diff --git a/Project.toml b/Project.toml
index 4f9cd4d..9364d5d 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,7 +1,7 @@
 name = "FunctionImplementations"
 uuid = "7c7cc465-9c6a-495f-bdd1-f42428e86d0c"
 authors = ["ITensor developers <support@itensor.org> and contributors"]
-version = "0.3.2"
+version = "0.4.0"
 
 [weakdeps]
 BlockArrays = "8e7c35d0-a365-5155-bbbb-fb81a777f24e"
diff --git a/docs/Project.toml b/docs/Project.toml
index 1475a9a..6bd95ce 100644
--- a/docs/Project.toml
+++ b/docs/Project.toml
@@ -9,4 +9,4 @@ FunctionImplementations = {path = ".."}
 [compat]
 Documenter = "1"
 Literate = "2"
-FunctionImplementations = "0.3"
+FunctionImplementations = "0.4"
diff --git a/examples/Project.toml b/examples/Project.toml
index 964c01d..2706863 100644
--- a/examples/Project.toml
+++ b/examples/Project.toml
@@ -5,4 +5,4 @@ FunctionImplementations = "7c7cc465-9c6a-495f-bdd1-f42428e86d0c"
 FunctionImplementations = {path = ".."}
 
 [compat]
-FunctionImplementations = "0.3"
+FunctionImplementations = "0.4"
diff --git a/ext/FunctionImplementationsLinearAlgebraExt/FunctionImplementationsLinearAlgebraExt.jl b/ext/FunctionImplementationsLinearAlgebraExt/FunctionImplementationsLinearAlgebraExt.jl
index a2bc3ba..7fe5808 100644
--- a/ext/FunctionImplementationsLinearAlgebraExt/FunctionImplementationsLinearAlgebraExt.jl
+++ b/ext/FunctionImplementationsLinearAlgebraExt/FunctionImplementationsLinearAlgebraExt.jl
@@ -3,9 +3,9 @@ module FunctionImplementationsLinearAlgebraExt
 import FunctionImplementations as FI
 import LinearAlgebra as LA
 
-struct DiagonalStyle <: FI.AbstractArrayStyle end
-FI.Style(::Type{<:LA.Diagonal}) = DiagonalStyle()
-const permuteddims_diag = DiagonalStyle()(FI.permuteddims)
+struct DiagonalImplementationStyle <: FI.AbstractArrayImplementationStyle end
+FI.ImplementationStyle(::Type{<:LA.Diagonal}) = DiagonalImplementationStyle()
+const permuteddims_diag = DiagonalImplementationStyle()(FI.permuteddims)
 function permuteddims_diag(a::AbstractArray, perm)
     (ndims(a) == length(perm) && isperm(perm)) ||
         throw(ArgumentError("no valid permutation of dimensions"))
diff --git a/src/style.jl b/src/style.jl
index 64ec3f4..5f66f1b 100644
--- a/src/style.jl
+++ b/src/style.jl
@@ -1,156 +1,156 @@
 ### This is based on the BroadcastStyle code in
 ### https://github.com/JuliaLang/julia/blob/master/base/broadcast.jl
-### Objects with customized behavior for a certain function should declare a Style
+### Objects with customized behavior for a certain function should declare a ImplementationStyle
 
 """
-`Style` is an abstract type and trait-function used to determine behavior of
-objects. `Style(typeof(x))` returns the style associated
+`ImplementationStyle` is an abstract type and trait-function used to determine behavior of
+objects. `ImplementationStyle(typeof(x))` returns the style associated
 with `x`. To customize the behavior of a type, one can declare a style
 by defining a type/method pair
 
-    struct MyContainerStyle <: Style end
-    FunctionImplementations.Style(::Type{<:MyContainer}) = MyContainerStyle()
+    struct MyContainerImplementationStyle <: ImplementationStyle end
+    FunctionImplementations.ImplementationStyle(::Type{<:MyContainer}) = MyContainerImplementationStyle()
     
