diff --git a/base/random/RNGs.jl b/base/random/RNGs.jl
index e27a24b42c2d6..aa559c5f4a8ed 100644
--- a/base/random/RNGs.jl
+++ b/base/random/RNGs.jl
@@ -284,12 +284,12 @@ rng_native_52(::MersenneTwister) = Float64
 #### helper functions
 
 # precondition: !mt_empty(r)
-rand_inbounds(r::MersenneTwister, ::Close1Open2_64) = mt_pop!(r)
-rand_inbounds(r::MersenneTwister, ::CloseOpen_64=CloseOpen()) =
-    rand_inbounds(r, Close1Open2()) - 1.0
+rand_inbounds(r::MersenneTwister, ::CloseOpen12_64) = mt_pop!(r)
+rand_inbounds(r::MersenneTwister, ::CloseOpen01_64=CloseOpen01()) =
+    rand_inbounds(r, CloseOpen12()) - 1.0
 
 rand_inbounds(r::MersenneTwister, ::UInt52Raw{T}) where {T<:BitInteger} =
-    reinterpret(UInt64, rand_inbounds(r, Close1Open2())) % T
+    reinterpret(UInt64, rand_inbounds(r, CloseOpen12())) % T
 
 function rand(r::MersenneTwister, x::SamplerTrivial{UInt52Raw{UInt64}})
     reserve_1(r)
@@ -308,7 +308,7 @@ end
 
 #### floats
 
-rand(r::MersenneTwister, sp::SamplerTrivial{Close1Open2_64}) =
+rand(r::MersenneTwister, sp::SamplerTrivial{CloseOpen12_64}) =
     (reserve_1(r); rand_inbounds(r, sp[]))
 
 #### integers
@@ -377,7 +377,7 @@ function _rand_max383!(r::MersenneTwister, A::UnsafeView{Float64}, I::FloatInter
         @gc_preserve r unsafe_copyto!(A.ptr+m*sizeof(Float64), pointer(r.vals), n-m)
         r.idxF = n-m
     end
-    if I isa CloseOpen
+    if I isa CloseOpen01
         for i=1:n
             A[i] -= 1.0
         end
@@ -386,10 +386,10 @@ function _rand_max383!(r::MersenneTwister, A::UnsafeView{Float64}, I::FloatInter
 end
 
 
-fill_array!(s::DSFMT_state, A::Ptr{Float64}, n::Int, ::CloseOpen_64) =
+fill_array!(s::DSFMT_state, A::Ptr{Float64}, n::Int, ::CloseOpen01_64) =
     dsfmt_fill_array_close_open!(s, A, n)
 
-fill_array!(s::DSFMT_state, A::Ptr{Float64}, n::Int, ::Close1Open2_64) =
+fill_array!(s::DSFMT_state, A::Ptr{Float64}, n::Int, ::CloseOpen12_64) =
     dsfmt_fill_array_close1_open2!(s, A, n)
 
 
@@ -440,10 +440,10 @@ mask128(u::UInt128, ::Type{Float32}) =
     (u & 0x007fffff007fffff007fffff007fffff) | 0x3f8000003f8000003f8000003f800000
 
 for T in (Float16, Float32)
-    @eval function rand!(r::MersenneTwister, A::Array{$T}, ::SamplerTrivial{Close1Open2{$T}})
+    @eval function rand!(r::MersenneTwister, A::Array{$T}, ::SamplerTrivial{CloseOpen12{$T}})
         n = length(A)
         n128 = n * sizeof($T) ÷ 16
-        _rand!(r, A, 2*n128, Close1Open2())
+        _rand!(r, A, 2*n128, CloseOpen12())
         @gc_preserve A begin
             A128 = UnsafeView{UInt128}(pointer(A), n128)
             for i in 1:n128
@@ -468,8 +468,8 @@ for T in (Float16, Float32)
         A
     end
 
