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# An Algebraic Approach to Functional Domain Modeling

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### An Algebraic Approach to Functional Domain Modeling

1. 1. An Algebraic Approach to Functional Domain Modeling Debasish Ghosh @debasishg Functional Conf 2016
2. 2. Domain Modeling
3. 3. Domain Modeling(Functional)
4. 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)
5. 5. The Functional Lens .. “domain API evolution through algebraic composition”
6. 6. The Functional Lens .. “domain API evolution through algebraic composition” Building larger domain behaviours out of smaller ones
7. 7. The Functional Lens .. “domain API evolution through algebraic composition” Use composition of pure functions and types
8. 8. Your domain model is a function
9. 9. Your domain model is a function
10. 10. Your domain model is a collection of functions
11. 11. Your domain model is a collection of functions some simpler models are ..
12. 12. https://msdn.microsoft.com/en-us/library/jj591560.aspx
13. 13. A Bounded Context • has a consistent vocabulary • a set of domain behaviours modelled as functions on domain objects implemented as types • each of the behaviours honour a set of business rules • related behaviors grouped as modules
14. 14. Domain Model = ∪(i) Bounded Context(i)
15. 15. Domain Model = ∪(i) Bounded Context(i) Bounded Context = { m[T1,T2,..] | T(i) ∈ Types } • a module parameterised on a set of types
16. 16. Domain Model = ∪(i) Bounded Context(i) Bounded Context = { m[T1,T2,..] | T(i) ∈ Types } Module = { f(x) | p(x) ∈ Domain Rules } • domain function • on an object of type x • composes with other functions • closed under composition • business rules
17. 17. • Functions / Morphisms • Types / Sets • Composition • Rules / Laws
18. 18. • Functions / Morphisms • Types / Sets • Composition • Rules / Laws algebra
19. 19. Domain Model Algebra
20. 20. Domain Model Algebra (algebra of types, functions & laws)
21. 21. Domain Model Algebra (algebra of types, functions & laws) explicit • types • type constraints • expression in terms of other generic algebra
22. 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
23. 23. Problem Domain
24. 24. Bank Account Trade Customer ... ... ... Problem Domain ... entities
25. 25. Bank Account Trade Customer ... ... ... do trade process execution place order Problem Domain ... entities behaviors
26. 26. Bank Account Trade Customer ... ... ... do trade process execution place order Problem Domain ... market regulations tax laws brokerage commission rates ... entities behaviors laws
27. 27. do trade process execution place order Solution Domain ... behaviors Functions ([Type] => Type)
28. 28. Bank Account Trade Customer ... ... ... do trade process execution place order Solution Domain ... entities behaviors functions ([Type] => Type) algebraic data type
29. 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
30. 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 ...
31. 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 ... Domain Algebra
32. 32. Domain Model = ∪(i) Bounded Context(i) Bounded Context = { m[T1,T2,..] | T(i) ∈ Types } Module = { 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
33. 33. Client places order - ﬂexible format 1
34. 34. Client places order - ﬂexible format Transform to internal domain model entity and place for execution 1 2
35. 35. Client places order - ﬂexible format Transform to internal domain model entity and place for execution Trade & Allocate to client accounts 1 2 3
36. 36. def clientOrders: ClientOrderSheet => List[Order] def execute: Market => Account => Order => List[Execution] def allocate: List[Account] => Execution => List[Trade]
37. 37. def clientOrders: ClientOrderSheet => List[Order] def execute[Account <: BrokerAccount]: Market => Account => Order => List[Execution] def allocate[Account <: TradingAccount]: List[Account] => Execution => List[Trade]
38. 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
39. 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)
40. 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
41. 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
42. 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
43. 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 ..
44. 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 ..
45. 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 ..
46. 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 ..
47. 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 ..
48. 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 ..
49. 49. def f: A => List[B] def g: B => List[C] def h: C => List[D] .. a problem of composition ..
50. 50. .. a problem of composition with effects .. def f: A => List[B] def g: B => List[C] def h: C => List[D]
51. 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 ..
52. 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 !
53. 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]
54. 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 ..
55. 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 ..
56. 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 ..
57. 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 ..
58. 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
59. 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 allow customisable handling of errors that may occur within our domain behaviors .. .. function composition with Effects ..
60. 60. more algebra, more types
61. 61. def clientOrders: Kleisli[List, ClientOrderSheet, Order] return type constructor
62. 62. def clientOrders: Kleisli[List, ClientOrderSheet, Order] return type constructor What happens in case the operation fails ?
63. 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]
64. 64. def clientOrders: Kleisli[List, ClientOrderSheet, Order] .. stacking of effects .. M[List[_]]
65. 65. def clientOrders: Kleisli[List, ClientOrderSheet, Order] .. stacking of effects .. M[List[_]]: M is a Monad
66. 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
67. 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
68. 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
69. 69. Monad Transformers • collapses the stack and gives us a single monad to deal with • order of stacking is important though
70. 70. def clientOrders: Kleisli[List, ClientOrderSheet, Order] .. stacking of effects .. case class ListT[M[_], A] (run: M[List[A]]) { //..
71. 71. 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 ..
72. 72. def execute(market: Market, brokerAccount: Account) = kleisli[List, Order, Execution] { order => order.items.map { item => Execution(brokerAccount, market, ..) } }
73. 73. 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 ) }
74. 74. List (aggregates) Algebra of types
75. 75. List (aggregates) Disjunction (error accumulation) Algebra of types
76. 76. List (aggregates) Disjunction (error accumulation) Kleisli (dependency injection) Algebra of types
77. 77. List (aggregates) Disjunction (error accumulation) Kleisli (dependency injection) Future (reactive non-blocking computation) Algebra of types
78. 78. List (aggregates) Disjunction (error accumulation) Kleisli (dependency injection) Future (reactive non-blocking computation) Algebra of types Monad
79. 79. List (aggregates) Disjunction (error accumulation) Kleisli (dependency injection) Future (reactive non-blocking computation) Algebra of types Monad Monoid
80. 80. List (aggregates) Disjunction (error accumulation) Kleisli (dependency injection) Future (reactive non-blocking computation) Algebra of types Monad Monoid Compositional
81. 81. List (aggregates) Disjunction (error accumulation) Kleisli (dependency injection) Future (reactive non-blocking computation) Algebra of types Monad Monoid Offers a suite of functional combinators
82. 82. 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
83. 83. 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
84. 84. 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 ..
85. 85. 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
86. 86. .. 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
87. 87. .. the algebra .. composition def tradeGeneration(market: Market, broker: Account, clientAccounts: List[Account]) = { clientOrders andThen execute(market, broker) andThen allocate(clientAccounts) }
88. 88. .. 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)
89. 89. Domain Rules as Algebraic Properties • part of the abstraction • equally important as the actual abstraction • veriﬁable as properties
90. 90. .. 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 ..
91. 91. https://www.manning.com/books/functional-and-reactive- domain-modeling
92. 92. ThankYou!