diff --git a/base/namedtuple.jl b/base/namedtuple.jl
index 37f3a3ef8436b..57d72bb3ea569 100644
--- a/base/namedtuple.jl
+++ b/base/namedtuple.jl
@@ -159,7 +159,7 @@ end
 length(t::NamedTuple) = nfields(t)
 iterate(t::NamedTuple, iter=1) = iter > nfields(t) ? nothing : (getfield(t, iter), iter + 1)
 rest(t::NamedTuple) = t
-@inline rest(t::NamedTuple{names}, i::Int) where {names} = NamedTuple{rest(names,i)}(t)
+@inline rest(t::NamedTuple{names}, i) where {names} = NamedTuple{rest(names,i::Int)}(t)
 firstindex(t::NamedTuple) = 1
 lastindex(t::NamedTuple) = nfields(t)
 getindex(t::NamedTuple, i::Int) = getfield(t, i)
diff --git a/base/tuple.jl b/base/tuple.jl
index ebc2cd1e53202..c2c2240296195 100644
--- a/base/tuple.jl
+++ b/base/tuple.jl
@@ -206,8 +206,12 @@ julia> first, Base.rest(a, state)
 """
 function rest end
 rest(t::Tuple) = t
-rest(t::Tuple, i::Int) = ntuple(x -> getfield(t, x+i-1), length(t)-i+1)
-rest(a::Union{Array,Memory,Core.SimpleVector}, i::Int=1) = a[i:end]
+function rest(t::Tuple, i)
+    let i = i::Int
+        ntuple(x -> getfield(t, x+i-1), length(t)-i+1)
+    end
+end
+rest(a::Union{Array,Memory,Core.SimpleVector}, i=1) = a[(i::Int):end]
 rest(itr, state...) = Iterators.rest(itr, state...)
 
 """
diff --git a/test/core.jl b/test/core.jl
index 84444ecb725d7..004a352f5f75f 100644
--- a/test/core.jl
+++ b/test/core.jl
@@ -8193,6 +8193,25 @@ foo46503(a::Int, b::Nothing) = @invoke foo46503(a::Any, b)
 foo46503(@nospecialize(a), b::Union{Nothing, Float64}) = rand() + 10
 @test 10 <= foo46503(1, nothing) <= 11
 
+@testset "inference for `rest` with unknown state argument types" begin
+    @testset "`Array`, `Memory`" begin
+        for typ in (Vector{Float32}, Matrix{Float32}, Memory{Float32})
+            @test (isconcretetype ∘ Base.infer_return_type)(Base.rest, Tuple{typ, Any})
+            for e in (Base.Compiler.is_terminates, Base.Compiler.is_notaskstate, Base.Compiler.is_nonoverlayed)
+                @test (e ∘ Base.infer_effects)(Base.rest, Tuple{typ, Any})
+            end
+        end
+    end
+    @testset "`Tuple`" begin
+        typ = NTuple{5, Float32}
+        @test Base.infer_return_type(Base.rest, Tuple{typ, Any}) <: Tuple
+    end
+    @testset "`NamedTuple`" begin
+        typ = NamedTuple{(:a, :b, :c, :d, :e), NTuple{5, Float32}}
+        @test Base.infer_return_type(Base.rest, Tuple{typ, Any}) <: NamedTuple
+    end
+end
+
 @testset "effect override on Symbol(::String)" begin
     @test Core.Compiler.is_foldable(Base.infer_effects(Symbol, (String,)))
 end