So I want to define a typeclass that looks like
class action =
fixes name :: "'a => 'b"
and params :: "'a => 'p"
This is so that I can create instantiations of datatypes that look like, for example
datatype ('b, 'c, 'd) actionT1 = Act 'b 'c 'd
where I would have
name (Act n c d) = n
params (Act n c d) = (c,d)
So in this case, the type 'p in the class would correspond to 'c \times 'd and 'b in the class would correspond to 'b in the example action.
Now I can use the functions name and params inside various functions, for example:
fun equalParams :: "'a :: action => 'a => bool" where
"equalParams a b = (params a = params b)"
Unfortunately, I can't actually achieve this because Isabelle seems to only accept one arbitrary datatype. Furthermore, if I try to do the following:
instantiation (string, int, int) actionT1 :: action
begin
.
.
.
end
I get an error saying that Isabelle expected a type constructor, but ( was found.
How can I achieve this functionality in Isabelle?
Unless you want to work with type, you can also work with locales. This avoids some limitations of the Isabelle class system. In your case:
text ‹Create the locale and define equalParams within the body of the locale›
locale mylocale =
fixes name :: "'a => 'b"
and params :: "'a => 'p"
begin
fun equalParams :: "'a => 'a => bool" where
"equalParams a b = (params a = params b)"
end
datatype ('b, 'c, 'd) actionT1 = Act (name: 'b) (c: 'c) (d: 'd)
abbreviation params where
‹params a ≡ (c a, d a)›
text ‹Instantiate the locale with our parameters.›
text ‹First in a named interpretation:›
interpretation action: mylocale where name = name and params = params
by unfold_locales
term action.equalParams
text ‹Second in a unnamed interpretation:›
interpretation mylocale where name = name and params = params
by unfold_locales
term equalParams
For more details on locales, refer to the documentation.
Related
F# does not (currently) support type-classes. However, F# does support the OOP aspects of C#.
I was wondering, what is lost doing this approach compared to true type-classes?
// A concrete type
type Foo =
{
Foo : int
}
// "Trait" for things that can be shown
type IShowable =
abstract member Show : unit -> string
module Showable =
let show (showable : IShowable) =
showable.Show()
// "Witness" of IShowable for Foo
module Foo =
let asShowable (foo : Foo) =
{
new IShowable with
member this.Show() = string foo.Foo
}
// Slightly awkward usage
{ Foo = 123 }
|> Foo.asShowable
|> Showable.show
|> printfn "%s"
Your suggestion works for simple typeclasses that operate on a single value of a type, like Show. However, what happens when you need a typeclass that isn't so object-oriented? For example, when we want to add two numbers, neither one corresponds to OO's this object:
// not real F#
typeclass Numeric<'a> = // e.g. Numeric<int> or Numeric<float>
abstract member (+) : 'a -> 'a -> 'a // e.g. 2 + 3 = 5 or 2.0 + 3.0 = 5.0
...
Also, keep in mind that many useful typeclasses require higher-kinded types. For example, consider the monad typeclass, which would look something like this:
// not real F#
typeclass Monad<'m<_>> = // e.g. Monad<Option<_>> or Monad<Async<_>>
abstract member Return<'a> : 'a -> 'm<'a>
abstract member Bind<'a, 'b> : 'm<'a> -> ('a -> 'm<'b>) -> 'm<'b>
There's no good way to do this with .NET interfaces.
Higher-kinded type classes are indeed impossible to model with interfaces, but that's just because F# does not support higher-kindedness, not because of type classes themselves.
The deeper thing to note is that your encoding isn't actually correct. Sure, if you just need to call show directly, you can do asShowable like that, but that's just the simplest case. Imagine you needed to pass the value to another function that wanted to show it later? And then imagine it was a list of values, not a single one:
let needsToShow (showable: IShowable) (xs: 'a list) =
xs |> List.iter (fun x -> ??? how do I show `x` ???)
