I want to create a struct which is based on another struct whose implementation can be switched.
signature Field =
sig
type field_type;
val zero : field_type;
val add : (field_type * field_type) -> field_type;
val f : int -> field_type;
end;
structure Reals :> Field =
struct
type field_type = real;
val zero = 0.0;
fun add (x,y) = x + y;
fun f x = Real.fromInt(x);
end;
structure Rat :> Field =
struct
type field_type = int * int;
val zero = (0, 1);
fun add ((i1,i2),(j1,j2)) = (i1*j2 + j1*i2, i2*j2);
fun f x = (x, 1);
end;
functor Useable(F : Field) =
struct
type field_type = F.field_type;
val zero = F.zero;
fun add(x,y) = F.add(x,y);
fun f x = F.f x;
end;
structure ReF = Useable(Reals);
structure RaF = Useable(Rat);
The idea is that I could plug in implementations of Field (Reals or Rat, ignore the inefficient implementations).
I can run this code ReF.add(ReF.zero, ReF,zero), but can't run ReF.add(0.0, 0.0) (or RaF.add((0,1),(0,1)))
To overcome this I created a constructor f: int -> field_types, but I found this to be not so elegant and also cumbersome. Can I do anything for being able to use ReF.add(0.0, 0.0)?
The simple answer is to use a transparent signature constraint
structure Reals : Field
rather than an opaque constraint.
structure Reals :> Field
When you use an opaque constraint types such as field_type in the signature are created as new types distinct from the types that are used to implement them. If you want to retain the link to the original type you need to use a transparent constraint. With a transparent constraint Reals.field_type and real are the same type so you can use
ReF.add(0.0, 0.0);
perfectly well.
> ReF.add(0.0, 0.0);
val it = 0.0: real
As an alternative to using a transparent constraint, if you have other types in your signature that you want to be created as new types, you can still get the desired effect by using an opaque constraint along with where type.
structure Reals :> Field where type field_type = real
Related
I have a struct Context that as a type takes an association list from string to a custom type process.
I'm trying to pattern match to see if my struct is empty (this seems to work fine) however checking whether my struct contains elements is giving me the following error.
File "src/main.ml", line 131, characters 13-30:
131 | | Context.((ext_ref,prc)::tl) ->
^^^^^^^^^^^^^^^^^
Error: This pattern matches values of type 'a list
but a pattern was expected which matches values of type t
Here is the code that won't compile:
(* Finds a recv corresponding to a send stmt *)
let rec find_recv (ctx: Context.t) (external_ref:variable) =
match ctx with
| Context.(empty) -> None
| Context.((ext_ref,prc)::tl) ->
begin
match prc with
| Prc(_, _,Recv(_,_,chn,_)) -> if chn = external_ref then Some prc else find_recv tl external_ref
|_ -> find_recv tl external_ref
end
Here is the signature for the 'Context' struct.
module type Context = sig
type t
val empty : t
val lookup : t -> string -> process
val extend : t->string ->process -> t
val filter : t->string ->t
end
Here is the instantiation of my Context module:
(** Instantiating a Process Table *)
module Context : Context = struct
type t = (string * process) list
let empty = []
let lookup (ctx:t) (x:string): process=
let chck = List.assoc_opt x ctx in match chck with
|Some i -> i
|None -> Null("")
let extend (ctx:t) (x:string) (ty:process) =
(x, ty) :: ctx
let filter ctx x =
List.remove_assoc x ctx
end
I got this code from the Real World Ocaml book.
Given the constraints of your Context signature, type t within the Context module is abstract.
Within the module, your functions know that empty is a list. However, outside of it, empty is merely of abstract type Context.t.
Let's look at a simpler example:
utop # module type S =
sig
type t
val empty : t
end
module M : S =
struct
type t = int list
let empty = []
end;;
module type S = sig type t val empty : t end
module M : S
utop # M.empty;;
- : M.t = <abstr>
utop # match M.empty with [] -> "hello" | _ -> "world";;
Error: This pattern matches values of type 'a list
but a pattern was expected which matches values of type M.t
M.t is abstract. We know it exists, but not how it is implemented. This abstraction is frequently useful in designing applications.
