diff --git a/src/composite/composite.jl b/src/composite/composite.jl
index 901347b72..d80d19bca 100644
--- a/src/composite/composite.jl
+++ b/src/composite/composite.jl
@@ -16,12 +16,12 @@ YaoBase.ishermitian(m::CompositeBlock) = all(ishermitian, subblocks(m)) || isher
 YaoBase.isreflexive(m::CompositeBlock) = all(isreflexive, subblocks(m)) || isreflexive(mat(m))
 
 """
-    AbstractContainer{N, T} <: CompositeBlock{N, T}
+    AbstractContainer{BT, N, T} <: CompositeBlock{N, T}
 
 Abstract type for container block. Container blocks are blocks contain a single
 block. Container block should have a
 """
-abstract type AbstractContainer{N, T, BT <: AbstractBlock} <: CompositeBlock{N, T} end
+abstract type AbstractContainer{BT <: AbstractBlock, N, T} <: CompositeBlock{N, T} end
 
 """
     content(x)
@@ -76,8 +76,8 @@ for METHOD in (:ishermitian, :isreflexive, :isunitary)
     end
 end
 
-function Base.:(==)(lhs::AbstractContainer{N, T, BT},
-        rhs::AbstractContainer{N, T, BT}) where {N, T, BT}
+function Base.:(==)(lhs::AbstractContainer{BT, N, T},
+        rhs::AbstractContainer{BT, N, T}) where {BT, N, T}
     return content(lhs) == content(rhs)
 end
 
diff --git a/src/composite/concentrator.jl b/src/composite/concentrator.jl
index 4bdf03f20..66e0c43bc 100644
--- a/src/composite/concentrator.jl
+++ b/src/composite/concentrator.jl
@@ -2,12 +2,12 @@ using YaoBase
 export Concentrator, concentrate
 
 """
-    Concentrator{N, T, BT <: AbstractBlock} <: AbstractContainer{N, T}
+    Concentrator{N, T, BT <: AbstractBlock} <: AbstractContainer{BT, N, T}
 
 concentrates serveral lines together in the circuit, and expose
 it to other blocks.
 """
-struct Concentrator{N, T, BT <: AbstractBlock, C} <: AbstractContainer{N, T, BT}
+struct Concentrator{N, T, BT <: AbstractBlock, C} <: AbstractContainer{BT, N, T}
     content::BT
     locations::NTuple{C, Int}
 end
diff --git a/src/composite/control.jl b/src/composite/control.jl
index a8a798b16..e6c0b8e65 100644
--- a/src/composite/control.jl
+++ b/src/composite/control.jl
@@ -3,7 +3,7 @@ using YaoArrayRegister: matvec
 
 export ControlBlock, control
 
-struct ControlBlock{N, BT<:AbstractBlock, C, M, T} <: AbstractContainer{N, T, BT}
+struct ControlBlock{N, BT<:AbstractBlock, C, M, T} <: AbstractContainer{BT, N, T}
     ctrl_locs::NTuple{C, Int}
     ctrl_config::NTuple{C, Int}
     content::BT
diff --git a/src/composite/put_block.jl b/src/composite/put_block.jl
index 3ec606cc4..281eafb2b 100644
--- a/src/composite/put_block.jl
+++ b/src/composite/put_block.jl
@@ -5,7 +5,7 @@ export PutBlock, put
 
 Type for putting a block at given locations.
 """
-struct PutBlock{N, C, T, GT <: AbstractBlock} <: AbstractContainer{N, T, GT}
+struct PutBlock{N, C, T, GT <: AbstractBlock} <: AbstractContainer{GT, N, T}
     content::GT
     locs::NTuple{C, Int}
 
diff --git a/src/composite/repeated.jl b/src/composite/repeated.jl
index e356efacc..cd558b6a3 100644
--- a/src/composite/repeated.jl
+++ b/src/composite/repeated.jl
@@ -6,7 +6,7 @@ export RepeatedBlock, repeat
 
