1.
Functional and Algebraic Domain
Modeling
Debasish Ghosh
@debasishg
関数型、代数的なドメイン・モデリングの方法
Saturday, 30 January 16

2.
Domain Modeling
ドメイン・モデリング
Saturday, 30 January 16

3.
Domain Modeling(Functional)
関数型なドメイン・モデリング
Saturday, 30 January 16

4.
What is a domain model ?
A domain model in problem solving and software engineering is a
conceptual model of all the topics related to a specific problem. It
describes the various entities, their attributes, roles, and
relationships, plus the constraints that govern the problem domain.
It does not describe the solutions to the problem.
Wikipedia (http://en.wikipedia.org/wiki/Domain_model)
特定の問題領域に関する概念モデル
エンティティ／関連／制約などを記述
Saturday, 30 January 16

5.
The Functional Lens ..
“domain API evolution through algebraic
composition”
関数型レンズ
代数的合成を通じたドメイン API の進化
Saturday, 30 January 16

6.
「サーバを関数として考える」
Saturday, 30 January 16

7.
Twitter 社でのサーバソフトウェアの構成は fp と同じ理念
（不変性、関数の合成、副作用の分離）に基づく
Saturday, 30 January 16

8.
Your domain model is a
function
ドメインモデルは関数である
Saturday, 30 January 16

9.
Your domain model is a
function
ドメインモデルは関数（...であって欲しい）
Saturday, 30 January 16

10.
Your domain model is a
collection of functions
ドメインモデルは関数の集合である
Saturday, 30 January 16

11.
Your domain model is a
collection of functions
some simpler models are ..
具体例で考えると...
Saturday, 30 January 16

12.
https://msdn.microsoft.com/en-us/library/jj591560.aspx
カンファレンス管理システム
Saturday, 30 January 16

13.
A Bounded Context
• has a consistent vocabulary
• a set of domain behaviors modeled as
functions on domain objects
implemented as types
• related behaviors grouped as modules
境界づけられたコンテキストは、統一された語彙を持つ
ドメインの振る舞いは関数、オブジェクトは型として実装するSaturday, 30 January 16

14.
Domain Model = ∪(i) Bounded Context(i)
Saturday, 30 January 16

15.
Domain Model = ∪(i) Bounded Context(i)
Bounded Context = { f(x) | p(x) ∈ Domain Rules }
Saturday, 30 January 16

16.
Domain Model = ∪(i) Bounded Context(i)
Bounded Context = { f(x) | p(x) ∈ Domain Rules }
• domain function
• on an object of type x
• composes with other functions
• closed under composition
• business rules
f はドメイン関数で、他の関数と合成できる
p はビジネスルール
Saturday, 30 January 16

17.
• Functions / Morphisms
• Types / Sets
• Composition
• Rules / Laws
関数と射、型と集合、合成、ルールと法則
Saturday, 30 January 16

18.
• Functions / Morphisms
• Types / Sets
• Composition
• Rules / Laws
algebra
要は代数ということ
Saturday, 30 January 16

19.
Domain Model Algebra
ドメインモデルの代数
Saturday, 30 January 16

20.
Domain Model Algebra
(algebra of types, functions & laws)
型と関数と法則の代数
Saturday, 30 January 16

21.
Domain Model Algebra
(algebra of types, functions & laws)
explicit
• types
• type constraints
• expression in terms of other generic algebra
これを明示的にすると、型、型の制約、他の代数を用いた表現
Saturday, 30 January 16

22.
Domain Model Algebra
(algebra of types, functions & laws)
explicit verifiable
• types
• type constraints
• expr in terms of other generic algebra
• type constraints
• more constraints if you have DT
• algebraic property based testing
確認可能なのは型制約、代数的プロパティーベースのテスト
依存型があればより強い制約を検証できる
Saturday, 30 January 16

