Fix type instability for exponent iterator with no variable

src/comparison.jl

@@ -459,11 +459,6 @@ struct ExponentsIterator{M,D<:Union{Nothing,Int},O}
                 ),
             )
         end
-        if length(object) == 0 && isnothing(maxdegree)
-            # Otherwise, it will incorrectly think that the iterator is infinite
-            # while it actually has zero elements
-            maxdegree = mindegree
-        end
         return new{M,typeof(maxdegree),typeof(object)}(
             object,
             mindegree,
@@ -474,24 +469,49 @@ struct ExponentsIterator{M,D<:Union{Nothing,Int},O}
 end
 
 Base.eltype(::Type{ExponentsIterator{M,D,O}}) where {M,D,O} = O
+# `IteratorSize` returns something different depending on whether it is called
+# in an instance or on the type. `Iterators.Cycle` has the same behavior,
+# see https://github.com/JuliaLang/julia/pull/54187
 function Base.IteratorSize(::Type{<:ExponentsIterator{M,Nothing}}) where {M}
+    # It could be `HasLength` is `IsInfinite` depending on whether `it.object`
+    # is empty so the size is unknown when we only have access to the type of
+    # the iterator. The method below gives the correct size when we have access
+    # to the instance.
+    return Base.SizeUnknown()
+end
+function Base.IteratorSize(it::ExponentsIterator{M,Nothing}) where {M}
+    if isempty(it.object)
+        return Base.HasLength()
+    end
     return Base.IsInfinite()
 end
 function Base.IteratorSize(::Type{<:ExponentsIterator{M,Int}}) where {M}
     return Base.HasLength()
 end
 
-function Base.length(it::ExponentsIterator{M,Int}) where {M}
-    if it.maxdegree < it.mindegree
+function _length(it::ExponentsIterator, maxdegree)
+    if maxdegree < it.mindegree
         return 0
     end
-    len = binomial(nvariables(it) + it.maxdegree, nvariables(it))
+    len = binomial(nvariables(it) + maxdegree, nvariables(it))
     if it.mindegree > 0
         len -= binomial(nvariables(it) + it.mindegree - 1, nvariables(it))
     end
     return len
 end
 
+function Base.length(it::ExponentsIterator{M,Int}) where {M}
+    return _length(it, it.maxdegree)
+end
+
+function Base.length(it::ExponentsIterator{M,Nothing}) where {M}
+    if isempty(it.object)
+        return _length(it, it.mindegree)
+    else
+        error("The iterator is infinity because `maxdegree` is `nothing`.")
+    end
+end
+
 nvariables(it::ExponentsIterator) = length(it.object)
 
 _last_lex_index(n, ::Type{LexOrder}) = n

test/comparison.jl

@@ -26,6 +26,11 @@ function test_errors()
         "Ordering `$M` is not a valid ordering, use `Graded{$M}` instead.",
     )
     @test_throws err ExponentsIterator{M}([0], maxdegree = 2)
+    exps = ExponentsIterator{LexOrder}([0])
+    err = ErrorException(
+        "The iterator is infinity because `maxdegree` is `nothing`.",
+    )
+    @test_throws err length(exps)
 end
 
 function test_exponents_iterator()