 """
-abstract type Style end
-Style(::Type{T}) where {T} = throw(MethodError(Style, (T,)))
+abstract type ImplementationStyle end
+ImplementationStyle(::Type{T}) where {T} = throw(MethodError(ImplementationStyle, (T,)))
 
-struct UnknownStyle <: Style end
-Style(::Type{Union{}}, slurp...) = UnknownStyle()  # ambiguity resolution
+struct UnknownImplementationStyle <: ImplementationStyle end
+ImplementationStyle(::Type{Union{}}, slurp...) = UnknownImplementationStyle()  # ambiguity resolution
 
 """
-    (s::Style)(f)
+    (s::ImplementationStyle)(f)
 
-Calling a Style `s` with a function `f` as `s(f)` is a shorthand for creating a
+Calling a ImplementationStyle `s` with a function `f` as `s(f)` is a shorthand for creating a
 [`FunctionImplementations.Implementation`](@ref) object wrapping the function `f` with
-Style `s`.
+ImplementationStyle `s`.
 """
-(s::Style)(f) = Implementation(f, s)
+(s::ImplementationStyle)(f) = Implementation(f, s)
 
 """
-`FunctionImplementations.AbstractArrayStyle <: Style` is the abstract supertype for any style
+`FunctionImplementations.AbstractArrayImplementationStyle <: ImplementationStyle` is the abstract supertype for any style
 associated with an `AbstractArray` type.
 
-Note that if two or more `AbstractArrayStyle` subtypes conflict, the resulting
+Note that if two or more `AbstractArrayImplementationStyle` subtypes conflict, the resulting
 style will fall back to that of `Array`s. If this is undesirable, you may need to
-define binary [`Style`](@ref) rules to control the output type.
+define binary [`ImplementationStyle`](@ref) rules to control the output type.
 
-See also [`FunctionImplementations.DefaultArrayStyle`](@ref).
+See also [`FunctionImplementations.DefaultArrayImplementationStyle`](@ref).
 """
-abstract type AbstractArrayStyle <: Style end
+abstract type AbstractArrayImplementationStyle <: ImplementationStyle end
 
 """
-`FunctionImplementations.DefaultArrayStyle()` is a [`FunctionImplementations.Style`](@ref)
-indicating that an object behaves as an array. Specifically, `DefaultArrayStyle` is
+`FunctionImplementations.DefaultArrayImplementationStyle()` is a [`FunctionImplementations.ImplementationStyle`](@ref)
+indicating that an object behaves as an array. Specifically, `DefaultArrayImplementationStyle` is
 used for any `AbstractArray` type that hasn't defined a specialized style, and in the
 absence of overrides from other arguments the resulting output type is `Array`.
 """
-struct DefaultArrayStyle <: AbstractArrayStyle end
-Style(::Type{<:AbstractArray}) = DefaultArrayStyle()
+struct DefaultArrayImplementationStyle <: AbstractArrayImplementationStyle end
+ImplementationStyle(::Type{<:AbstractArray}) = DefaultArrayImplementationStyle()
 
-# `ArrayConflict` is an internal type signaling that two or more different `AbstractArrayStyle`
+# `ArrayImplementationConflict` is an internal type signaling that two or more different `AbstractArrayImplementationStyle`
 # objects were supplied as arguments, and that no rule was defined for resolving the
 # conflict. The resulting output is `Array`. While this is the same output type
-# produced by `DefaultArrayStyle`, `ArrayConflict` "poisons" the Style so that
-# 3 or more arguments still return an `ArrayConflict`.
-struct ArrayConflict <: AbstractArrayStyle end
+# produced by `DefaultArrayImplementationStyle`, `ArrayImplementationConflict` "poisons" the ImplementationStyle so that
+# 3 or more arguments still return an `ArrayImplementationConflict`.
+struct ArrayImplementationConflict <: AbstractArrayImplementationStyle end
 