-    @eval function rand!(r::MersenneTwister, A::Array{$T}, ::SamplerTrivial{CloseOpen{$T}})
-        rand!(r, A, Close1Open2($T))
+    @eval function rand!(r::MersenneTwister, A::Array{$T}, ::SamplerTrivial{CloseOpen01{$T}})
+        rand!(r, A, CloseOpen12($T))
         I32 = one(Float32)
         for i in eachindex(A)
             @inbounds A[i] = Float32(A[i])-I32 # faster than "A[i] -= one(T)" for T==Float16
@@ -484,7 +484,7 @@ function rand!(r::MersenneTwister, A::UnsafeView{UInt128}, ::SamplerType{UInt128
     n::Int=length(A)
     i = n
     while true
-        rand!(r, UnsafeView{Float64}(A.ptr, 2i), Close1Open2())
+        rand!(r, UnsafeView{Float64}(A.ptr, 2i), CloseOpen12())
         n < 5 && break
         i = 0
         while n-i >= 5
diff --git a/base/random/generation.jl b/base/random/generation.jl
index 363d09817699e..0d36a6a7c9f5b 100644
--- a/base/random/generation.jl
+++ b/base/random/generation.jl
@@ -17,29 +17,29 @@
 ### random floats
 
 Sampler(rng::AbstractRNG, ::Type{T}, n::Repetition) where {T<:AbstractFloat} =
-    Sampler(rng, CloseOpen(T), n)
+    Sampler(rng, CloseOpen01(T), n)
 
 # generic random generation function which can be used by RNG implementors
 # it is not defined as a fallback rand method as this could create ambiguities
 
-rand(r::AbstractRNG, ::SamplerTrivial{CloseOpen{Float16}}) =
+rand(r::AbstractRNG, ::SamplerTrivial{CloseOpen01{Float16}}) =
     Float16(reinterpret(Float32,
                         (rand(r, UInt10(UInt32)) << 13)  | 0x3f800000) - 1)
 
-rand(r::AbstractRNG, ::SamplerTrivial{CloseOpen{Float32}}) =
+rand(r::AbstractRNG, ::SamplerTrivial{CloseOpen01{Float32}}) =
     reinterpret(Float32, rand(r, UInt23()) | 0x3f800000) - 1
 
-rand(r::AbstractRNG, ::SamplerTrivial{Close1Open2_64}) =
+rand(r::AbstractRNG, ::SamplerTrivial{CloseOpen12_64}) =
     reinterpret(Float64, 0x3ff0000000000000 | rand(r, UInt52()))
 
-rand(r::AbstractRNG, ::SamplerTrivial{CloseOpen_64}) = rand(r, Close1Open2()) - 1.0
+rand(r::AbstractRNG, ::SamplerTrivial{CloseOpen01_64}) = rand(r, CloseOpen12()) - 1.0
 
 #### BigFloat
 
 const bits_in_Limb = sizeof(Limb) << 3
 const Limb_high_bit = one(Limb) << (bits_in_Limb-1)
 
-struct SamplerBigFloat{I<:FloatInterval{BigFloat}} <: Sampler
+struct SamplerBigFloat{I<:FloatInterval{BigFloat}} <: Sampler{BigFloat}
     prec::Int
     nlimbs::Int
     limbs::Vector{Limb}
@@ -70,13 +70,13 @@ function _rand(rng::AbstractRNG, sp::SamplerBigFloat)
     (z, randbool)
 end
 
-function _rand(rng::AbstractRNG, sp::SamplerBigFloat, ::Close1Open2{BigFloat})
+function _rand(rng::AbstractRNG, sp::SamplerBigFloat, ::CloseOpen12{BigFloat})
     z = _rand(rng, sp)[1]
     z.exp = 1
     z
 end
 
-function _rand(rng::AbstractRNG, sp::SamplerBigFloat, ::CloseOpen{BigFloat})
+function _rand(rng::AbstractRNG, sp::SamplerBigFloat, ::CloseOpen01{BigFloat})
     z, randbool = _rand(rng, sp)
     z.exp = 0
     randbool &&
@@ -88,8 +88,8 @@ end
 
 # alternative, with 1 bit less of precision
 # TODO: make an API for requesting full or not-full precision
-function _rand(rng::AbstractRNG, sp::SamplerBigFloat, ::CloseOpen{BigFloat}, ::Nothing)
-    z = _rand(rng, sp, Close1Open2(BigFloat))
+function _rand(rng::AbstractRNG, sp::SamplerBigFloat, ::CloseOpen01{BigFloat}, ::Nothing)
+    z = _rand(rng, sp, CloseOpen12(BigFloat))
     ccall((:mpfr_sub_ui, :libmpfr), Int32, (Ref{BigFloat}, Ref{BigFloat}, Culong, Int32),
           z, z, 1, Base.MPFR.ROUNDING_MODE[])
     z
@@ -108,7 +108,7 @@ rand(r::AbstractRNG, ::SamplerTrivial{UInt23Raw{UInt32}}) = rand(r, UInt32)
 rand(r::AbstractRNG, ::SamplerTrivial{UInt52Raw{UInt64}}) =
     _rand52(r, rng_native_52(r))
 
