diff --git a/base/compiler/abstractinterpretation.jl b/base/compiler/abstractinterpretation.jl
index b28e531cad6f29..1b1ca75a4599e0 100644
--- a/base/compiler/abstractinterpretation.jl
+++ b/base/compiler/abstractinterpretation.jl
@@ -149,6 +149,21 @@ function abstract_call_gf_by_type(@nospecialize(f), argtypes::Vector{Any}, @nosp
     return rettype
 end
 
+
+function const_prop_profitable(arg)
+    # have new information from argtypes that wasn't available from the signature
+    if isa(arg, PartialStruct)
+        for b in arg.fields
+            isconstType(b) && return true
+            const_prop_profitable(b) && return true
+        end
+    elseif !isa(arg, Const) || (isa(arg.val, Symbol) || isa(arg.val, Type) || (!isa(arg.val, String) && isimmutable(arg.val)))
+        # don't consider mutable values or Strings useful constants
+        return true
+    end
+    return false
+end
+
 function abstract_call_method_with_const_args(@nospecialize(rettype), @nospecialize(f), argtypes::Vector{Any}, match::SimpleVector, sv::InferenceState)
     method = match[3]::Method
     nargs::Int = method.nargs
@@ -158,12 +173,8 @@ function abstract_call_method_with_const_args(@nospecialize(rettype), @nospecial
     for a in argtypes
         a = widenconditional(a)
         if has_nontrivial_const_info(a)
-            # have new information from argtypes that wasn't available from the signature
-            if !isa(a, Const) || (isa(a.val, Symbol) || isa(a.val, Type) || (!isa(a.val, String) && isimmutable(a.val)))
-                # don't consider mutable values or Strings useful constants
-                haveconst = true
-                break
-            end
+            haveconst = const_prop_profitable(a)
+            haveconst && break
         end
     end
     haveconst || improvable_via_constant_propagation(rettype) || return Any
@@ -189,7 +200,7 @@ function abstract_call_method_with_const_args(@nospecialize(rettype), @nospecial
             # in this case, see if all of the arguments are constants
             for a in argtypes
                 a = widenconditional(a)
-                if !isa(a, Const) && !isconstType(a)
+                if !isa(a, Const) && !isconstType(a) && !isa(a, PartialStruct)
                     return Any
                 end
             end
@@ -384,7 +395,7 @@ end
 # Union of Tuples of the same length is converted to Tuple of Unions.
 # returns an array of types
 function precise_container_type(@nospecialize(typ), vtypes::VarTable, sv::InferenceState)
-    if isa(typ, PartialTuple)
+    if isa(typ, PartialStruct) && typ.typ.name === Tuple.name
         return typ.fields
     end
 