23.
Problem Domain
問題ドメインの例として証券取引口座を考察する
Saturday, 30 January 16

24.
Bank
Account
Trade
Customer
...
...
...
Problem Domain
...
entities
エンティティとなるのは、口座、顧客、取引、銀行
Saturday, 30 January 16

25.
Bank
Account
Trade
Customer
...
...
...
do trade
process
execution
place
order
Problem Domain
...
entities
behaviors
振る舞いとなるのは、注文、取引、執行処理
Saturday, 30 January 16

26.
Bank
Account
Trade
Customer
...
...
...
do trade
process
execution
place
order
Problem Domain
...
market
regulations
tax laws
brokerage
commission
rates
...
entities
behaviors
laws
法則となるのは株式市場規則、税法、手数料
Saturday, 30 January 16

27.
do trade
process
execution
place
order
Solution Domain
...
behaviors
Functions
(Type => Type)
ソリューションドメインでは、振る舞いは関数 (型 型)
Saturday, 30 January 16

28.
Bank
Account
Trade
Customer
...
...
...
do trade
process
execution
place
order
Solution Domain
...
entities
behaviors
functions
(Type => Type)
algebraic data type
エンティティは代数的データ型
Saturday, 30 January 16

29.
Bank
Account
Trade
Customer
...
...
...
do trade
process
execution
place
order
Solution Domain
...
market
regulations
tax laws
brokerage
commission
rates
...
entities
behaviors
laws
functions
(Type => Type)
algebraic data type business rules / invariants
法則はビジネス・ルールもしくは不変関係
Saturday, 30 January 16

30.
Bank
Account
Trade
Customer
...
...
...
do trade
process
execution
place
order
Solution Domain
...
market
regulations
tax laws
brokerage
commission
rates
...
entities
behaviors
laws
functions
(Type => Type)
algebraic data type business rules / invariants
Monoid
Monad
...
モノイドやモナドといった型クラス
Saturday, 30 January 16

31.
Bank
Account
Trade
Customer
...
...
...
do trade
process
execution
place
order
Solution Domain
...
market
regulations
tax laws
brokerage
commission
rates
...
entities
behaviors
laws
functions
(Type => Type)
algebraic data type business rules / invariants
Monoid
Monad
...
これを全部やるとドメイン代数
Domain Algebra
Saturday, 30 January 16

32.
Domain Model = ∪(i) Bounded Context(i)
Bounded Context = { f(x) | p(x) ∈ Domain Rules }
• domain function
• on an object of type x
• composes with other functions
• closed under composition
• business rules
Domain Algebra
Domain Algebra
「境界づけられたコンテキスト」はドメイン代数のこと
Saturday, 30 January 16

33.
Client places order
- flexible format
1
クライアントが注文を出す
フォーマットは様々
Saturday, 30 January 16

34.
Client places order
- flexible format
Transform to internal domain
model entity and place for execution
1 2
内部でのドメインモデルエンティティに変換して、
実際に注文を出す
Saturday, 30 January 16

35.
Client places order
- flexible format
Transform to internal domain
model entity and place for execution
Trade & Allocate to
client accounts
1 2
3
取引し、結果をクライアントのアカウントに紐づける
Saturday, 30 January 16

36.
def clientOrders: ClientOrderSheet => List[Order]
def execute: Market => Account => Order => List[Execution]
def allocate: List[Account] => Execution => List[Trade]
Saturday, 30 January 16

37.
def clientOrders: ClientOrderSheet => List[Order]
def execute[Account <: BrokerAccount]: Market => Account
=> Order => List[Execution]
def allocate[Account <: TradingAccount]: List[Account]
=> Execution => List[Trade]
Saturday, 30 January 16

38.
def clientOrders: ClientOrderSheet => List[Order]
def execute: Market => Account => Order => List[Execution]
def allocate: List[Account] => Execution => List[Trade]
Types out of thin air No implementation till now
Type names resonate domain language
どこからともなく降ってきた型。今の所実装の話はゼロ。
型の名前はドメイン言語を反映
Saturday, 30 January 16

39.
def clientOrders: ClientOrderSheet => List[Order]
def execute: Market => Account => Order => List[Execution]
def allocate: List[Account] => Execution => List[Trade]
•Types (domain entities)
• Functions operating on types (domain behaviors)
• Laws (business rules)
型 (エンティティ)、関数 (ドメインの振る舞い)、
法則 (ビジネス・ルール)
Saturday, 30 January 16

