# Functional and Algebraic Domain Modeling

Principal Engineer at Lightbend
Feb. 1, 2016
1 of 95

### Functional and Algebraic Domain Modeling

• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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