@@ -498,8 +509,9 @@ end
 # do apply(af, fargs...), where af is a function value
 function abstract_apply(@nospecialize(aft), aargtypes::Vector{Any}, vtypes::VarTable, sv::InferenceState,
                         max_methods = sv.params.MAX_METHODS)
-    if !isa(aft, Const) && (!isType(aft) || has_free_typevars(aft))
-        if !isconcretetype(aft) || (aft <: Builtin)
+    aftw = widenconst(aft)
+    if !isa(aft, Const) && (!isType(aftw) || has_free_typevars(aftw))
+        if !isconcretetype(aftw) || (aftw <: Builtin)
             # non-constant function of unknown type: bail now,
             # since it seems unlikely that abstract_call will be able to do any better after splitting
             # this also ensures we don't call abstract_call_gf_by_type below on an IntrinsicFunction or Builtin
@@ -891,26 +903,37 @@ function abstract_eval(@nospecialize(e), vtypes::VarTable, sv::InferenceState)
         t = instanceof_tfunc(abstract_eval(e.args[1], vtypes, sv))[1]
         if isconcretetype(t) && !t.mutable
             args = Vector{Any}(undef, length(e.args)-1)
-            isconst = true
+            ats = Vector{Any}(undef, length(e.args)-1)
+            anyconst = false
+            allconst = true
             for i = 2:length(e.args)
                 at = abstract_eval(e.args[i], vtypes, sv)
+                if !anyconst
+                    anyconst = has_nontrivial_const_info(at)
+                end
+                ats[i-1] = at
                 if at === Bottom
                     t = Bottom
-                    isconst = false
+                    allconst = anyconst = false
                     break
                 elseif at isa Const
                     if !(at.val isa fieldtype(t, i - 1))
                         t = Bottom
-                        isconst = false
+                        allconst = anyconst = false
                         break
                     end
                     args[i-1] = at.val
                 else
-                    isconst = false
+                    allconst = false
                 end
             end
-            if isconst
-                t = Const(ccall(:jl_new_structv, Any, (Any, Ptr{Cvoid}, UInt32), t, args, length(args)))
+            # For now, don't allow partially initialized Const/PartialStruct
+            if t !== Bottom && fieldcount(t) == length(ats)
+                if allconst
+                    t = Const(ccall(:jl_new_structv, Any, (Any, Ptr{Cvoid}, UInt32), t, args, length(args)))
+                elseif anyconst
+                    t = PartialStruct(t, ats)
+                end
             end
         end
     elseif e.head === :splatnew
@@ -1077,7 +1100,7 @@ function typeinf_local(frame::InferenceState)
             elseif hd === :return
                 pc´ = n + 1
                 rt = widenconditional(abstract_eval(stmt.args[1], s[pc], frame))
-                if !isa(rt, Const) && !isa(rt, Type) && !isa(rt, PartialTuple)
+                if !isa(rt, Const) && !isa(rt, Type) && !isa(rt, PartialStruct)
                     # only propagate information we know we can store
                     # and is valid inter-procedurally
                     rt = widenconst(rt)
diff --git a/base/compiler/inferenceresult.jl b/base/compiler/inferenceresult.jl
index ac60ed16c21bfa..8ad8cab76d1237 100644
--- a/base/compiler/inferenceresult.jl
+++ b/base/compiler/inferenceresult.jl
@@ -22,7 +22,7 @@ end
 function is_argtype_match(@nospecialize(given_argtype),
                           @nospecialize(cache_argtype),
                           overridden_by_const::Bool)
-    if isa(given_argtype, Const) || isa(given_argtype, PartialTuple)
+    if isa(given_argtype, Const) || isa(given_argtype, PartialStruct)
         return is_lattice_equal(given_argtype, cache_argtype)
     end
     return !overridden_by_const
@@ -66,7 +66,7 @@ function matching_cache_argtypes(linfo::MethodInstance, ::Nothing)
     nargs::Int = toplevel ? 0 : linfo.def.nargs
     cache_argtypes = Vector{Any}(undef, nargs)
     # First, if we're dealing with a varargs method, then we set the last element of `args`
-    # to the appropriate `Tuple` type or `PartialTuple` instance.
+    # to the appropriate `Tuple` type or `PartialStruct` instance.
     if !toplevel && linfo.def.isva
         if linfo.specTypes == Tuple
             if nargs > 1
diff --git a/base/compiler/ssair/inlining.jl b/base/compiler/ssair/inlining.jl
index 902a0d1aa9a044..9e8c7ab2672e9e 100644
--- a/base/compiler/ssair/inlining.jl
+++ b/base/compiler/ssair/inlining.jl
@@ -583,7 +583,8 @@ function rewrite_apply_exprargs!(ir::IRCode, idx::Int, argexprs::Vector{Any}, at
     for i in 3:length(argexprs)
         def = argexprs[i]
         def_type = atypes[i]
-        if def_type isa PartialTuple
+        if def_type isa PartialStruct
+            # def_type.typ <: Tuple is assumed
             def_atypes = def_type.fields
         else
             def_atypes = Any[]
diff --git a/base/compiler/tfuncs.jl b/base/compiler/tfuncs.jl
index 8cab5eaab4ffbc..c53045c214e376 100644
--- a/base/compiler/tfuncs.jl
+++ b/base/compiler/tfuncs.jl
@@ -716,9 +716,12 @@ function getfield_tfunc(@nospecialize(s00), @nospecialize(name))
             end
         end
         s = typeof(sv)
-    elseif isa(s, PartialTuple)
+    elseif isa(s, PartialStruct)
         if isa(name, Const)
             nv = name.val
+            if isa(nv, Symbol)
+                nv = fieldindex(widenconst(s), nv, false)
+            end
             if isa(nv, Int) && 1 <= nv <= length(s.fields)
                 return s.fields[nv]
             end
@@ -1139,7 +1142,7 @@ function tuple_tfunc(atypes::Vector{Any})
     typ = Tuple{params...}
     # replace a singleton type with its equivalent Const object
     isdefined(typ, :instance) && return Const(typ.instance)
-    return anyinfo ? PartialTuple(typ, atypes) : typ
+    return anyinfo ? PartialStruct(typ, atypes) : typ
 end
 