40.
def clientOrders: ClientOrderSheet => List[Order]
def execute: Market => Account => Order => List[Execution]
def allocate: List[Account] => Execution => List[Trade]
•Types (domain entities)
• Functions operating on types (domain behaviors)
• Laws (business rules)
Algebra of the API
これが API の代数
Saturday, 30 January 16

41.
trait Trading[Account, Trade, ClientOrderSheet, Order,
Execution, Market] {
def clientOrders: ClientOrderSheet => List[Order]
def execute: Market => Account => Order => List[Execution]
def allocate: List[Account] => Execution => List[Trade]
def tradeGeneration(market: Market, broker: Account,
clientAccounts: List[Account]) = ???
}
parameterized on typesmodule
モジュール、型パラメータ
Saturday, 30 January 16

42.
Algebraic Design
• The algebra is the binding contract of the
API
• Implementation is NOT part of the algebra
• An algebra can have multiple interpreters
(aka implementations)
• One of the core principles of functional
programming is to decouple the algebra from
the interpreter
代数的設計手法: 代数は API が準拠する制約
実装は代数に含まれず、実装からは分離されている
Saturday, 30 January 16

43.
def clientOrders: ClientOrderSheet => List[Order]
def execute: Market => Account => Order => List[Execution]
def allocate: List[Account] => Execution => List[Trade]
let’s do some algebra ..
代数の練習
Saturday, 30 January 16

44.
def clientOrders: ClientOrderSheet => List[Order]
def execute(m: Market, broker: Account): Order => List[Execution]
def allocate(accounts: List[Account]): Execution => List[Trade]
let’s do some algebra ..
Saturday, 30 January 16

45.
def clientOrders: ClientOrderSheet => List[Order]
def execute(m: Market, broker: Account): Order => List[Execution]
def allocate(accounts: List[Account]): Execution => List[Trade]
let’s do some algebra ..
Saturday, 30 January 16

46.
def clientOrders: ClientOrderSheet => List[Order]
def execute(m: Market, broker: Account): Order => List[Execution]
def allocate(accounts: List[Account]): Execution => List[Trade]
let’s do some algebra ..
Saturday, 30 January 16

47.
def clientOrders: ClientOrderSheet => List[Order]
def execute(m: Market, broker: Account): Order => List[Execution]
def allocate(accounts: List[Account]): Execution => List[Trade]
let’s do some algebra ..
Saturday, 30 January 16

48.
def clientOrders: ClientOrderSheet => List[Order]
def execute(m: Market, broker: Account): Order => List[Execution]
def allocate(accounts: List[Account]): Execution => List[Trade]
let’s do some algebra ..
Saturday, 30 January 16

49.
def f: A => List[B]
def g: B => List[C]
def h: C => List[D]
.. a problem of composition ..
これは ... 合成の問題だ
Saturday, 30 January 16

50.
.. a problem of
composition with effects ..
def f: A => List[B]
def g: B => List[C]
def h: C => List[D]
これは ... 作用付きの合成の問題だ
Saturday, 30 January 16

51.
def f[M: Monad]: A => M[B]
def g[M: Monad]: B => M[C]
def h[M: Monad]: C => M[D]
.. a problem of composition with
effects that can be generalized ..
これはモナドとして抽象化できる作用付きの合成の問題だ
Saturday, 30 January 16

52.
case class Kleisli[M[_], A, B](run: A => M[B]) {
def andThen[C](f: B => M[C])
(implicit M: Monad[M]): Kleisli[M, A, C] =
Kleisli((a: A) => M.flatMap(run(a))(f))
}
.. function composition with
Effects ..
It’s a Kleisli !
作用付きの関数の合成と言えば、Kleisli！
Saturday, 30 January 16