No, this wouldn't do of course. The key is that Show should be a function 'a -> string, not unit -> string. And this means that IShowable itself should be generic:
// Haskell: class Showable a where show :: a -> String
type IShowable<'a> with
abstract member Show : 'a -> string
// Haskell: instance Showable Foo where show (Foo i) = show i
module Foo =
let showable = { new IShowable<Foo> with member _.Show foo = string foo.Foo }
// Haskell: needsToShow :: Show a => [a] -> IO ()
let needsToShow (showable: IShowable<'a>) (xs: 'a list) =
xs |> List.iter (fun x -> printfn "%s" (showable.Show x))
// Haskell: needsToShow [Foo 1, Foo 42]
needsToShow Foo.showable [ { Foo: 1 }; { Foo: 42 } ]
And this is, essentially, what type classes are: they're indeed merely dictionaries of functions that are passed everywhere as extra parameters. Every type has such dictionary either available right away (like Foo above) or constructable from other such dictionaries, e.g.:
type Bar<'a> = Bar of 'a
// Haskell: instance Show a => Show (Bar a) where show (Bar a) = "Bar: " <> show a
module Bar =
let showable (showA: IShowable<'a>) =
{ new IShowable<Bar<'a>> with member _.Show (Bar a) = "Bar: " + showA.Show a }
This is completely equivalent to type classes. And in fact, this is exactly how they're implemented in languages like Haskell or PureScript in the first place: like dictionaries of functions being passed as extra parameters. It's not a coincidence that constraints on function type signatures even kinda look like parameters - just with a fat arrow instead of a thin one.
The only real difference is that in F# you have to do that yourself, while in Haskell the compiler figures out all the instances and passes them for you.
And this difference turns out to be kind of important in practice. I mean, sure, for such a simple example as Show for the immediate parameter, you can just pass the damn instance yourself. And even if it's more complicated, I guess you could suck it up and pass a dozen extra parameters.
But where this gets really inconvenient is operators. Operators are functions too, but with operators there is nowhere to stick an extra parameter (or dozen). Check this out:
x = getY >>= \y -> getZ y <&> \z -> y + 42 > z
Here I used four operators from four different classes:
>>= comes from Monad
<&> from Functor
+ from Num
> from Ord
An equivalent in F# with passing instances manually might look something like:
let x =
bind Foo.monad getY <| fun y ->
map Bar.functor (getZ y) <| fun z ->
gt Int.ord (add Int.num y 42) z
Having to do that everywhere is quite unreasonable, you have to agree.
And this is why many F# operators either use SRTPs (e.g. +) or rely on "known" interfaces (e.g. <) - all so you don't have to pass instances manually.
I have a type that I'm trying to understand by writing unit tests against it, however I can't reason what to do with PrintfFormat
type ValueFormat<'p,'st,'rd,'rl,'t,'a> = {
format: PrintfFormat<'p,'st,'rd,'rl,'t>
paramNames: (string list) option
handler: 't -> 'a
}
with
static member inline construct (this: ValueFormat<_,_,_,_,_,_>) =
let parser s =
s |> tryKsscanf this.format this.handler
|> function Ok x -> Some x | _ -> None
let defaultNames =
this.format.GetFormatterNames()
|> List.map (String.replace ' ' '_' >> String.toUpperInvariant)
|> List.map (sprintf "%s_VALUE")
let names = (this.paramNames ?| defaultNames) |> List.map (sprintf "<%s>")
let formatTokens = this.format.PrettyTokenize names
(parser, formatTokens)
I feel confident that I can figure everything out but PrintfFormat is throwing me with all those generics.
The file I'm looking at for the code I want to unit test is here for the FSharp.Commandline framework.
My question is, what is PrintfFormat and how should it be used?
A link to the printf.fs file is here. It contains the definition of PrintfFormat
The PrintfFormat<'Printer,'State,'Residue,'Result,'Tuple> type, as defined in the F# source code, has four type parameters:
'Result is the type that your formatting/parsing function produces. This is string for sprintf
'Printer is a type of a function generated based on the format string, e.g. "%d and %s" will give you a function type int -> string -> 'Result
'Tuple is a tuple type generated based on the format string, e.g. "%d and %s" will give you a tuple type int * string.
