Improve foldl's stability on nested Iterators (#45789)

* Make `Fix1(f, Int)` inference-stable
* split `_xfadjoint` into `_xfadjoint_unwrap` and `_xfadjoint_wrap`
* Improve `(c::ComposedFunction)(x...)`'s inferability
* and fuse it in `Base._xfadjoint`.
* define a `Typeof` operator that will partly work around internal type-system bugs

Closes #45715

(cherry picked from commit d58289c)

base/operators.jl

@@ -910,6 +910,9 @@ julia> [1:5;] |> (x->x.^2) |> sum |> inv
 """
 |>(x, f) = f(x)
 
+_stable_typeof(x) = typeof(x)
+_stable_typeof(::Type{T}) where {T} = @isdefined(T) ? Type{T} : DataType
+
 """
     f = Returns(value)
 
@@ -936,7 +939,7 @@ julia> f.value
 struct Returns{V} <: Function
     value::V
     Returns{V}(value) where {V} = new{V}(value)
-    Returns(value) = new{Core.Typeof(value)}(value)
+    Returns(value) = new{_stable_typeof(value)}(value)
 end
 
 (obj::Returns)(args...; kw...) = obj.value
@@ -1027,7 +1030,19 @@ struct ComposedFunction{O,I} <: Function
     ComposedFunction(outer, inner) = new{Core.Typeof(outer),Core.Typeof(inner)}(outer, inner)
 end
 
-(c::ComposedFunction)(x...; kw...) = c.outer(c.inner(x...; kw...))
+function (c::ComposedFunction)(x...; kw...)
+    fs = unwrap_composed(c)
+    call_composed(fs[1](x...; kw...), tail(fs)...)
+end
+unwrap_composed(c::ComposedFunction) = (unwrap_composed(c.inner)..., unwrap_composed(c.outer)...)
+unwrap_composed(c) = (maybeconstructor(c),)
+call_composed(x, f, fs...) = (@inline; call_composed(f(x), fs...))
+call_composed(x, f) = f(x)
+
+struct Constructor{F} <: Function end
+(::Constructor{F})(args...; kw...) where {F} = (@inline; F(args...; kw...))
+maybeconstructor(::Type{F}) where {F} = Constructor{F}()
+maybeconstructor(f) = f
 
 ∘(f) = f
 ∘(f, g) = ComposedFunction(f, g)
@@ -1074,8 +1089,8 @@ struct Fix1{F,T} <: Function
     f::F
     x::T
 
-    Fix1(f::F, x::T) where {F,T} = new{F,T}(f, x)
-    Fix1(f::Type{F}, x::T) where {F,T} = new{Type{F},T}(f, x)
+    Fix1(f::F, x) where {F} = new{F,_stable_typeof(x)}(f, x)
+    Fix1(f::Type{F}, x) where {F} = new{Type{F},_stable_typeof(x)}(f, x)
 end
 
 (f::Fix1)(y) = f.f(f.x, y)
@@ -1091,8 +1106,8 @@ struct Fix2{F,T} <: Function
     f::F
     x::T
 
-    Fix2(f::F, x::T) where {F,T} = new{F,T}(f, x)
-    Fix2(f::Type{F}, x::T) where {F,T} = new{Type{F},T}(f, x)
+    Fix2(f::F, x) where {F} = new{F,_stable_typeof(x)}(f, x)
+    Fix2(f::Type{F}, x) where {F} = new{Type{F},_stable_typeof(x)}(f, x)
 end
 
 (f::Fix2)(y) = f.f(y, f.x)

base/reduce.jl

@@ -140,17 +140,25 @@ what is returned is `itr′` and
 
     op′ = (xfₙ ∘ ... ∘ xf₂ ∘ xf₁)(op)
 """
-_xfadjoint(op, itr) = (op, itr)
-_xfadjoint(op, itr::Generator) =
-    if itr.f === identity
-        _xfadjoint(op, itr.iter)
-    else
-        _xfadjoint(MappingRF(itr.f, op), itr.iter)
-    end
-_xfadjoint(op, itr::Filter) =
-    _xfadjoint(FilteringRF(itr.flt, op), itr.itr)
-_xfadjoint(op, itr::Flatten) =
-    _xfadjoint(FlatteningRF(op), itr.it)
+function _xfadjoint(op, itr)
+    itr′, wrap = _xfadjoint_unwrap(itr)
+    wrap(op), itr′
+end
+
+_xfadjoint_unwrap(itr) = itr, identity
+function _xfadjoint_unwrap(itr::Generator)
+    itr′, wrap = _xfadjoint_unwrap(itr.iter)
+    itr.f === identity && return itr′, wrap
+    return itr′, wrap ∘ Fix1(MappingRF, itr.f)
+end
+function _xfadjoint_unwrap(itr::Filter)
+    itr′, wrap = _xfadjoint_unwrap(itr.itr)
+    return itr′, wrap ∘ Fix1(FilteringRF, itr.flt)
+end
+function _xfadjoint_unwrap(itr::Flatten)
+    itr′, wrap = _xfadjoint_unwrap(itr.it)
+    return itr′, wrap ∘ FlatteningRF
+end
 
 """
     mapfoldl(f, op, itr; [init])

test/operators.jl

@@ -175,6 +175,15 @@ Base.promote_rule(::Type{T19714}, ::Type{Int}) = T19714
 
 end
 
+@testset "Nested ComposedFunction's stability" begin
+    f(x) = (1, 1, x...)
+    g = (f ∘ (f ∘ f)) ∘ (f ∘ f ∘ f)
+    @test (@inferred (g∘g)(1)) == ntuple(Returns(1), 25)
+    @test (@inferred g(1)) == ntuple(Returns(1), 13)
+    h = (-) ∘ (-) ∘ (-) ∘ (-) ∘ (-) ∘ (-) ∘ sum
+    @test (@inferred h((1, 2, 3); init = 0.0)) == 6.0
+end
+
 @testset "function negation" begin
     str = randstring(20)
     @test filter(!isuppercase, str) == replace(str, r"[A-Z]" => "")
@@ -302,6 +311,9 @@ end
     val = [1,2,3]
     @test Returns(val)(1) === val
     @test sprint(show, Returns(1.0)) == "Returns{Float64}(1.0)"
+
+    illtype = Vector{Core._typevar(:T, Union{}, Any)}
+    @test Returns(illtype) == Returns{DataType}(illtype)
 end
 
 @testset "<= (issue #46327)" begin

test/reduce.jl

@@ -677,3 +677,16 @@ end
         @test mapreduce(+, +, oa, oa) == 2len
     end
 end
+
+# issue #45748
+@testset "foldl's stability for nested Iterators" begin
+    a = Iterators.flatten((1:3, 1:3))
+    b = (2i for i in a if i > 0)
+    c = Base.Generator(Float64, b)
+    d = (sin(i) for i in c if i > 0)
+    @test @inferred(sum(d)) == sum(collect(d))
+    @test @inferred(extrema(d)) == extrema(collect(d))
+    @test @inferred(maximum(c)) == maximum(collect(c))
+    @test @inferred(prod(b)) == prod(collect(b))
+    @test @inferred(minimum(a)) == minimum(collect(a))
+end