It is possible to break this abstraction. Whether it's a good idea is a matter of opinion and outside of Stack Overflow's scope.
utop # module M2 : S with type t = int list =
struct
type t = int list
let empty = []
end;;
module M2 : sig type t = int list val empty : t end
utop # match M2.empty with [] -> "hello" | _ -> "world";;
- : string = "hello"
As kindly pointed out by #glennsl and as is explained better than I can in this thread Unbound constructor error when using module signature
My problem can be solved by including the find_recv function within the Modules signature as below.
module type Context = sig
type t
val empty : t
val lookup : t -> string -> process
val extend : t->string ->process -> t
val filter : t->string ->t
val find_recv: t -> variable -> process option
end
Obviously this must then be instantiated before use.
So I have a record type with mutable field:
type mpoint = { mutable x:int ; mutable y: int };;
let apoint = { x=3 ; y=4};;
And I have a function that expects a 'ref' and does something to its contents.
For example:
let increment x = x := !x+1;;
val increment : int ref -> unit = <fun>
Is there a way to get a 'reference' from a mutable field so that I can pass it to the function. I.e. I want to do something like:
increment apoint.x;; (* increment value of the x field 'in place' *)
Error: This expression has type int but an expression was expected of type
int ref
But the above doesn't work because apoint.x returns the value of the field not its 'ref'. If this was golang or C++ maybe we could use the & operator to indicate we want the address instead of the value of the field: &apoint.x.
(How) can we do this in Ocaml?
PS: Yes, I know its probably more common to avoid using side-effects in this way. But I promise, I am doing this for a good reason in a context where it makes more sense than this simplified/contrived example might suggest.
There's no way to do exactly what you ask for. The type of a reference is very specific:
# let x = ref 3
val x : int ref = {contents = 3}
A reference is a record with one mutable field named contents. You can't really fabricate this up from an arbitrary mutable field of some other record. Even if you are willing to lie to the type system, a field of a record is not represented at all the same as a record.
You could declare your fields as actual references:
type mpoint = { x: int ref; y: int ref; }
Then there is no problem, apoint.x really is a reference. But this representation is not as efficient, i.e., it takes more memory and there are more dereferences to access the values.
If an API is designed in an imperative style it will be difficult to use in OCaml. That's how I look at it anyway. Another way to say this is that ints are small. The interface should perhaps accept an int and return a new int, rather than accepting a reference to an int and modifying it in place.
Jeffrey Scofield explained why this can't be done in ocaml from the point of the type system.
But you can also look at it from the point of the GC (garbage collector). In ocaml internally everything is either a trivial type (int, bool, char, ...) that is stored as a 31/63 bit value or a pointer to a block of memory. Each block of memory has a header that describes the contents to the GC and has some extra bits used by GC.
When you look at a reference internally it is a pointer to the block of memory containing the record with a mutable contents. Through that pointger the GC can access the header and know the block of memory is still reachable.
But lets just assume you could pass apoint.y to a function taking a reference. Then internally the pointer would point to the middle of apoint and the GC would fail when it tries to access the header of that block because it has no idea at what offset to the pointer the header is located.
Now how to work around this?
One way that was already mentioned is to use references instead of mutable. Another way would be to use a getter and setter:
# type 'a mut = (unit -> 'a) * ('a -> unit);;
type 'a mut = (unit -> 'a) * ('a -> unit)
# type mpoint = { mutable x:int ; mutable y: int };;
type mpoint = { mutable x : int; mutable y : int; }
# let mut_x p = (fun () -> p.x), (fun x -> p.x <- x);;
val mut_x : mpoint -> (unit -> int) * (int -> unit) = <fun>
# let mut_y p = (fun () -> p.y), (fun y -> p.y <- y);;
val mut_y : mpoint -> (unit -> int) * (int -> unit) = <fun>
If you only want to incr the variable you can pass an incrementer function instead of getter/setter. Or any other collection of helper functions. A getter/setter pait is just the most generic interface.
You can always copy temporarily the content of field, call the function on that, and back again:
let increment_point_x apoint =
let x = ref apoint.x in
increment x;
apoint.x <- !x
Certainly not as efficient (nor elegant) as it could, but it works.
It is impossible to do exactly what the question asks for (#JeffreyScofield explains why, so I won't repeat that). Some workarounds have been suggested.
Here is another workaround that might work if you can change the implementation of the increment function to use a 'home made' ref type. This comes very close to what was asked for.
