| [x] -> [x]
| a :: b :: rest -> combine ((a <||> b) :: rest)
Note you need let rec.
I'm trying to implement flatten : 'a list list -> 'a list list in SML.
I thought this should be relatively straight forward with higher order functions. My implementation is
val flatten = List.reduce (op #) []
However I'm getting a bizarre error message: "append.sml:1.6-1.36 Warning: type vars not generalized because of
value restriction are instantiated to dummy types (X1,X2,...)". Thus when I try to flatten an int list list I get a type error:
:> flatten [[1,2],[3]];
stdIn:2.1-2.20 Error: operator and operand don't agree [literal]
operator domain: ?.X1 list list
operand: int list list
in expression:
flatten ((1 :: 2 :: nil) :: (3 :: nil) :: nil)
As the error message hints, you ran into the value restriction -- see here for an explanation. The solution is very simple: just "eta-expand" your definition, i.e., make the parameter explicit instead of relying on partial application:
fun flatten xs = List.reduce op# [] xs