53.
def clientOrders: Kleisli[List, ClientOrderSheet, Order]
def execute(m: Market, b: Account): Kleisli[List, Order, Execution]
def allocate(acts: List[Account]): Kleisli[List, Execution, Trade]
Follow the types
.. function composition with
Effects ..
def clientOrders: ClientOrderSheet => List[Order]
def execute(m: Market, broker: Account): Order => List[Execution]
def allocate(accounts: List[Account]): Execution => List[Trade]
型に任せて考える
Saturday, 30 January 16

54.
def clientOrders: Kleisli[List, ClientOrderSheet, Order]
def execute(m: Market, b: Account): Kleisli[List, Order, Execution]
def allocate(acts: List[Account]): Kleisli[List, Execution, Trade]
Domain algebra composed with the
categorical algebra of a Kleisli Arrow
.. function composition with
Effects ..
Klieisli 射によって合成されたドメイン代数
Saturday, 30 January 16

55.
def clientOrders: Kleisli[List, ClientOrderSheet, Order]
def execute(m: Market, b: Account): Kleisli[List, Order, Execution]
def allocate(acts: List[Account]): Kleisli[List, Execution, Trade]
.. that implements the semantics of our
domain algebraically ..
.. function composition with
Effects ..
ドメインの意味論を代数的に実装する作用付きの関数の合成
Saturday, 30 January 16

56.
def tradeGeneration(
market: Market,
broker: Account,
clientAccounts: List[Account]) = {
clientOrders andThen
execute(market, broker) andThen
allocate(clientAccounts)
}
Implementation follows the specification
.. the complete trade generation
logic ..
実装は仕様に従う
Saturday, 30 January 16

57.
def tradeGeneration(
market: Market,
broker: Account,
clientAccounts: List[Account]) = {
clientOrders andThen
execute(market, broker) andThen
allocate(clientAccounts)
}
Implementation follows the specification
and we get the Ubiquitous Language for
free :-)
.. the complete trade generation
logic ..
実装は仕様に従い、
そこからユビキタス言語を読み取ることが出来る
Saturday, 30 January 16

58.
algebraic & functional
• Just Pure Functions. Lower cognitive load -
don’t have to think of the classes & data
members where behaviors will reside
• Compositional. Algebras compose - we
defined the algebras of our domain APIs in
terms of existing, time tested algebras of
Kleislis and Monads
代数的かつ関数型の設計は、
純粋関数のみで構成する、合成可能な設計
Saturday, 30 January 16

59.
def clientOrders: Kleisli[List, ClientOrderSheet, Order]
def execute(m: Market, b: Account): Kleisli[List, Order, Execution]
def allocate(acts: List[Account]): Kleisli[List, Execution, Trade]
.. our algebra still doesn’t handle errors
that may occur within our domain
behaviors ..
.. function composition with
Effects ..
そう言えばエラー処理どうする?
Saturday, 30 January 16

60.
more algebra,
more types
代数と型、大盛りで追加！
Saturday, 30 January 16

61.
def clientOrders: Kleisli[List, ClientOrderSheet, Order]
return type constructor
List は戻り値の型コンストラクタ
Saturday, 30 January 16

62.
def clientOrders: Kleisli[List, ClientOrderSheet, Order]
return type constructor
What happens in case the operation fails ?
演算が失敗したらどうなる?
Saturday, 30 January 16

63.
Error handling as an
Effect
• pure and functional
• with an explicit and published algebra
• stackable with existing effects
def clientOrders: Kleisli[List, ClientOrderSheet, Order]
モナド作用としてのエラー処理
純粋で関数型に。明示的な代数。既存の作用と積み上げ可能。
Saturday, 30 January 16

64.
def clientOrders: Kleisli[List, ClientOrderSheet, Order]
.. stacking of effects ..
M[List[_]]
作用の積み上げ
Saturday, 30 January 16

65.
def clientOrders: Kleisli[List, ClientOrderSheet, Order]
.. stacking of effects ..
M[List[_]]: M is a Monad
List をエラー処理のためのモナド M で囲む
Saturday, 30 January 16

66.
type Response[A] = String / Option[A]
val count: Response[Int] = some(10).right
for {
maybeCount <- count
} yield {
for {
c <- maybeCount
// use c
} yield c
}
Monad Transformers
モナド変換子
Saturday, 30 January 16

