A monad is a triple (T, η, μ) where T is an
endofunctor T: X->X and η: I->T and μ: T x T-
>T are 2 natural transformations satisfying these
laws:
• Identity law: μ(η(T)) = T = μ(T(η))
• Associative law: μ(μ(T × T) × T)) = μ(T ×
μ(T × T))
A monad in X is just a monoid in the
category of endofunctors of X, with product
× replaced by composition of endofunctors
and unit set by the identity endofunctor
What is a monad?
software developer @ codiceplastico
@amelchiori
alessandro@codiceplastico.com
About me
let myString = "original value"
let myString = "new value”
Immutability: values, not variables!
Duplicate definition of value ‘myString’
let add x y = x + y
add 2 2
x:int -> y:int -> int
Type inference
void ProcessItems(Item[] items, Action<Item> action)
{
for(int i = 0; i < items.Length; i++)
{
var item = items[i];
action(item);
}
}
Recursion
let rec processItems action = function
| [] -> ()
| head :: tail ->
action head;
processItems tail
Recursion
let add x y = x + y
x:int -> y:int -> int
Partial function application
let add5 x = add 5
x:int -> int
let value = add5 10
(value = 15)
let f x = x * x
x:int -> int
let g x = -x/2 + 5
x:int -> int
Functions composition
let (<<) f g x = f (g x)
('b -> 'c) -> ('a -> 'b) -> 'a -> ’c
let h x = f << g
x:int -> int
let square x = x * x
let add x y = x + y
let toString x = x.ToString()
let complexFunction x = toString (add 5 (square x))
Pipeline operator
let (|>) x f = f x
let complexFunction x = x |> square |> add 5 |> toString
let div x y = x / y
x:int -> y:int -> int
div 10 5 // 2
div 10 0 // System.DivideByZeroException
Option type
let safeDiv x y =
if y = 0 then None
else Some(x/y)
x:int -> y:int -> int option
let safeDiv x y =
match y with
| 0 -> None
| _ -> Some(x/y)
Pattern matching
let safeDiv x y =
match y with
| 0 -> None
| 1 -> Some(x/y)
Incomplete pattern matches on this expression.
For example, the value '2' may indicate a case not covered
by the pattern(s)
type State =
| On
| Off
let x = On
let y = Off
Discriminated unions
let div (x, y) = …
(int * int) - > int
Tuples
let div (x, y) =
match (x, y) with
| (_, 0) -> None
| (_, _) -> Some(x/ y)
type site = { Title : string; Url : string }
Records
let homepage =
{ Title = "Google"; Url = "http://www.google.com" }
let next = { homepage with Title = "NextPage" }
public class Company
{
public String BusinessName { get; set; }
public String TaxCode { get; set; }
public String VatNumber { get; set; }
public String AssignedBank { get; set; }
public Boolean IsBankAuthorized { get; set; }
}
Value object
An immutable object, like money or a date
range, whose equality isn't based on identity
(in general equality is based on all fields
equality)
Martin Fowler
Value object
An immutable object, like money or a date
range, whose equality isn't based on identity
(in general equality is based on all fields
equality)
Martin Fowler
public class CompanyProfile
{
public String BusinessName { get; private set; }
public String TaxCode { get; private set; }
public String VatNumber { get; private set; }
public CompanyProfile(String businessName, String taxCode,
String vatNumber=null)
{
// check if parameters are valid
BusinessName = businessName;
TaxCode = taxCode;
VatNumber = vatNumber;
}
}
Value object
public class CompanyProfile
{
// same as before…
public override Boolean Equals(Object other)
{
var target = other as CompanyProfile;
return target == null ? false :
target.BusinessName == this.BusinessName
&& target.TaxCode == this.TaxCode
&& target.VatCode == this.VatCode;
}
public override Int32 GetHashCode()
{
// ...