-### Binary Style rules
+### Binary ImplementationStyle rules
 """
-    Style(::Style1, ::Style2) = Style3()
+    ImplementationStyle(::ImplementationStyle1, ::ImplementationStyle2) = ImplementationStyle3()
 
-Indicate how to resolve different `Style`s. For example,
+Indicate how to resolve different `ImplementationStyle`s. For example,
 
-    Style(::Primary, ::Secondary) = Primary()
+    ImplementationStyle(::Primary, ::Secondary) = Primary()
 
 would indicate that style `Primary` has precedence over `Secondary`.
 You do not have to (and generally should not) define both argument orders.
 The result does not have to be one of the input arguments, it could be a third type.
 """
-Style(::S, ::S) where {S <: Style} = S() # homogeneous types preserved
-# Fall back to UnknownStyle. This is necessary to implement argument-swapping
-Style(::Style, ::Style) = UnknownStyle()
-# UnknownStyle loses to everything
-Style(::UnknownStyle, ::UnknownStyle) = UnknownStyle()
-Style(::S, ::UnknownStyle) where {S <: Style} = S()
+ImplementationStyle(::S, ::S) where {S <: ImplementationStyle} = S() # homogeneous types preserved
+# Fall back to UnknownImplementationStyle. This is necessary to implement argument-swapping
+ImplementationStyle(::ImplementationStyle, ::ImplementationStyle) = UnknownImplementationStyle()
+# UnknownImplementationStyle loses to everything
+ImplementationStyle(::UnknownImplementationStyle, ::UnknownImplementationStyle) = UnknownImplementationStyle()
+ImplementationStyle(::S, ::UnknownImplementationStyle) where {S <: ImplementationStyle} = S()
 # Precedence rules
-Style(::A, ::A) where {A <: AbstractArrayStyle} = A()
-function Style(a::A, b::B) where {A <: AbstractArrayStyle, B <: AbstractArrayStyle}
+ImplementationStyle(::A, ::A) where {A <: AbstractArrayImplementationStyle} = A()
+function ImplementationStyle(a::A, b::B) where {A <: AbstractArrayImplementationStyle, B <: AbstractArrayImplementationStyle}
     if Base.typename(A) ≡ Base.typename(B)
         return A()
     end
-    return UnknownStyle()
+    return UnknownImplementationStyle()
 end
-# Any specific array type beats DefaultArrayStyle
-Style(a::AbstractArrayStyle, ::DefaultArrayStyle) = a
+# Any specific array type beats DefaultArrayImplementationStyle
+ImplementationStyle(a::AbstractArrayImplementationStyle, ::DefaultArrayImplementationStyle) = a
 
-## logic for deciding the Style
+## logic for deciding the ImplementationStyle
 
 """
-    style(cs...)::Style
+    style(cs...)::ImplementationStyle
 
-Decides which `Style` to use for any number of value arguments.
-Uses [`Style`](@ref) to get the style for each argument, and uses
+Decides which `ImplementationStyle` to use for any number of value arguments.
+Uses [`ImplementationStyle`](@ref) to get the style for each argument, and uses
 [`result_style`](@ref) to combine styles.
 
 # Examples
 ```jldoctest
 julia> FunctionImplementations.style([1], [1 2; 3 4])
-FunctionImplementations.DefaultArrayStyle()
+FunctionImplementations.DefaultArrayImplementationStyle()
 ```
 """
 function style end
 
-style() = DefaultArrayStyle()
-style(c) = result_style(Style(typeof(c)))
+style() = DefaultArrayImplementationStyle()
+style(c) = result_style(ImplementationStyle(typeof(c)))
 style(c1, c2) = result_style(style(c1), style(c2))
 @inline style(c1, c2, cs...) = result_style(style(c1), style(c2, cs...))
 
 """
-    result_style(s1::Style[, s2::Style])::Style
+    result_style(s1::ImplementationStyle[, s2::ImplementationStyle])::ImplementationStyle
 
-Takes one or two `Style`s and combines them using [`Style`](@ref) to
-determine a common `Style`.
+Takes one or two `ImplementationStyle`s and combines them using [`ImplementationStyle`](@ref) to
+determine a common `ImplementationStyle`.
 