67.
type Response[A] = String / Option[A]
val count: Response[Int] = some(10).right
for {
maybeCount <- count
} yield {
for {
c <- maybeCount
// use c
} yield c
}
type Error[A] = String / A
type Response[A] = OptionT[Error, A]
val count: Response[Int] = 10.point[Response]
for{
c <- count
// use c : c is an Int here
} yield (())
Monad Transformers
Saturday, 30 January 16

68.
type Response[A] = String / Option[A]
val count: Response[Int] = some(10).right
for {
maybeCount <- count
} yield {
for {
c <- maybeCount
// use c
} yield c
}
type Error[A] = String / A
type Response[A] = OptionT[Error, A]
val count: Response[Int] = 10.point[Response]
for{
c <- count
// use c : c is an Int here
} yield (())
Monad Transformers
richer algebra
代数として扱いやすいのは OptionT を使った方
Saturday, 30 January 16

69.
Monad Transformers
• collapses the stack and gives us a single
monad to deal with
• order of stacking is important though
モナド変換子は積み上げたモナドを一つに潰すことができる
ただし積み上げる順番は大切
Saturday, 30 January 16

70.
def clientOrders: Kleisli[List, ClientOrderSheet, Order]
.. stacking of effects ..
case class ListT[M[_], A] (run: M[List[A]]) { //..
ListT モナド変換子を使う
Saturday, 30 January 16

71.
これは代数にとって小さな一歩だが、
ドメインモデルにとっては巨大な跳躍である
Saturday, 30 January 16

72.
type StringOr[A] = String / A
type Valid[A] = ListT[StringOr, A]
これは代数にとって小さな一歩だが、
ドメインモデルにとっては巨大な跳躍である
Saturday, 30 January 16

73.
type StringOr[A] = String / A
type Valid[A] = ListT[StringOr, A]
def clientOrders: Kleisli[Valid, ClientOrderSheet, Order]
def execute(m: Market, b: Account): Kleisli[Valid, Order, Execution]
def allocate(acts: List[Account]): Kleisli[Valid, Execution, Trade]
これは代数にとって小さな一歩だが、
ドメインモデルにとっては巨大な跳躍である
Saturday, 30 January 16

74.
type StringOr[A] = String / A
type Valid[A] = ListT[StringOr, A]
def clientOrders: Kleisli[Valid, ClientOrderSheet, Order]
def execute(m: Market, b: Account): Kleisli[Valid, Order, Execution]
def allocate(acts: List[Account]): Kleisli[Valid, Execution, Trade]
.. a small change in algebra, a huge step
for our domain model ..
これは代数にとって小さな一歩だが、
ドメインモデルにとっては巨大な跳躍である
Saturday, 30 January 16

75.
def execute(market: Market, brokerAccount: Account) =
kleisli[List, Order, Execution] { order =>
order.items.map { item =>
Execution(brokerAccount, market, ..)
}
}
Saturday, 30 January 16

76.
private def makeExecution(brokerAccount: Account,
item: LineItem, market: Market): String / Execution = //..
def execute(market: Market, brokerAccount: Account) =
kleisli[Valid, Order, Execution] { order =>
listT[StringOr](
order.items.map { item =>
makeExecution(brokerAccount, market, ..)
}.sequenceU
)
}
Saturday, 30 January 16

77.
List
(aggregates)
Algebra of types
型の代数
集約のための List
Saturday, 30 January 16

78.
List
(aggregates)
Disjunction
(error accumulation)
Algebra of types
エラー蓄積のためのDisjunction
Saturday, 30 January 16

79.
List
(aggregates)
Disjunction
(error accumulation)
Kleisli
(dependency injection)
Algebra of types
依存性注入のための Kleisli
Saturday, 30 January 16

80.
List
(aggregates)
Disjunction
(error accumulation)
Kleisli
(dependency injection)
Future
(reactive non-blocking computation)
Algebra of types
リアクティブでノンブロッキングな処理のための Future
Saturday, 30 January 16

