Expose ComposedFunction as a public API (#37517)

* document ComposedFunction
* add ComposedFunction to News.md
* Give more descriptive names to the fields of ComposedFunction
* export ComposedFunction

Co-authored-by: Jonas Schulze <jonas.schulze7@t-online.de>
Co-authored-by: Takafumi Arakaki <aka.tkf@gmail.com>

NEWS.md

@@ -105,6 +105,7 @@ Standard library changes
 * `RegexMatch` objects can now be probed for whether a named capture group exists within it through `haskey()` ([#36717]).
 * For consistency `haskey(r::RegexMatch, i::Integer)` has also been added and returns if the capture group for `i` exists ([#37300]).
 * A new standard library `TOML` has been added for parsing and printing [TOML files](https://toml.io) ([#37034]).
+* The composition operator `∘` now returns a `Base.ComposedFunction` instead of an anonymous function ([#37517]).
 * A new standard library `Downloads` has been added, which replaces the old `Base.download` function with `Downloads.download`, providing cross-platform, multi-protocol, in-process download functionality implemented with [libcurl](https://curl.haxx.se/libcurl/) ([#37340]).
 * The `Pkg.BinaryPlatforms` module has been moved into `Base` as `Base.BinaryPlatforms` and heavily reworked.
   Applications that want to be compatible with the old API should continue to import `Pkg.BinaryPlatforms`,

base/exports.jl

@@ -38,6 +38,7 @@ export
     ComplexF64,
     ComplexF32,
     ComplexF16,
+    ComposedFunction,
     DenseMatrix,
     DenseVecOrMat,
     DenseVector,

base/operators.jl

@@ -871,26 +871,58 @@ julia> fs = [
 julia> ∘(fs...)(3)
 3.0
 ```
+See also [`ComposedFunction`](@ref).
 """
 function ∘ end
 
-struct ComposedFunction{F,G} <: Function
-    f::F
-    g::G
-    ComposedFunction{F, G}(f, g) where {F, G} = new{F, G}(f, g)
-    ComposedFunction(f, g) = new{Core.Typeof(f),Core.Typeof(g)}(f, g)
+"""
+    ComposedFunction{Outer,Inner} <: Function
+
+Represents the composition of two callable objects `outer::Outer` and `inner::Inner`. That is
+```julia
+ComposedFunction(outer, inner)(args...; kw...) === outer(inner(args...; kw...))
+```
+The preferred way to construct instance of `ComposedFunction` is to use the composition operator [`∘`](@ref):
+```jldoctest
+julia> sin ∘ cos === ComposedFunction(sin, cos)
+true
+
+julia> typeof(sin∘cos)
+ComposedFunction{typeof(sin), typeof(cos)}
+```
+The composed pieces are stored in the fields of `ComposedFunction` and can be retrieved as follows:
+```jldoctest
+julia> composition = sin ∘ cos
+sin ∘ cos
+
+julia> composition.outer === sin
+true
+
+julia> composition.inner === cos
+true
+```
+!!! compat "Julia 1.6"
+    ComposedFunction requires at least Julia 1.6. In earlier versions `∘` returns an anonymous function instead.
+
+See also [`∘`](@ref).
+"""
+struct ComposedFunction{O,I} <: Function
+    outer::O
+    inner::I
+    ComposedFunction{O, I}(outer, inner) where {O, I} = new{O, I}(outer, inner)
+    ComposedFunction(outer, inner) = new{Core.Typeof(outer),Core.Typeof(inner)}(outer, inner)
 end
 
-(c::ComposedFunction)(x...) = c.f(c.g(x...))
+(c::ComposedFunction)(x...) = c.outer(c.inner(x...))
 
 ∘(f) = f
 ∘(f, g) = ComposedFunction(f, g)
 ∘(f, g, h...) = ∘(f ∘ g, h...)
 
 function show(io::IO, c::ComposedFunction)
-    show(io, c.f)
+    show(io, c.outer)
     print(io, " ∘ ")
-    show(io, c.g)
+    show(io, c.inner)
 end
 
 """

doc/src/base/base.md

@@ -237,6 +237,7 @@ Base.invokelatest
 new
 Base.:(|>)
 Base.:(∘)
+Base.ComposedFunction
 ```
 
 ## Syntax