diff --git a/base/abstractarray.jl b/base/abstractarray.jl
index 62547c8d7e01b..9f0ae669caaca 100644
--- a/base/abstractarray.jl
+++ b/base/abstractarray.jl
@@ -1190,13 +1190,13 @@ mightalias(A::AbstractArray, B::AbstractArray) = !isbits(A) && !isbits(B) && !_i
 mightalias(x, y) = false
 
 _isdisjoint(as::Tuple{}, bs::Tuple{}) = true
-_isdisjoint(as::Tuple{}, bs::Tuple{Any}) = true
+_isdisjoint(as::Tuple{}, bs::Tuple{UInt}) = true
 _isdisjoint(as::Tuple{}, bs::Tuple) = true
-_isdisjoint(as::Tuple{Any}, bs::Tuple{}) = true
-_isdisjoint(as::Tuple{Any}, bs::Tuple{Any}) = as[1] != bs[1]
-_isdisjoint(as::Tuple{Any}, bs::Tuple) = !(as[1] in bs)
+_isdisjoint(as::Tuple{UInt}, bs::Tuple{}) = true
+_isdisjoint(as::Tuple{UInt}, bs::Tuple{UInt}) = as[1] != bs[1]
+_isdisjoint(as::Tuple{UInt}, bs::Tuple) = !(as[1] in bs)
 _isdisjoint(as::Tuple, bs::Tuple{}) = true
-_isdisjoint(as::Tuple, bs::Tuple{Any}) = !(bs[1] in as)
+_isdisjoint(as::Tuple, bs::Tuple{UInt}) = !(bs[1] in as)
 _isdisjoint(as::Tuple, bs::Tuple) = !(as[1] in bs) && _isdisjoint(tail(as), bs)
 
 """
diff --git a/base/broadcast.jl b/base/broadcast.jl
index defd53aff6adf..913111e6481c2 100644
--- a/base/broadcast.jl
+++ b/base/broadcast.jl
@@ -555,7 +555,7 @@ Base.@propagate_inbounds _newindex(ax::Tuple{}, I::Tuple{}) = ()
 @inline function _newindexer(indsA::Tuple)
     ind1 = indsA[1]
     keep, Idefault = _newindexer(tail(indsA))
-    (Base.length(ind1)!=1, keep...), (first(ind1), Idefault...)
+    (Base.length(ind1)::Integer != 1, keep...), (first(ind1), Idefault...)
 end
 
 @inline function Base.getindex(bc::Broadcasted, I::Union{Integer,CartesianIndex})
diff --git a/base/namedtuple.jl b/base/namedtuple.jl
index 790a080bd4129..17f1d9c38684a 100644
--- a/base/namedtuple.jl
+++ b/base/namedtuple.jl
@@ -64,7 +64,7 @@ Core.NamedTuple
 if nameof(@__MODULE__) === :Base
 
 @eval function NamedTuple{names,T}(args::Tuple) where {names, T <: Tuple}
-    if length(args) != length(names)
+    if length(args) != length(names::Tuple)
         throw(ArgumentError("Wrong number of arguments to named tuple constructor."))
     end
     # Note T(args) might not return something of type T; e.g.
@@ -251,8 +251,8 @@ julia> merge((a=1, b=2, c=3), [:b=>4, :d=>5])
 function merge(a::NamedTuple, itr)
     names = Symbol[]
     vals = Any[]
-    inds = IdDict()
-    for (k,v) in itr
+    inds = IdDict{Symbol,Int}()
+    for (k::Symbol, v) in itr
         oldind = get(inds, k, 0)
         if oldind > 0
             vals[oldind] = v
diff --git a/base/ntuple.jl b/base/ntuple.jl
index 0967066f3447e..1fdbc016ee39d 100644
--- a/base/ntuple.jl
+++ b/base/ntuple.jl
@@ -55,12 +55,13 @@ ntuple(f, ::Val{3}) = (@_inline_meta; (f(1), f(2), f(3)))
     end
 end
 
-@inline function fill_to_length(t::Tuple, val, ::Val{N}) where {N}
+@inline function fill_to_length(t::Tuple, val, ::Val{_N}) where {_N}
     M = length(t)
+    N = _N::Int
     M > N && throw(ArgumentError("input tuple of length $M, requested $N"))
     if @generated
         quote
-            (t..., $(fill(:val, N-length(t.parameters))...))
+            (t..., $(fill(:val, (_N::Int) - length(t.parameters))...))
         end
     else
         (t..., fill(val, N-M)...)
diff --git a/base/reflection.jl b/base/reflection.jl
index c2a8f4d0bc95f..813ab0f4bc1ee 100644
--- a/base/reflection.jl
+++ b/base/reflection.jl
@@ -147,7 +147,7 @@ function fieldname(t::DataType, i::Integer)
         throw(ArgumentError("type does not have definite field names"))
     end
     names = _fieldnames(t)
-    n_fields = length(names)
+    n_fields = length(names)::Int
     field_label = n_fields == 1 ? "field" : "fields"
     i > n_fields && throw(ArgumentError("Cannot access field $i since type $t only has $n_fields $field_label."))
     i < 1 && throw(ArgumentError("Field numbers must be positive integers. $i is invalid."))
diff --git a/base/show.jl b/base/show.jl
index e97a1eda9756c..22ff592ace180 100644
--- a/base/show.jl
+++ b/base/show.jl
@@ -523,7 +523,7 @@ end
 function show_datatype(io::IO, x::DataType)
     istuple = x.name === Tuple.name
     if (!isempty(x.parameters) || istuple) && x !== Tuple
-        n = length(x.parameters)
+        n = length(x.parameters)::Int
 
         # Print homogeneous tuples with more than 3 elements compactly as NTuple{N, T}
         if istuple && n > 3 && all(i -> (x.parameters[1] === i), x.parameters)