Instead of having it take a 'built-in' reference, we can define our own type of reference. The spirit of a 'reference' is something you can set and get. So we can characterise/represent it as a combination of a get and set function.
type 'a ref = {
set: 'a -> unit;
get: unit -> 'a;
};;
type 'a ref = { set : 'a -> unit; get : unit -> 'a; }
We can define the usual ! and := operators on this type:
let (!) cell = cell.get ();;
val ( ! ) : 'a ref -> 'a = <fun>
let (:=) cell = cell.set;;
val ( := ) : 'a ref -> 'a -> unit = <fun>
The increment function's code can remain the same even its type 'looks' the same (but it is subtly 'different' as it is now using our own kind of ref instead of built-in ref).
let increment cell = cell := !cell + 1;;
val increment : int ref -> unit = <fun>
When we want a reference to a field we can now make one. For example a function to make a reference to x:
let xref pt = {
set = (fun v -> pt.x <- v);
get = (fun () -> pt.x);
};;
val xref : mpoint -> int ref = <fun>
And now we can call increment on the x field:
increment (xref apoint);;
- : unit = ()
See code example below. It won't compile. I had thought that maybe it's because it has to have a single type for the first parameter in the test function. But that doesn't make sense because if I don't pattern match on it so it will compile, I can call it with both MyObj11 5 and MyObj21 5 which are two different types.
So what is it that restricts so you can't pattern match on constructors with a type class constrained parameter? Or is there some mechanism by which you can?
class SomeClass a where toString :: a -> String
instance SomeClass MyType1 where toString v = "MyType1"
instance SomeClass MyType2 where toString v = "MyType2"
data MyType1 = MyObj11 Int | MyObj12 Int Int
data MyType2 = MyObj21 Int | MyObj22 Int Int
test :: SomeClass a => a -> String
test (MyObj11 x) = "11"
test (MyObj12 x y) = "12" -- Error here if remove 3rd line: rigid type bound error
test (MyObj22 x y) = "22" -- Error here about not match MyType1.
what is it that restricts so you can't pattern match on constructors with a type class constrained parameter?
When you pattern match on an explicit constructor, you commit to a specific data type representation. This data type is not shared among all instances of the class, and so it is simply not possible to write a function that works for all instances in this way.
Instead, you need to associate the different behaviors your want with each instance, like so:
class C a where
toString :: a -> String
draw :: a -> String
instance C MyType1 where
toString v = "MyType1"
draw (MyObj11 x) = "11"
draw (MyObj12 x y) = "12"
instance C MyType2 where
toString v = "MyType2"
draw (MyObj22 x y) = "22"
data MyType1 = MyObj11 Int | MyObj12 Int Int
data MyType2 = MyObj21 Int | MyObj22 Int Int
test :: C a => a -> String
test x = draw x
The branches of your original test function are now distributed amongst the instances.
Some alternative tricks involve using class-associated data types (where you prove to the compiler that a data type is shared amongst all instances), or view patterns (which let you generalize pattern matching).
View patterns
We can use view patterns to clean up the connection between pattern matching and type class instances, a little, allowing us to approximate pattern matching across instances by pattern matching on a shared type.
Here's an example, where we write one function, with two cases, that lets us pattern match against anything in the class.
{-# LANGUAGE ViewPatterns #-}
class C a where
view :: a -> View
data View = One Int
| Two Int Int
data MyType1 = MyObj11 Int | MyObj12 Int Int
instance C MyType1 where
view (MyObj11 n) = One n
view (MyObj12 n m) = Two n m
data MyType2 = MyObj21 Int | MyObj22 Int Int
instance C MyType2 where
view (MyObj21 n) = One n
view (MyObj22 n m) = Two n m
test :: C a => a -> String
test (view -> One n) = "One " ++ show n
test (view -> Two n m) = "Two " ++ show n ++ show m
Note how the -> syntax lets us call back to the right view function in each instance, looking up a custom data type encoding per-type, in order to pattern match on it.
The design challenge is to come up with a view type that captures all the behavior variants you're interested in.
In your original question, you wanted every constructor to have a different behavior, so there's actually no reason to use a view type (dispatching directly to that behavior in each instance already works well enough).
Many functional programming languages have support for curried parameters.
To support currying functions the parameters to the function are essentially a tuple where the last parameter can be omitted making a new function requiring a smaller tuple.
