scala - Understanding Type Parameters -

looking @ part of io monad's signatures functional programming in scala:

trait io[+a] { self =>   def run:   def map[b](f: => b): io[b] =     new io[b] { def run = f(self.run) } 

as understand, io[+a] means io type takes type parameter of "a or subclasses."

looking @ def map[b]..., b type involved in function. it's useful use map[b](f: => b): io[b] since, understand, can list b return type of f, returned type parameter of io?

so, following implementation cause compile-time problem:

map(f: int => string): io[int]

so +a means similar thing t <: a. means "for subtypes of including a". "limitation" useful here because supposed pass f function map method , restricting specific type a , it's subtypes. when extend trait in class allow substitution of f while being typesafe.

b here result of applying f a. since it's monad not b io[b]. in other words might fail , might b wrapped in "success" or sort of "failure".

notice type of self +a, , newly created io[b] not compute anything, wraps around result of run has b. since expect failures occur in io , since it's monad wrap around result of application of f(self.run) creating monad io[b] (as promised map method signature).

finally, said map(f: int => string): io[int] should not compile since int not subtype of string.