-_rand52(r::AbstractRNG, ::Type{Float64}) = reinterpret(UInt64, rand(r, Close1Open2()))
+_rand52(r::AbstractRNG, ::Type{Float64}) = reinterpret(UInt64, rand(r, CloseOpen12()))
 _rand52(r::AbstractRNG, ::Type{UInt64})  = rand(r, UInt64)
 
 rand(r::AbstractRNG, ::SamplerTrivial{UInt104Raw{UInt128}}) =
@@ -182,7 +182,7 @@ uint_sup(::Type{<:Union{Int128,UInt128}}) = UInt128
 
 #### Fast
 
-struct SamplerRangeFast{U<:BitUnsigned,T<:BitInteger} <: Sampler
+struct SamplerRangeFast{U<:BitUnsigned,T<:BitInteger} <: Sampler{T}
     a::T      # first element of the range
     bw::UInt  # bit width
     m::U      # range length - 1
@@ -243,7 +243,7 @@ maxmultiple(k::T, sup::T=zero(T)) where {T<:Unsigned} =
 unsafe_maxmultiple(k::T, sup::T) where {T<:Unsigned} =
     div(sup, k + (k == 0))*k - one(k)
 
-struct SamplerRangeInt{T<:Integer,U<:Unsigned} <: Sampler
+struct SamplerRangeInt{T<:Integer,U<:Unsigned} <: Sampler{T}
     a::T      # first element of the range
     bw::Int   # bit width
     k::U      # range length or zero for full range
@@ -298,7 +298,7 @@ end
 
 ### BigInt
 
-struct SamplerBigInt <: Sampler
+struct SamplerBigInt <: Sampler{BigInt}
     a::BigInt         # first
     m::BigInt         # range length - 1
     nlimbs::Int       # number of limbs in generated BigInt's (z ∈ [0, m])
@@ -364,9 +364,10 @@ end
 
 ## random values from Set
 
-Sampler(rng::AbstractRNG, t::Set, n::Repetition) = SamplerTag{Set}(Sampler(rng, t.dict, n))
+Sampler(rng::AbstractRNG, t::Set{T}, n::Repetition) where {T} =
+    SamplerTag{Set{T}}(Sampler(rng, t.dict, n))
 
-rand(rng::AbstractRNG, sp::SamplerTag{Set,<:Sampler}) = rand(rng, sp.data).first
+rand(rng::AbstractRNG, sp::SamplerTag{<:Set,<:Sampler}) = rand(rng, sp.data).first
 
 ## random values from BitSet
 
diff --git a/base/random/random.jl b/base/random/random.jl
index 2af2bcc31935c..a8d18aedf6c86 100644
--- a/base/random/random.jl
+++ b/base/random/random.jl
@@ -26,6 +26,7 @@ export srand,
 
 abstract type AbstractRNG end
 
+
 ### integers
 
 # we define types which encode the generation of a specific number of bits
@@ -67,15 +68,15 @@ end
 
 abstract type FloatInterval{T<:AbstractFloat} end
 
-struct CloseOpen{  T<:AbstractFloat} <: FloatInterval{T} end # interval [0,1)
-struct Close1Open2{T<:AbstractFloat} <: FloatInterval{T} end # interval [1,2)
+struct CloseOpen01{T<:AbstractFloat} <: FloatInterval{T} end # interval [0,1)
+struct CloseOpen12{T<:AbstractFloat} <: FloatInterval{T} end # interval [1,2)
 
 const FloatInterval_64 = FloatInterval{Float64}
-const CloseOpen_64     = CloseOpen{Float64}
-const Close1Open2_64   = Close1Open2{Float64}
+const CloseOpen01_64   = CloseOpen01{Float64}
+const CloseOpen12_64   = CloseOpen12{Float64}
 
-CloseOpen(  ::Type{T}=Float64) where {T<:AbstractFloat} = CloseOpen{T}()
-Close1Open2(::Type{T}=Float64) where {T<:AbstractFloat} = Close1Open2{T}()
+CloseOpen01(::Type{T}=Float64) where {T<:AbstractFloat} = CloseOpen01{T}()
+CloseOpen12(::Type{T}=Float64) where {T<:AbstractFloat} = CloseOpen12{T}()
 