}
}
Value object’s equality
type CompanyProfile = {
BusinessName : string;
TaxCode : string;
VatNumber : string
}
Value object in F#
option;
let profile = {
BusinessName = “CodicePlastico”;
TaxNumber = “1234567890”;
}
Ubiquitous Language is the concept of
defining a language (spoken and written)
that is equally used across developers and
domain experts
Ubiquitous language
Rule 1:
A company must have a bank to work with
Rule 2:
A company can be authorized to work with its
assigned bank
Rule 3:
A company can be not authorized to work with
its assigned bank
Business logic
type Bank = Bank of string
type UnauthorizedBank = UnauthorizedBank of Bank
type AuthorizedBank = AuthorizedBank of Bank
type AssignedBank =
| Unauthorized of UnauthorizedBank
| Authorized of AuthorizedBank
Business logic in F#
type CompanyProfile = {
BusinessName: string,
TaxCode: string,
VatCode: string option
}
type Bank = Bank of string
type UnauthorizedBank =
UnauthorizedBank of Bank
type AuthorizedBank =
AuthorizedBank of Bank
type AssignedBank =
| Unauthorized of UnauthorizedBank
| Authorized of AuthorizedBank
type Company = {
Profile: CompanyProfile,
Bank: AssignedBank
}
Ubiquitous language to the rescue
The central idea of specification is to
separate the statement of how to match
a candidate, from the candidate object
that it is matched against
Specification
type Category =
| Default
| Premium
| Gold
type Customer = {
Name: string;
Category: Category;
}
Specification: our (simple) domain
type Item = {
Code: string;
Quantity: int;
}
type Order = {
Number: string;
Customer: Customer;
Items: Item list;
}
let isOrderFullFilled : Spec<Order> =
let p order =
match Seq.isEmpty order.Items with
| true -> Failure("Items' list empty")
| false -> Success
in p
let isGoldCustomer : Spec<Customer> =
let p customer =
match customer.Category with
| Gold -> Success
| _ -> Failure("No-gold customer")
in p
Specification
let And (left: Spec<'a>) (right: Spec<'a>) : Spec<'a> =
let p entity =
match left entity with
| Success -> right entity
| _ -> Failure("And specification is not satisfied")
in p
Specification
let order = {
Number = "1234";
Customer = { Name = "Alessandro"; Category = Gold};
Items = [
{ Code = "Code1"; Quantity = 1};
{ Code = "Code2"; Quantity = 2};
];
}
let isOrderValid = And
isOrderFullFilled
(adapt isGoldCustomer (fun order -> order.Customer))
let isValid = isOrderValid order
Specification
Cart.Apply(
Cart.Apply(
Cart.Apply(
Cart.Apply(null, new CartCreated { CartId=1}),
new ItemAddedToCart { CartId = 1, ItemId = "A"
}
),
new ItemAddedToCart { CartId = 1, ItemId = "B" }
),
new ItemRemovedFromCart { CartId = 1, ItemId = "A" }
)
Commands, events and…fold (step 5)
Executing a command:
type Exec =
( CartState * Command ) -> DomainEvent
Applying an event:
type Apply =
( CartState * DomainEvent ) -> CartState
Commands, events and…fold (step 6)
type Command =
| Create of string
| AddItem of int
| RemoveItem of int
| RemoveAllItems
| Checkout
type Event =
| Created of string
| ItemAdded of int
| ItemRemoved of
int
| AllItemsRemoved
| Checkedout
Commands, events and…fold (step 7)
type CartState = {
Name: string;
Items: List<int>;
Active: bool;
}
let apply state = function
| Created x -> { Cart.empty with Name = x }
| ItemAdded x -> { state with Items = List.append state.Items [x] }
| ItemRemoved x ->
{ state with Items = List.filter (fun i -> i <> x ) state.Items }
| Removed _ -> { state with Items = List.empty }
| Checkedout _ -> { state with Active = false }
Commands, events and…fold (step 8)
let domainEvents = [
Created("cart1");
ItemAdded(1);
ItemAdded(2);
Removed;
ItemAdded(3);
Checkedout;
]
let state = List.fold apply Cart.empty domainEvents
Commands, events and…fold (step 9)