'State and 'Residue are type parameters that are used when you have a custom formatter using %a, but I'll ignore that for now for simplicity (it's never needed unless you have %a format string)
There are two ways of using the type. Either for formatting, in which case you'll want to write a function that returns 'Printer as the result. The hard thing about this is that you need to construct the return function using reflection. Here is an example that works only with one format string:
open Microsoft.FSharp.Reflection
let myformat (fmt:PrintfFormat<'Printer,obj,obj,string,'Tuple>) : 'Printer =
unbox <| FSharpValue.MakeFunction(typeof<'Printer>, fun o ->
box (o.ToString()) )
myformat "%d" 1
myformat "%s" "Yo"
This simply returns the parameter passed as a value for %d or %s. To make this work for multiple arguments, you'd need to construct the function recursively (so that it's not just e.g. int -> string but also int -> (int -> string))
In the other use, you define a function that returns 'Tuple and it needs to create a tuple containing values according to the specified formatting string. Here is a small sample that only handles %s and %d format strings:
open FSharp.Reflection
let myscan (fmt:PrintfFormat<'Printer,obj,obj,string,'Tuple>) : 'Tuple =
let args =
fmt.Value
|> Seq.pairwise
|> Seq.choose (function
| '%', 'd' -> Some(box 123)
| '%', 's' -> Some(box "yo")
| _ -> None)
unbox <| FSharpValue.MakeTuple(Seq.toArray args, typeof<'Tuple>)
myscan "%d %s %d"
I wish to create a function that return the largest value in a given list, Here is what I did:
let findMax aalist: 'a list=
let rec helper (l:'a list,m:'a)=
match m,l with
|m,li::lf-> if compare m li<0 then helper (lf,li)
else helper (lf,m)
|m,[] -> m
helper(aalist, aalist.Head )
But I get errors when trying to run the function :
I don't know if this is the best way to create this function. Please help.
Drop the list type annotation, so you have this:
let findMax aalist: 'a =
let rec helper (l:'a list,m:'a) =
match m,l with
| m,li::lf -> if li > m then helper (lf,li)
else helper (lf,m)
| m,[] -> m
helper(aalist, aalist.Head)
The problem is in your declaration of the parameter.
This:
let findMax aalist: 'a list=
should be:
let findMax (aalist: 'a list) =
When no parenthesis are used the compiler thinks you are specifying the return type of the function. If the return type is 'a list then the parameter aalist must be a list of lists: 'a list list.
If you do not specify any types at all, the compiler correctly deduces the type of findMax as 'a list -> 'a.
The rule is always specify parameter types within parenthesis.
I am still confused on how to read function signatures.
The Option.map signature is the following:
/// map f inp evaluates to match inp with None -> None | Some x -> Some (f x).
/// mapping: A function to apply to the option value.
/// option: The input option.
val map : mapping:('T -> 'U) -> option:'T option -> 'U option
However, I have no clue what that signature means.
I read it as the following:
There's a function called map that takes a function as an input that we'll call "mapping" and it will yield a result that is also a function that we'll call "option".
Mapping Parameter:
mapping:('T -> 'U)
The function that we pass in as input takes Titanium (i.e. 'T) as the input and yields Uranium (i.e. 'U) as output.
The Option returned
option:'T option -> 'U option
We'll call the output of the map function "option".
Thus, this "option" that is returned from executing the map function is also a function as referenced above. It's takes a Titanium option and yields a Uranium option.
Example:
type String20 = String20 of string
type Name = { First:String20
Last:String20
Suffix:String20 option }
let tryCreateName (first:string) (last:string) (suffix:string option) =
let isValid = [first; last]
|> List.forall (fun x -> x.Length > 2 && x.Length <= 20)
if isValid then
Some { First = String20(first);
Last = String20(last);
Suffix = Option.map String20 suffix }
else None
How does the following expression map:
Option.map String20 suffix
Based on the expression above, where is the "returned function" of Titanium option -> Uranium option?
First off take a look at Option.map<'T,'U> Function (F#) and notice
The expression map f inp evaluates to match inp with None -> None |
Some x -> Some (f x).