 Base.eltype(::Type{<:FloatInterval{T}}) where {T<:AbstractFloat} = T
 
@@ -83,7 +84,9 @@ const BitFloatType = Union{Type{Float16},Type{Float32},Type{Float64}}
 
 ### Sampler
 
-abstract type Sampler end
+abstract type Sampler{E} end
+
+Base.eltype(::Sampler{E}) where {E} = E
 
 # temporarily for BaseBenchmarks
 RangeGenerator(x) = Sampler(GLOBAL_RNG, x)
@@ -109,41 +112,48 @@ Sampler(rng::AbstractRNG, ::Type{X}) where {X} = Sampler(rng, X, Val(Inf))
 #### pre-defined useful Sampler types
 
 # default fall-back for types
-struct SamplerType{T} <: Sampler end
+struct SamplerType{T} <: Sampler{T} end
 
 Sampler(::AbstractRNG, ::Type{T}, ::Repetition) where {T} = SamplerType{T}()
 
-Base.getindex(sp::SamplerType{T}) where {T} = T
+Base.getindex(::SamplerType{T}) where {T} = T
 
 # default fall-back for values
-struct SamplerTrivial{T} <: Sampler
+struct SamplerTrivial{T,E} <: Sampler{E}
     self::T
 end
 
-Sampler(::AbstractRNG, X, ::Repetition) = SamplerTrivial(X)
+SamplerTrivial(x::T) where {T} = SamplerTrivial{T,eltype(T)}(x)
+
+Sampler(::AbstractRNG, x, ::Repetition) = SamplerTrivial(x)
 
 Base.getindex(sp::SamplerTrivial) = sp.self
 
 # simple sampler carrying data (which can be anything)
-struct SamplerSimple{T,S} <: Sampler
+struct SamplerSimple{T,S,E} <: Sampler{E}
     self::T
     data::S
 end
 
+SamplerSimple(x::T, data::S) where {T,S} = SamplerSimple{T,S,eltype(T)}(x, data)
+
 Base.getindex(sp::SamplerSimple) = sp.self
 
 # simple sampler carrying a (type) tag T and data
-struct SamplerTag{T,S} <: Sampler
+struct SamplerTag{T,S,E} <: Sampler{E}
     data::S
-    SamplerTag{T}(s::S) where {T,S} = new{T,S}(s)
+    SamplerTag{T}(s::S) where {T,S} = new{T,S,eltype(T)}(s)
 end
 
 
 #### helper samplers
 
+# TODO: make constraining constructors to enforce that those
+# types are <: Sampler{T}
+
 ##### Adapter to generate a randome value in [0, n]
 
-struct LessThan{T<:Integer,S} <: Sampler
+struct LessThan{T<:Integer,S} <: Sampler{T}
     sup::T
     s::S    # the scalar specification/sampler to feed to rand
 end
@@ -155,7 +165,7 @@ function rand(rng::AbstractRNG, sp::LessThan)
     end
 end
 
-struct Masked{T<:Integer,S} <: Sampler
+struct Masked{T<:Integer,S} <: Sampler{T}
     mask::T
     s::S
 end
@@ -164,7 +174,7 @@ rand(rng::AbstractRNG, sp::Masked) = rand(rng, sp.s) & sp.mask
 
 ##### Uniform
 
-struct UniformT{T} <: Sampler end
+struct UniformT{T} <: Sampler{T} end
 
 uniform(::Type{T}) where {T} = UniformT{T}()
 
diff --git a/test/random.jl b/test/random.jl
index 392afc86a662c..2bfc6651d0120 100644
--- a/test/random.jl
+++ b/test/random.jl
@@ -289,8 +289,8 @@ let mt = MersenneTwister(0)
     @test rand!(mt, AF64)[end] == 0.957735065345398
     @test rand!(mt, AF64)[end] == 0.6492481059865669
     resize!(AF64, 2*length(mt.vals))
-    @test invoke(rand!, Tuple{MersenneTwister,AbstractArray{Float64},Base.Random.SamplerTrivial{Base.Random.CloseOpen_64}},
-                 mt, AF64, Base.Random.SamplerTrivial(Base.Random.CloseOpen()))[end]  == 0.1142787906708973
+    @test invoke(rand!, Tuple{MersenneTwister,AbstractArray{Float64},Base.Random.SamplerTrivial{Base.Random.CloseOpen01_64}},
+                 mt, AF64, Base.Random.SamplerTrivial(Base.Random.CloseOpen01()))[end]  == 0.1142787906708973
 end
 
 # Issue #9037