I'm thinking of designing a language that always uses records (aka named parameters) for function parameters.
Thus simple math functions in my make believe language would be:
add { left : num, right : num } = ...
minus { left : num, right : num } = ..
You can pass in any record to those functions so long as they have those two named parameters (they can have more just "left" and "right").
If they have only one of the named parameter it creates a new function:
minus5 :: { left : num } -> num
minus5 = minus { right : 5 }
I borrow some of haskell's notation for above.
Has any one seen a language that does this?
OCaml has named parameters and currying is automatic (though sometimes type annotation is required when dealing with optional parameters), but they are not tupled :
Objective Caml version 3.11.2
# let f ~x ~y = x + y;;
val f : x:int -> y:int -> int = <fun>
# f ~y:5;;
- : x:int -> int = <fun>
# let g = f ~y:5;;
val g : x:int -> int = <fun>
# g ~x:3;;
- : int = 8
Sure, Mathematica can do that sort of thing.
The comments on Steve Yegge's post about server-side Javascript started discussing the merits of type systems in languages and this comment describes:
... examples from H-M style systems where you can get things like:
expected signature Int*Int->Int but got Int*Int->Int
Can you give an example of a function definition (or two?) and a function call that would produce that error? That looks like it might be quite hard to debug in a large-ish program.
Also, might I have seen a similar error in Miranda? (I have not used it in 15 years and so my memory of it is vague)
I'd take Yegge's (and Ola Bini's) opinions on static typing with a grain of salt. If you appreciate what static typing gives you, you'll learn how the type system of the programming language you choose works.
IIRC, ML uses the '*' syntax for tuples. <type> * <type> is a tuple type with two elements. So, (1, 2) would have int * int type.
Both Haskell and ML use -> for functions. In ML, int * int -> int would be the type of a function that takes a tuple of int and int and maps it to an int.
One of the reasons you might see an error that looks vaguely like the one Ola quoted when coming to ML from a different language, is if you try and pass arguments using parentheses and commas, like one would in C or Pascal, to a function that takes two parameters.
The trouble is, functional languages generally model functions of more than one parameter as functions returning functions; all functions only take a single argument. If the function should take two arguments, it instead takes an argument and returns a function of a single argument, which returns the final result, and so on. To make all this legible, function application is done simply by conjunction (i.e. placing the expressions beside one another).
So, a simple function in ML (note: I'm using F# as my ML) might look a bit like:
let f x y = x + y;;
It has type:
val f : int -> int -> int
(A function taking an integer and returning a function which itself takes an integer and returns an integer.)
However, if you naively call it with a tuple:
f(1, 2)
... you'll get an error, because you passed an int*int to something expecting an int.
I expect that this is the "problem" Ola was trying to cast aspersions at. I don't think the problem is as bad as he thinks, though; certainly, it's far worse in C++ templates.
It's possible that this was in reference to a badly-written compiler which failed to insert parentheses to disambiguate error messages. Specifically, the function expected a tuple of int and returned an int, but you passed a tuple of int and a function from int to int. More concretely (in ML):
fun f g = g (1, 2);
f (42, fn x => x * 2)
This will produce a type error similar to the following:
Expected type int * int -> int, got type int * (int -> int)
If the parentheses are omitted, this error can be annoyingly ambiguous.
It's worth noting that this problem is far from being specific to Hindley-Milner. In fact, I can't think of any weird type errors which are specific to H-M. At least, none like the example given. I suspect that Ola was just blowing smoke.
Since many functional language allow you to rebind type names in the same way you can rebind variables, it's actually quite easy to end up with an error like this, especially if you use somewhat generic names for your types (e.g., t) in different modules. Here's a simple example in OCaml:
# let f x = x + 1;;
val f : int -> int = <fun>
# type int = Foo of string;;
type int = Foo of string
# f (Foo "hello");;
This expression has type int but is here used with type int
What I've done here is rebind the type identifier int to a new type that is incompatible with the built-in int type. With a little bit more effort, we can get more-or-less the same error as above:
# let f g x y = g(x,y) + x + y;;
val f : (int * int -> int) -> int -> int -> int = <fun>
# type int = Foo of int;;
type int = Foo of int
# let h (Foo a, Foo b) = (Foo a);;
val h : int * int -> int = <fun>
# f h;;
This expression has type int * int -> int but is here used with type
int * int -> int