Scala in depth 6 Scala's type system

1. Upper bound and lower bound
   

Declare Lower bound with:>, which is the parent class constraint, a:> B, a must be the parent of B

With <: declares Upper bound, i.e. subclass constraint, A <: b A must be a subclass of B

Examples of Lower bound

Package Ch6object Test4 {println ("Welcome to the Scala Worksheet") class A {type B;: List[int] def foo (A: B) = a} val x = new A {type b = Traversable[int]} Set (1) X.foo (set (1))//Val y = new A {type b = set[int ]}//Compilation Error}

Thus, the meaning of a:> B is: The parent class of B or a type with a common parent class with B

<:b is usually not used because it has the same effect as: B

2. High-order type

Like higher-order functions, sometimes a type requires another type to do the argument.

Type callback[t] = function1[t, Unit]

3.type Lambda

Similar to a function represented by a lambda expression, the type can be defined in such a flexible way, given an example from

Stackoverflow:http://stackoverflow.com/questions/8736164/what-are-type-lambdas-in-scala-and-what-are-their-benefits

Trait Monad[m[_]] {def point[a] (A:A): M[a] def Bind[a, B] (M:m[a]) (f:a = M[b]): M[b]} class Eithermonad[a] Extends monad[({typeλ[α] = either[a,α]}) #λ] {def point[b] (b:b): Either[a, B] def Bind[b, C] (M:either[a, B]) ( F:b = Either[a, c]): Either[a, C]}

4. For a high-order type a[t], the compatibility of a[t] varies with the specific type of T in three cases

Suppose s<: T

(1) Invariant <=> A[s] incompatible a[t]

(2) covariant <=> a[s] <: a[t]

(3) contravariant <=> a[t] <: A[s]

Original:

AHigher-kinded type that's invariant implies that for any typesT,A, andBIfT[a]c Onforms to T[B " Span style= "font-family: ' Newbaskerville-roman '; Font-size:10pt;color:rgb (0,0,0); Font-style:normal;font-variant: normal; " >then must be the equivalent type of b
T[a] Conforms T[b] can be understood as a reference to a type of T[a] object that can be assigned to the T[B] type

covarianceRefers to the ability to substitute a type parameter with its parent type:
For any typesT,AandBi F conforms to then

The type of 5.mutable must be invariant. such as array

Type of parameter of type 6.Function, must be contraviriant

Package ch6object test4 {  println ("welcome to the scala  Worksheet ")        //> Welcome to the Scala  Worksheet  def foo (X: any):string =  "hello, i received a " +  x                                                    //> foo:   (X: any) String  def bar (x: string):  any = foo (x)                  //> bar:  (x:  string) Any  bar ("test")                                        //> res0: any = hello, i received a test  foo ("Test ")                                        //> res1: string = hello, i received a test}

Foo is of type Function1[any, String]

Bar is of type function1[string, any]

Foo can be assigned a value to bar

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Scala in depth 6 Scala's type system