 Repeat the same block on given locations.
 """
-struct RepeatedBlock{N, C, GT <: AbstractBlock, T} <: AbstractContainer{N, T, GT}
+struct RepeatedBlock{N, C, GT <: AbstractBlock, T} <: AbstractContainer{GT, N, T}
     content::GT
     locs::NTuple{C, Int}
 end
diff --git a/src/composite/tag/cache.jl b/src/composite/tag/cache.jl
index 589362c77..e80f02fad 100644
--- a/src/composite/tag/cache.jl
+++ b/src/composite/tag/cache.jl
@@ -38,14 +38,14 @@ CacheServers.pull(frag::CacheFragment) = frag.storage[cache_key(frag.ref)]
 CacheServers.clear!(frag::CacheFragment) = (empty!(frag.storage); frag)
 
 """
-    CachedBlock{ST, BT, N, T} <: AbstractContainer{N, T, BT}
+    CachedBlock{ST, BT, N, T} <: TagBlock{BT, N, T}
 
 A label type that tags an instance of type `BT`. It forwards
 every methods of the block it contains, except [`mat`](@ref)
 and [`apply!`](@ref), it will cache the matrix form whenever
 the program has.
 """
-struct CachedBlock{ST, BT, N, T} <: TagBlock{N, T, BT}
+struct CachedBlock{ST, BT, N, T} <: TagBlock{BT, N, T}
     server::ST
     content::BT
     level::Int
diff --git a/src/composite/tag/dagger.jl b/src/composite/tag/dagger.jl
index 0bf87ae77..03dd0b788 100644
--- a/src/composite/tag/dagger.jl
+++ b/src/composite/tag/dagger.jl
@@ -5,12 +5,12 @@ export Daggered
 
 Wrapper block allowing to execute the inverse of a block of quantum circuit.
 """
-struct Daggered{N, T, BT <: AbstractBlock} <: TagBlock{N, T, BT}
+struct Daggered{BT <: AbstractBlock, N, T} <: TagBlock{BT, N, T}
     content::BT
 end
 
 Daggered(x::BT) where {N, T, BT<:AbstractBlock{N, T}} =
-    Daggered{N, T, BT}(x)
+    Daggered{BT, N, T}(x)
 
 PreserveStyle(::Daggered) = PreserveAll()
 mat(blk::Daggered) = adjoint(mat(content(blk)))
diff --git a/src/composite/tag/scale.jl b/src/composite/tag/scale.jl
index 51b70673f..4004bb06b 100644
--- a/src/composite/tag/scale.jl
+++ b/src/composite/tag/scale.jl
@@ -2,7 +2,7 @@ using LinearAlgebra
 
 export Scale
 
-struct Scale{S <: Union{Number, Val}, N, T, BT <: AbstractBlock{N, T}} <: TagBlock{N, T, BT}
+struct Scale{S <: Union{Number, Val}, N, T, BT <: AbstractBlock{N, T}} <: TagBlock{BT, N, T}
     alpha::S
     content::BT
 end
diff --git a/src/composite/tag/tag.jl b/src/composite/tag/tag.jl
index 88af563df..43e698309 100644
--- a/src/composite/tag/tag.jl
+++ b/src/composite/tag/tag.jl
@@ -1,12 +1,12 @@
 export TagBlock
 
 """
-    TagBlock{N, T} <: AbstractContainer{N, T}
+    TagBlock{BT, N, T} <: AbstractContainer{BT, N, T}
 
 `TagBlock` is a special kind of Container block, it forwards most of the methods
 but tag the block with some extra information.
 """
-abstract type TagBlock{N, T, BT} <: AbstractContainer{N, T, BT} end
+abstract type TagBlock{BT, N, T} <: AbstractContainer{BT, N, T} end
 
 cache_key(tb::TagBlock) = cache_key(content(tb))
 occupied_locs(x::TagBlock) = occupied_locs(content(x))
diff --git a/src/layout.jl b/src/layout.jl
index 88fb8312d..b576c8012 100644
--- a/src/layout.jl
+++ b/src/layout.jl
@@ -57,7 +57,7 @@ Base.show(io::IO, ::MIME"plain/text", blk::AbstractBlock) = print_tree(io, blk)
 
 
 function Base.show(io::IO, ::MIME"plain/text",
-        blk::TagBlock{N, T, <:PrimitiveBlock}) where {N, T}
+        blk::TagBlock{<:PrimitiveBlock})
     return print_tree(io, blk; title=false, compact=false)
 end