 # Examples
 
 ```jldoctest
-julia> FunctionImplementations.result_style(FunctionImplementations.DefaultArrayStyle(), FunctionImplementations.DefaultArrayStyle())
-FunctionImplementations.DefaultArrayStyle()
+julia> FunctionImplementations.result_style(FunctionImplementations.DefaultArrayImplementationStyle(), FunctionImplementations.DefaultArrayImplementationStyle())
+FunctionImplementations.DefaultArrayImplementationStyle()
 
-julia> FunctionImplementations.result_style(FunctionImplementations.UnknownStyle(), FunctionImplementations.DefaultArrayStyle())
-FunctionImplementations.DefaultArrayStyle()
+julia> FunctionImplementations.result_style(FunctionImplementations.UnknownImplementationStyle(), FunctionImplementations.DefaultArrayImplementationStyle())
+FunctionImplementations.DefaultArrayImplementationStyle()
 ```
 """
 function result_style end
 
-result_style(s::Style) = s
-function result_style(s1::S, s2::S) where {S <: Style}
+result_style(s::ImplementationStyle) = s
+function result_style(s1::S, s2::S) where {S <: ImplementationStyle}
     return s1 ≡ s2 ? s1 : error("inconsistent styles, custom rule needed")
 end
 # Test both orders so users typically only have to declare one order
-result_style(s1, s2) = result_join(s1, s2, Style(s1, s2), Style(s2, s1))
+result_style(s1, s2) = result_join(s1, s2, ImplementationStyle(s1, s2), ImplementationStyle(s2, s1))
 
-# result_join is the final arbiter. Because `Style` for undeclared pairs results in UnknownStyle,
-# we defer to any case where the result of `Style` is known.
-result_join(::Any, ::Any, ::UnknownStyle, ::UnknownStyle) = UnknownStyle()
-result_join(::Any, ::Any, ::UnknownStyle, s::Style) = s
-result_join(::Any, ::Any, s::Style, ::UnknownStyle) = s
+# result_join is the final arbiter. Because `ImplementationStyle` for undeclared pairs results in UnknownImplementationStyle,
+# we defer to any case where the result of `ImplementationStyle` is known.
+result_join(::Any, ::Any, ::UnknownImplementationStyle, ::UnknownImplementationStyle) = UnknownImplementationStyle()
+result_join(::Any, ::Any, ::UnknownImplementationStyle, s::ImplementationStyle) = s
+result_join(::Any, ::Any, s::ImplementationStyle, ::UnknownImplementationStyle) = s
 # For AbstractArray types with undefined precedence rules,
-# we have to signal conflict. Because ArrayConflict is a subtype of AbstractArray,
-# this will "poison" any future operations (if we instead returned `DefaultArrayStyle`, then for
+# we have to signal conflict. Because ArrayImplementationConflict is a subtype of AbstractArray,
+# this will "poison" any future operations (if we instead returned `DefaultArrayImplementationStyle`, then for
 # 3-array functions returned type would depend on argument order).
-result_join(::AbstractArrayStyle, ::AbstractArrayStyle, ::UnknownStyle, ::UnknownStyle) =
-    ArrayConflict()
+result_join(::AbstractArrayImplementationStyle, ::AbstractArrayImplementationStyle, ::UnknownImplementationStyle, ::UnknownImplementationStyle) =
+    ArrayImplementationConflict()
 # Fallbacks in case users define `rule` for both argument-orders (not recommended)
-result_join(::Any, ::Any, s1::S, s2::S) where {S <: Style} = result_style(s1, s2)
+result_join(::Any, ::Any, s1::S, s2::S) where {S <: ImplementationStyle} = result_style(s1, s2)
 
