empty function composition ∘() should return Base.identity?

[stevengj]

Currently, ∘() gives a MethodError:

julia> ∘(sin, cos, tan)
sin ∘ cos ∘ tan

julia> ∘(sin, cos)
sin ∘ cos

julia> ∘(sin,)
sin (generic function with 14 methods)

julia> ∘()
ERROR: MethodError: no method matching ∘()

whereas it should arguably return Base.identity.

Similarly, reduce_empty(∘) should return Base.identity so that empty reductions work:

julia> foldl(∘, (sin, cos, tan))
sin ∘ cos ∘ tan

julia> foldl(∘, (sin, cos))
sin ∘ cos

julia> foldl(∘, (sin,))
sin (generic function with 14 methods)

julia> foldl(∘, ())
ERROR: MethodError: reducing over an empty collection is not allowed; consider supplying `init` to the reducer
Stacktrace:
 [1] reduce_empty(op::Base.BottomRF{typeof(∘)}, ::Type{Union{}})
   @ Base ./reduce.jl:360

Update: The 1-arg method was added in #34251, and I see that at this point the possibility for a zero-argument version ∘() = identity was explicitly proposed, and rejected on the grounds that ∘ might be applicable to more than just Functions, in which case the identity element becomes ambiguous:

That's based on the desire to have ∘ for other "morphisms" than functions, which has been requested before, e.g. in the discussion where compose was requested as an ASCII name for ∘.

[stevengj]

Closing as a duplicate of the discussion in #34251.

There is also an explicit comment about this in the source code:

julia/test/operators.jl

Lines 171 to 174 in c0c676b

	# Like +() and *() we leave ∘() undefined.
	# While `∘() = identity` is a reasonable definition for functions, this
	# would cause headaches for composition of user defined morphisms.
	# See also #34251

[stevengj]

Also duplicate of #52436.