 function array_type_undefable(@nospecialize(a))
diff --git a/base/compiler/typelattice.jl b/base/compiler/typelattice.jl
index 5a5061102ea94a..e496323ad49540 100644
--- a/base/compiler/typelattice.jl
+++ b/base/compiler/typelattice.jl
@@ -70,7 +70,7 @@ struct StateUpdate
     state::VarTable
 end
 
-struct PartialTuple
+struct PartialStruct
     typ
     fields::Vector{Any} # elements are other type lattice members
 end
@@ -125,8 +125,8 @@ function ⊑(@nospecialize(a), @nospecialize(b))
     elseif isa(b, Conditional)
         return false
     end
-    if isa(a, PartialTuple)
-        if isa(b, PartialTuple)
+    if isa(a, PartialStruct)
+        if isa(b, PartialStruct)
             if !(length(a.fields) == length(b.fields) && a.typ <: b.typ)
                 return false
             end
@@ -137,9 +137,15 @@ function ⊑(@nospecialize(a), @nospecialize(b))
             return true
         end
         return isa(b, Type) && a.typ <: b
-    elseif isa(b, PartialTuple)
+    elseif isa(b, PartialStruct)
         if isa(a, Const)
             nfields(a.val) == length(b.fields) || return false
+            widenconst(b).name === widenconst(a).name || return false
+            # We can skip the subtype check if b is a Tuple, since in that
+            # case, the ⊑ of the elements is sufficient.
+            if b.typ.name !== Tuple.name && !(widenconst(a) <: widenconst(b))
+                return false
+            end
             for i in 1:nfields(a.val)
                 # XXX: let's handle varargs later
                 ⊑(Const(getfield(a.val, i)), b.fields[i]) || return false
@@ -173,15 +179,16 @@ end
 # `a ⊑ b && b ⊑ a` but with extra performance optimizations.
 function is_lattice_equal(@nospecialize(a), @nospecialize(b))
     a === b && return true
-    if isa(a, PartialTuple)
-        isa(b, PartialTuple) || return false
+    if isa(a, PartialStruct)
+        isa(b, PartialStruct) || return false
         length(a.fields) == length(b.fields) || return false
+        widenconst(a) == widenconst(b) || return false
         for i in 1:length(a.fields)
             is_lattice_equal(a.fields[i], b.fields[i]) || return false
         end
         return true
     end
-    isa(b, PartialTuple) && return false
+    isa(b, PartialStruct) && return false
     a isa Const && return false
     b isa Const && return false
     return a ⊑ b && b ⊑ a
@@ -200,7 +207,7 @@ function widenconst(c::Const)
 end
 widenconst(m::MaybeUndef) = widenconst(m.typ)
 widenconst(c::PartialTypeVar) = TypeVar
-widenconst(t::PartialTuple) = t.typ
+widenconst(t::PartialStruct) = t.typ
 widenconst(@nospecialize(t)) = t
 