 @noinline function result_join(::S, ::T, ::U, ::V) where {S, T, U, V}
     error(
         """
         conflicting rules defined
-          FunctionImplementations.Style(::$S, ::$T) = $U()
-          FunctionImplementations.Style(::$T, ::$S) = $V()
-        One of these should be undefined (and thus return FunctionImplementations.UnknownStyle)."""
+          FunctionImplementations.ImplementationStyle(::$S, ::$T) = $U()
+          FunctionImplementations.ImplementationStyle(::$T, ::$S) = $V()
+        One of these should be undefined (and thus return FunctionImplementations.UnknownImplementationStyle)."""
     )
 end
diff --git a/test/Project.toml b/test/Project.toml
index b74165f..db796c7 100644
--- a/test/Project.toml
+++ b/test/Project.toml
@@ -19,7 +19,7 @@ Adapt = "4"
 Aqua = "0.8"
 BlockArrays = "1.4"
 FillArrays = "1.15"
-FunctionImplementations = "0.3"
+FunctionImplementations = "0.4"
 JLArrays = "0.3"
 LinearAlgebra = "1.10"
 SafeTestsets = "0.1"
diff --git a/test/test_basics.jl b/test/test_basics.jl
index ce3f353..b872604 100644
--- a/test/test_basics.jl
+++ b/test/test_basics.jl
@@ -12,78 +12,78 @@ using Test: @test, @testset
         @test f.f ≡ +
         @test f.style ≡ MyAddAlgorithm()
     end
-    @testset "(s::Style)(f)" begin
-        # Test the shorthand for creating an Implementation by calling a Style with a
+    @testset "(s::ImplementationStyle)(f)" begin
+        # Test the shorthand for creating an Implementation by calling a ImplementationStyle with a
         # function.
         @test FI.style([1, 2, 3])(getindex) ≡
-            FI.Implementation(getindex, FI.DefaultArrayStyle())
+            FI.Implementation(getindex, FI.DefaultArrayImplementationStyle())
     end
-    @testset "Style" begin
-        # Test basic Style trait for different array types
-        @test FI.Style(typeof([1, 2, 3])) ≡ FI.DefaultArrayStyle()
-        @test FI.style([1, 2, 3]) ≡ FI.DefaultArrayStyle()
-        @test FI.Style(typeof([1 2; 3 4])) ≡ FI.DefaultArrayStyle()
-        @test FI.Style(typeof(rand(2, 3, 4))) ≡ FI.DefaultArrayStyle()
+    @testset "ImplementationStyle" begin
+        # Test basic ImplementationStyle trait for different array types
+        @test FI.ImplementationStyle(typeof([1, 2, 3])) ≡ FI.DefaultArrayImplementationStyle()
+        @test FI.style([1, 2, 3]) ≡ FI.DefaultArrayImplementationStyle()
+        @test FI.ImplementationStyle(typeof([1 2; 3 4])) ≡ FI.DefaultArrayImplementationStyle()
+        @test FI.ImplementationStyle(typeof(rand(2, 3, 4))) ≡ FI.DefaultArrayImplementationStyle()
 
-        # Test custom Style definition
-        struct CustomStyle <: FI.Style end
+        # Test custom ImplementationStyle definition
+        struct CustomImplementationStyle <: FI.ImplementationStyle end
         struct CustomArray end
-        FI.Style(::Type{CustomArray}) = CustomStyle()
-        @test FI.Style(CustomArray) isa CustomStyle
+        FI.ImplementationStyle(::Type{CustomArray}) = CustomImplementationStyle()
+        @test FI.ImplementationStyle(CustomArray) isa CustomImplementationStyle
 
-        # Test custom AbstractArrayStyle definition
+        # Test custom AbstractArrayImplementationStyle definition
         struct MyArray{T, N} <: AbstractArray{T, N}
             data::Array{T, N}
         end
-        struct MyArrayStyle <: FI.AbstractArrayStyle end
-        FI.Style(::Type{<:MyArray}) = MyArrayStyle()
-        @test FI.Style(MyArray) isa MyArrayStyle
+        struct MyArrayImplementationStyle <: FI.AbstractArrayImplementationStyle end
+        FI.ImplementationStyle(::Type{<:MyArray}) = MyArrayImplementationStyle()
+        @test FI.ImplementationStyle(MyArray) isa MyArrayImplementationStyle
 
