Does F# documentation have a way to search for functions by their types?

Question

Say I want to know if F# has a library function of type

(\'T -> bool) -> \'T list -> int

ie, something that counts how many items

Answer 1

I don't know of any such tool. However it might be a fun exercise to write one using System.Reflection (or even better, the Metadata library in the PowerPack), so that you could take equivalence modulo type variable names, etc. into account.

EDIT - I was right - it was a fun exercise. What follows has a lot of warts, but isn't too bad for ~150 lines of code. Hopefully this will be enough to get someone started who wants to work on a real tool. It doesn't do anything advanced like checking for functions with reordered parameters, and the Metadata library is a bit picky about using fully qualified names so you need to be a bit careful. To answer the question in your original post, I executed

find "('a -> Microsoft.FSharp.Core.bool) -> Microsoft.FSharp.Collections.list`1<'a> -> Microsoft.FSharp.Core.int" 

and got the following list of candidates:

Microsoft.FSharp.Core.Operators.( + )
Microsoft.FSharp.Core.Operators.( - )
Microsoft.FSharp.Core.Operators.( * )
Microsoft.FSharp.Core.Operators.( / )
Microsoft.FSharp.Core.Operators.( % )
Microsoft.FSharp.Core.Operators.sqrt
Microsoft.FSharp.Core.LanguagePrimitives.EnumOfValue
Microsoft.FSharp.Core.LanguagePrimitives.EnumToValue
Microsoft.FSharp.Core.LanguagePrimitives.AdditionDynamic
Microsoft.FSharp.Core.LanguagePrimitives.CheckedAdditionDynamic
Microsoft.FSharp.Core.LanguagePrimitives.MultiplyDynamic
Microsoft.FSharp.Core.LanguagePrimitives.CheckedMultiplyDynamic
Microsoft.FSharp.Core.LanguagePrimitives.GenericZero
Microsoft.FSharp.Core.LanguagePrimitives.GenericOne
Microsoft.FSharp.Collections.List.find
Microsoft.FSharp.Collections.List.findIndex
Microsoft.FSharp.Collections.List.maxBy
Microsoft.FSharp.Collections.List.minBy

Of these, only List.findIndex has exactly the generic type you're looking for, but with the right combination of type parameters so do the others (e.g. if 'a = int then List.find has the desired type). Unfortunately, constraints aren't taken into account in the search so the non-List functions can't actually match.

Without further ado, here's the code I used - you'll need to add a reference to the FSharp.PowerPack.Metadata assembly to get it to work.

open Microsoft.FSharp.Metadata
open System.Text.RegularExpressions

(* type parameters let us switch out representation if need be *)
type Tag<'ty> = | Tuple | Arr | Ground of 'ty
type Ty<'ty,'a> = Param of 'a | Complex of Tag<'ty> * Ty<'ty,'a> list

(* Gets something stable from an FSharpEntity so that we can see if two are identical *)
let rec getType (e:FSharpEntity) =
  if (e.IsAbbreviation) then
    getType e.AbbreviatedType.NamedEntity
  else
    e.ReflectionType

(* FSharpType -> Ty *)
let rec cvt (e:FSharpType) =
  if e.IsTuple then
    Complex(Tuple, e.GenericArguments |> Seq.map cvt |> List.ofSeq)
  elif e.IsFunction then
    Complex(Arr, e.GenericArguments |> Seq.map cvt |> List.ofSeq)
  elif e.IsGenericParameter then
    Param e.GenericParameter.Name
  else
    Complex(Ground(e.NamedEntity |> getType), e.GenericArguments |> Seq.map cvt |> List.ofSeq)

(* substitute type for variable within another type *)
let rec subst v t = function
| Complex(tag,l) -> Complex(tag, l |> List.map (subst v t))
| Param i when i = v -> t
| Param j -> Param j

(* get type variables used in a type *)
let rec usedVars = function
| Param i -> Set.singleton i
| Complex(tag, l) -> Set.unionMany (List.map usedVars l)

(* Find most general unifier (if any) for two types *)
let mgu t1 t2 =
  let rec mgu subs = function
  | [] -> Some subs
  | (Complex(tag1,l1),Complex(tag2,l2))::rest ->
       if tag1 <> tag2 then
         None
       else
         let rec loop r = function
         | [],[] -> mgu subs r
         | [],_ | _,[] -> None
         | x::xs, y::ys -> loop ((x,y)::r) (xs,ys)
         loop rest (l1,l2)
  | (Param i, Param j)::rest when i = j -> mgu subs rest
  | ((Param i, x) | (x, Param i))::rest ->
       if (Set.contains i (usedVars x)) then
         None (* type would be infinite when unifying *)
       else
         mgu ((i,x)::subs) (rest |> List.map (fun (t1,t2) -> (subst i x t1, subst i x t2)))
  mgu [] [t1,t2]