So lets convert this comment to working code. First map is a method of the type Option, but to make it easier we will make it a function outside of a type and to avoid conflicts with other map functions we will give it the name OptionMap.
let OptionMap = f inp =
match inp with
| None -> None
| Some x -> Some (f x)
Now to get the signature of this function just send it to F# Interactive
val OptionMap : f:('a -> 'b) -> inp:'a option -> 'b option
and to make the types obvious we will type the parameters of the function.
let optionMap (f : ('a -> 'b)) (inp : 'a option) : 'b option =
match inp with
| None -> None
| Some x -> Some (f x)
Now to test this we can use
let (test : String20 option) = optionMap String20 (Some("something"))
printfn "test: %A" test
// test: Some (String20 "something")
So what happened in OptionMap that allowed this to work
If we add some print statements let sees what happens
let optionMap (f : ('a -> 'b)) (inp : 'a option) : 'b option =
printfn "f: %A" f
printfn "inp: %A" inp
match inp with
| None -> None
| Some x ->
let result = Some (f x)
printfn "result: %A" result
result
we get
f: <fun:test#63>
inp: Some "something"
result: Some (String20 "something")
we see that f is a function which is String20
So how can String20 be a function?
If we send String20 to F# Interactive it gives.
> String20;;
val it : arg0:string -> String20 = <fun:clo#4>
So String20 is a function that takes a string and returns a type of String20. That smells of a constructor.
Let's test that out in F# interactive.
> let test1 = String20 "something";;
val test1 : String20 = String20 "something"
Sure enough, String20 is a constructor, but we didn't specifically create a constructor as is done in the Object-Oriented world.
You have to think of a type, even a discriminated union as having constructors. The constructors are not specifically written but do exist. So String20 is a constructor that takes one value, a string, which is a function with the correct type signature for the Option.map function.
I gave the answer a lot more detail so that one can learn a process on how to break down problems and look at the inner workings as a tool to solving these kinds of problems.
To learn more about the lower level details of how functional programming works one needs to understand lambda calculus. The best way I know to learn it is to read An Introduction To Functional Programming Through Lambda Calculus by Greg Michaelson and look at the info in the lambda calculus tag.
Also if you like the book, you should buy a copy instead of using the free version.
There are two ways of looking at it.
let f x y = x + y
// val f: x:int -> y:int -> int
One way is to say that function f takes two parameters, x of type int and y of type int, and returns an int. So I can supply two arguments and get the result:
let a = f 4 5
// val a: int = 9
The other way is that the function takes one parameter, x of type int, and returns another function, which takes one parameter, y of type int, and returns an int. So I can supply one argument and get a function as result:
let b = f 4
// val b: int -> int
Mathematically, it's always the second way - all functions are one-parameter functions. This notion is very convenient for programming with higher-order functions.
But the first way is usually more understandable to humans, so you will often see functions discussed as if they take multiple parameters.
String20 is the case constructor for the String20 Discriminated Union case. It's a function with the type string -> String20. So string takes the place of 'T, and String20 takes the place of 'U in the mapping you supply to Option.map.
Generally, if you have a function T1 -> T2 -> ... and you apply it to one parameter, you get a function T2 -> .... In the case of Option.map, T1 is itself a function, but that is of no consequence to the way the arguments are applied.
I find it confusing to call a function "option", a string "Titanium" and a type called String20 "Uranium", so I'll stick with type names.
You ask where the "returned function" that maps a string option to a String20 option is in the expression Option.map String20 suffix. It is simply
Option.map String20
Since String20 constructs a String20 from a string, Option.map String20 is a function that maps a string to a String20 if it is present, and to None otherwise.
If you write Option.map String20 suffix, this function is applied to suffix, which would be a string option. The result of this expression is a String20 option.
I'm playing around with quotations and I can't see an expression pattern for type definitions. Is there really not one, or am I missing something?
<## type MyType (name:string) =
member x.Name = name ##>
Gives "Unexpected keyword 'type' in quotation literal."
You can't. You can only quote code, that is to say, any valid F# expression. Type definitions are not considered as code, but definitions.
What you might want to do is put ReflectedDefinition attribute on a type members:
type MyType (name : string) =
[<ReflectedDefinition>] member x.Name = name
If you want to retrieve the AST of members that have ReflectedDefinition you can use Expr.TryGetReflectedDefinition function.
E.g, this sample code prints ASTs of all reflected definition members of MyType:
open Microsoft.FSharp.Quotations
open System.Reflection
type MyType (name : string) =
[<ReflectedDefinition>] member x.Name = name
let mis = typeof<MyType>.GetMembers()
for mi in mis do
try
match Expr.TryGetReflectedDefinition(mi :?> MethodBase) with
| Some(e) -> printfn "%A" e
| None -> ()
with _ -> ()
()