         # Test style homogeneity rule (same type returns preserved)
-        s1 = FI.DefaultArrayStyle()
-        s2 = FI.DefaultArrayStyle()
-        @test FI.Style(s1, s2) ≡ FI.DefaultArrayStyle()
+        s1 = FI.DefaultArrayImplementationStyle()
+        s2 = FI.DefaultArrayImplementationStyle()
+        @test FI.ImplementationStyle(s1, s2) ≡ FI.DefaultArrayImplementationStyle()
 
-        # Test UnknownStyle precedence
-        unknown = FI.UnknownStyle()
-        known = FI.DefaultArrayStyle()
-        @test FI.Style(known, unknown) ≡ known
-        @test FI.Style(unknown, unknown) ≡ unknown
+        # Test UnknownImplementationStyle precedence
+        unknown = FI.UnknownImplementationStyle()
+        known = FI.DefaultArrayImplementationStyle()
+        @test FI.ImplementationStyle(known, unknown) ≡ known
+        @test FI.ImplementationStyle(unknown, unknown) ≡ unknown
 
-        # Test ArrayConflict
-        conflict = FI.ArrayConflict()
-        @test conflict isa FI.ArrayConflict
-        @test conflict isa FI.AbstractArrayStyle
+        # Test ArrayImplementationConflict
+        conflict = FI.ArrayImplementationConflict()
+        @test conflict isa FI.ArrayImplementationConflict
+        @test conflict isa FI.AbstractArrayImplementationStyle
 
         # Test style with no arguments
-        @test FI.style() ≡ FI.DefaultArrayStyle()
+        @test FI.style() ≡ FI.DefaultArrayImplementationStyle()
 
         # Test style with single argument
-        @test FI.style([1, 2]) ≡ FI.DefaultArrayStyle()
-        @test FI.style([1 2; 3 4]) ≡ FI.DefaultArrayStyle()
+        @test FI.style([1, 2]) ≡ FI.DefaultArrayImplementationStyle()
+        @test FI.style([1 2; 3 4]) ≡ FI.DefaultArrayImplementationStyle()
 
         # Test style with two arguments
         result = FI.style([1, 2], [1 2; 3 4])
-        @test result ≡ FI.DefaultArrayStyle()
+        @test result ≡ FI.DefaultArrayImplementationStyle()
 
         # Test style with same dimensions
         result = FI.style([1], [2])
-        @test result ≡ FI.DefaultArrayStyle()
+        @test result ≡ FI.DefaultArrayImplementationStyle()
 
         # Test style with multiple arguments
         result = FI.style([1], [1 2], rand(2, 3, 4))
-        @test result ≡ FI.DefaultArrayStyle()
+        @test result ≡ FI.DefaultArrayImplementationStyle()
 
         # Test result_style with single argument
-        @test FI.result_style(FI.DefaultArrayStyle()) isa FI.DefaultArrayStyle
+        @test FI.result_style(FI.DefaultArrayImplementationStyle()) isa FI.DefaultArrayImplementationStyle
 
         # Test result_style with two identical styles
-        s = FI.DefaultArrayStyle()
+        s = FI.DefaultArrayImplementationStyle()
         @test FI.result_style(s, s) ≡ s
 
-        # Test result_style with UnknownStyle
-        known = FI.DefaultArrayStyle()
-        unknown = FI.UnknownStyle()
+        # Test result_style with UnknownImplementationStyle
+        known = FI.DefaultArrayImplementationStyle()
+        unknown = FI.UnknownImplementationStyle()
         @test FI.result_style(known, unknown) ≡ known
         @test FI.result_style(unknown, known) ≡ known
     end