(* Active patterns for parsing - this is ugly... *)
let (|StartsWith|_|) r s =
  let m = Regex.Match(s, r)
  if m.Success && m.Index = 0 then
    Some(m.Value, s.Substring(m.Length))
  else None

let rec (|Any|) (|P|_|) = function
| P(x,Any (|P|_|) (l,r)) -> x::l, r
| s -> [],s

let rec (|Any1|_|) (|P|_|) = function
| P(x,Any (|P|_|) (l,r)) -> Some(x::l, r)
| _ -> None

let (|Seq|_|) (|P|_|) (|Q|_|) = function
| P(x,Q(y,r)) -> Some((x,y),r)
| _ -> None

let (|Choice|_|) (|P|_|) (|Q|_|) = function
| P(p) -> Some p
| Q(p) -> Some p
| _ -> None

let (|Delimit|_|) s (|P|_|) = function
| P(x,Any ((|Seq|_|) ((|StartsWith|_|) s) (|P|_|)) (l,r)) -> Some(x::(List.map snd l), r)
| _ -> None

let (|Delimit1|_|) s (|P|_|) = function
| P(x,StartsWith s (_,Delimit s (|P|_|) (l,r))) -> Some(x::l, r)
| _ -> None

(* Basically a BNF grammar for types *)
let rec (|TyE|_|) = function
| ArrE(p) | TupleE(p) | AtomE(p) -> Some(p)
| _ -> None
and (|ArrE|_|) = function
| Choice (|TupleE|_|) (|AtomE|_|) (dom,StartsWith "->" (_,TyE(rng,r))) -> Some(Complex(Arr,[dom;rng]), r)
| _ -> None
and (|TupleE|_|) = function
| Delimit1 @"\*" (|AtomE|_|) (l,r) -> Some(Complex(Tuple,l), r)
| _ -> None
and (|AtomE|_|) = function
| ParamE(x,r) | GroundE(x,r) | StartsWith @"\(" (_,TyE(x,StartsWith @"\)" (_,r))) -> Some(x,r)
| _ -> None
and (|ParamE|_|) = function
| StartsWith "'[a-zA-Z0-9]+" (s,r) -> Some(Param s, r)
| _ -> None
and (|GroundE|_|) = function
| StartsWith "[`.a-zA-Z0-9]+" (gnd, StartsWith "<" (_, Delimit "," (|TyE|_|) (l, StartsWith ">" (_,r)))) -> 
      let ty = FSharpAssembly.FSharpLibrary.GetEntity gnd |> getType
      Some(Complex(Ground(ty), l), r)
| StartsWith "[`.a-zA-Z0-9]+" (gnd, r) ->
      let ty = FSharpAssembly.FSharpLibrary.GetEntity gnd |> getType
      Some(Complex(Ground(ty), []), r)
| _ -> None

(* parse a string into a type *)
let parse (s:string) =
  (* remove whitespace before matching *)
  match s.Replace(" ","") with
  | TyE(ty,"") -> ty
  | _ -> failwith "Not a well-formed type"

(* an infinite stream of possible variable names - for performing renaming *)
let rec names = 
  let letters = ['a' .. 'z'] |> List.map string
  seq {
    yield! letters
    for n in names do
      for l in letters do
        yield n + l
  }

(* finds entities in the F# library with the requested signature, modulo type parameter unification *)
let find s =
  let ty = parse s
  let vars = usedVars ty
  seq {
    for e in FSharpAssembly.FSharpLibrary.Entities do
    for m in e.MembersOrValues do
      (* need try/catch to avoid error on weird types like "[]`1" *)
      match (try Some(cvt m.Type) with _ -> None) with
      | Some ty2 ->
        (* rename all type variables from the query to avoid incorrectly unifying with type variables in signatures *)
        let used = usedVars ty2
        let newVars = Seq.choose (fun v -> if Set.contains v used then None else Some(Param v)) names
        let varMap = Map.ofSeq (Seq.zip vars newVars)
        let ty = Map.fold (fun t v p -> subst v p t) ty varMap
        match mgu ty ty2 with
        | None -> ()
        | Some _ -> yield sprintf "%s.%s.%s" e.Namespace e.DisplayName m.DisplayName 
      | _ -> () }