81.
List
(aggregates)
Disjunction
(error accumulation)
Kleisli
(dependency injection)
Future
(reactive non-blocking computation)
Algebra of types
Monad
モナド
Saturday, 30 January 16

82.
List
(aggregates)
Disjunction
(error accumulation)
Kleisli
(dependency injection)
Future
(reactive non-blocking computation)
Algebra of types
Monad
Monoid
モノイド
Saturday, 30 January 16

83.
List
(aggregates)
Disjunction
(error accumulation)
Kleisli
(dependency injection)
Future
(reactive non-blocking computation)
Algebra of types
Monad
Monoid
Compositional
合成可能
Saturday, 30 January 16

84.
List
(aggregates)
Disjunction
(error accumulation)
Kleisli
(dependency injection)
Future
(reactive non-blocking computation)
Algebra of types
Monad
Monoid
Offers a suite of functional
combinators
さまざまな関数型コンビネータを提供する
Saturday, 30 January 16

85.
List
(aggregates)
Disjunction
(error accumulation)
Kleisli
(dependency injection)
Future
(reactive non-blocking computation)
Algebra of types
Monad
Monoid
Handles edge cases so your
domain logic remains clean
ドメインロジックを綺麗保てるように、
エッジケースはこっちで処理する
Saturday, 30 January 16

86.
List
(aggregates)
Disjunction
(error accumulation)
Kleisli
(dependency injection)
Future
(reactive non-blocking computation)
Algebra of types
Monad
Monoid
Implicitly encodes quite a bit
of domain rules
暗黙的にかなり多くのドメインルールをエンコードする
Saturday, 30 January 16

87.
def clientOrders: Kleisli[List, ClientOrderSheet, Order]
def execute(m: Market, b: Account): Kleisli[List, Order, Execution]
def allocate(acts: List[Account]): Kleisli[List, Execution, Trade]
.. the algebra ..
代数的な考え方
Saturday, 30 January 16

88.
def clientOrders: Kleisli[List, ClientOrderSheet, Order]
def execute(m: Market, b: Account): Kleisli[List, Order, Execution]
def allocate(acts: List[Account]): Kleisli[List, Execution, Trade]
.. the algebra ..
functions
関数
Saturday, 30 January 16

89.
.. the algebra ..
def clientOrders: Kleisli[List, ClientOrderSheet, Order]
def execute(m: Market, b: Account): Kleisli[List, Order, Execution]
def allocate(acts: List[Account]): Kleisli[List, Execution, Trade]
types
型
Saturday, 30 January 16

90.
.. the algebra ..
composition
def tradeGeneration(market: Market, broker: Account,
clientAccounts: List[Account]) = {
clientOrders andThen
execute(market, broker) andThen
allocate(clientAccounts)
}
合成
Saturday, 30 January 16

91.
.. the algebra ..
trait OrderLaw {
def sizeLaw: Seq[ClientOrder] => Seq[Order] => Boolean =
{ cos => orders =>
cos.size == orders.size
}
def lineItemLaw: Seq[ClientOrder] => Seq[Order] => Boolean =
{ cos => orders =>
cos.map(instrumentsInClientOrder).sum ==
orders.map(_.items.size).sum
}
}
laws of the algebra
(domain rules)
代数の法則
Saturday, 30 January 16

92.
Domain Rules as
Algebraic Properties
• part of the abstraction
• equally important as the actual
abstraction
• verifiable as properties
代数的プロパティとしてのドメインルール
プロパティとして検証可能となる
Saturday, 30 January 16

93.
.. domain rules verification ..
property("Check Client Order laws") =
forAll((cos: Set[ClientOrder]) => {
val orders = for {
os <- clientOrders.run(cos.toList)
} yield os
sizeLaw(cos.toSeq)(orders) == true
lineItemLaw(cos.toSeq)(orders) == true
})
property based testing FTW ..
プロパティベーステスト最強
Saturday, 30 January 16

94.
https://www.manning.com/books/functional-and-reactive-
domain-modeling
本書いてます
Saturday, 30 January 16

95.
ThankYou!
Saturday, 30 January 16