 issubstate(a::VarState, b::VarState) = (a.typ ⊑ b.typ && a.undef <= b.undef)
diff --git a/base/compiler/typelimits.jl b/base/compiler/typelimits.jl
index 2864e0f93fe7a0..980cfe5f2115b0 100644
--- a/base/compiler/typelimits.jl
+++ b/base/compiler/typelimits.jl
@@ -317,6 +317,27 @@ function tmerge(@nospecialize(typea), @nospecialize(typeb))
         end
         return Bool
     end
+    if (isa(typea, PartialStruct) || isa(typea, Const)) &&
+       (isa(typeb, PartialStruct) || isa(typeb, Const)) &&
+        widenconst(typea) === widenconst(typeb)
+
+       typea_nfields = nfields_tfunc(typea)
+       typeb_nfields = nfields_tfunc(typeb)
+       if !isa(typea_nfields, Const) || !isa(typea_nfields, Const) || typea_nfields.val !== typeb_nfields.val
+            return widenconst(typea)
+       end
+
+       type_nfields = typea_nfields.val::Int
+       fields = Vector{Any}(undef, type_nfields)
+       anyconst = false
+       for i = 1:type_nfields
+            fields[i] = tmerge(getfield_tfunc(typea, Const(i)),
+                               getfield_tfunc(typeb, Const(i)))
+            anyconst |= has_nontrivial_const_info(fields[i])
+       end
+       return anyconst ? PartialStruct(widenconst(typea), fields) :
+            widenconst(typea)
+    end
     # no special type-inference lattice, join the types
     typea, typeb = widenconst(typea), widenconst(typeb)
     typea === typeb && return typea
diff --git a/base/compiler/typeutils.jl b/base/compiler/typeutils.jl
index becbde8bc12a7f..60c7d76f354b5c 100644
--- a/base/compiler/typeutils.jl
+++ b/base/compiler/typeutils.jl
@@ -33,7 +33,7 @@ function issingletontype(@nospecialize t)
 end
 
 function has_nontrivial_const_info(@nospecialize t)
-    isa(t, PartialTuple) && return true
+    isa(t, PartialStruct) && return true
     return isa(t, Const) && !isdefined(typeof(t.val), :instance) && !(isa(t.val, Type) && issingletontype(t.val))
 end
 
diff --git a/base/complex.jl b/base/complex.jl
index 555674b3a5700b..23117f755b7991 100644
--- a/base/complex.jl
+++ b/base/complex.jl
@@ -8,9 +8,6 @@ Complex number type with real and imaginary part of type `T`.
 `ComplexF16`, `ComplexF32` and `ComplexF64` are aliases for
 `Complex{Float16}`, `Complex{Float32}` and `Complex{Float64}` respectively.
 """
-
-import Base.+
-
 struct Complex{T<:Real} <: Number
     re::T
     im::T
@@ -275,10 +272,6 @@ muladd(z::Complex, w::Complex, x::Complex) =
     Complex(muladd(real(z), real(w), real(x)) - imag(z)*imag(w), # TODO: use mulsub given #15985
             muladd(real(z), imag(w), muladd(imag(z), real(w), imag(x))))
 
-#unary + handling Complex{Bool}
-
-+(z::Complex{Bool}) = Complex(+z.re , +z.im)
-
 # handle Bool and Complex{Bool}
 # avoid type signature ambiguity warnings
 +(x::Bool, z::Complex{Bool}) = Complex(x + real(z), imag(z))
diff --git a/src/llvm-late-gc-lowering.cpp b/src/llvm-late-gc-lowering.cpp
index a9831d941d98d6..85ef5deb2e0d4a 100644
--- a/src/llvm-late-gc-lowering.cpp
+++ b/src/llvm-late-gc-lowering.cpp
@@ -821,9 +821,9 @@ void LateLowerGCFrame::NoteUse(State &S, BBState &BBS, Value *V, BitVector &Uses
     else if (isSpecialPtrVec(V->getType())) {
         std::vector<int> Nums = NumberVector(S, V);
         for (int Num : Nums) {
-            MaybeResize(BBS, Num);
             if (Num < 0)
                 continue;
+            MaybeResize(BBS, Num);
             Uses[Num] = 1;
         }
     }
diff --git a/stdlib/LinearAlgebra/src/dense.jl b/stdlib/LinearAlgebra/src/dense.jl
index ae0eb16b8d6628..5ff99e982f2b3e 100644
--- a/stdlib/LinearAlgebra/src/dense.jl
+++ b/stdlib/LinearAlgebra/src/dense.jl
@@ -291,6 +291,8 @@ function diagm_container(kv::Pair{<:Integer,<:BitVector}...)
     return falses(n, n)
 end
 
+diagm(v::AbstractVector) = diagm(0=>v)
+
 
 function tr(A::Matrix{T}) where T
     n = checksquare(A)
diff --git a/stdlib/LinearAlgebra/src/generic.jl b/stdlib/LinearAlgebra/src/generic.jl
index 998e4c1b150eca..471338ceacb18f 100644
--- a/stdlib/LinearAlgebra/src/generic.jl
+++ b/stdlib/LinearAlgebra/src/generic.jl
@@ -785,8 +785,7 @@ julia> rank(diagm(0 => [1, 0.001, 2]), atol=1.5)
 function rank(A::AbstractMatrix; atol::Real = 0.0, rtol::Real = (min(size(A)...)*eps(real(float(one(eltype(A))))))*iszero(atol))
     isempty(A) && return 0 # 0-dimensional case
     s = svdvals(A)
-    sz = size(A)
-    tol = max(atol, sz[1]*sz[2]*rtol*s[1])
+    tol = max(atol, rtol*s[1])
     count(x -> x > tol, s)
 end
 rank(x::Number) = x == 0 ? 0 : 1
diff --git a/test/compiler/inference.jl b/test/compiler/inference.jl
index bc82124de67dd2..e6cac4dd684640 100644
--- a/test/compiler/inference.jl
+++ b/test/compiler/inference.jl
@@ -1338,8 +1338,8 @@ let egal_tfunc
     @test egal_tfunc(Union{Int64, Float64}, AbstractArray) === Const(false)
 end
 
-using Core.Compiler: PartialTuple, nfields_tfunc, sizeof_tfunc, sizeof_nothrow
-let PT = PartialTuple(Tuple{Int64,UInt64}, Any[Const(10, false), UInt64])
+using Core.Compiler: PartialStruct, nfields_tfunc, sizeof_tfunc, sizeof_nothrow
+let PT = PartialStruct(Tuple{Int64,UInt64}, Any[Const(10, false), UInt64])
     @test sizeof_tfunc(PT) === Const(16, false)
     @test nfields_tfunc(PT) === Const(2, false)
     @test sizeof_nothrow(PT) === true
@@ -2261,3 +2261,30 @@ f_incr(x::Tuple, y::Tuple, args...) = f_incr((x, y), args...)
 f_incr(x::Tuple) = x
 @test @inferred(f_incr((), (), (), (), (), (), (), ())) ==
     ((((((((), ()), ()), ()), ()), ()), ()), ())
+
+# Test PartialStruct for closures
+@noinline use30783(x) = nothing
+function foo30783(b)
+    a = 1
+    f = ()->(use30783(b); Val(a))
+    f()
+end
+@test @inferred(foo30783(2)) == Val(1)
+
+# PartialStruct tmerge
+using Core.Compiler: PartialStruct, tmerge, Const, ⊑
+struct FooPartial
+    a::Int
+    b::Int
+    c::Int
+end
+let PT1 = PartialStruct(FooPartial, Any[Const(1), Const(2), Int]),
+    PT2 = PartialStruct(FooPartial, Any[Const(1), Int, Int]),
+    PT3 = PartialStruct(FooPartial, Any[Const(1), Int, Const(3)])
+
+    @test PT1 ⊑ PT2
+    @test !(PT1 ⊑ PT3) && !(PT2 ⊑ PT1)
+    let (==) = (a, b)->(a ⊑ b && b ⊑ a)
+        @test tmerge(PT1, PT3) == PT2
+    end
+end