java11-category-theory-reader-functor

Reference: https://bartoszmilewski.com/2015/01/20/functors/

preface

Basic knowledge and intuition about functors is provided in: https://github.com/mtumilowicz/java11-category-theory-optional-is-not-functor

Reader functor:

Type constructor: (-> a) // curried (-> a b) or equivallent (a -> b)

map :: (a -> b) -> (r -> a) -> (r -> b)
map f g = (.) f g

proof

1. map id = id

   map id g
   = { definition of map }
   (.) id g
   

2. map (g . f) = map g . map f

   map (g . f) h 
   = { definition of map }
   (.) (g . f) h
   = { associativity of composition }
   (.) g (f . h)
   = { definition of map }
   map g (f h)
   = { definition of map }
   map g (map f h)
   = { definition of composition }
   (map g . map f) h
   

project description

• We provide simple implementation of Reader Functor:

  @FunctionalInterface
  interface Reader<R, A> extends Function<R, A> {
      default <B> Reader<R, B> map(Function<A, B> f) {
          return asReader(f.compose(this));
      }
      
      default <X, Y> Reader<X, Y> asReader(Function<X, Y> f) {
          return f::apply;
      }
  }
  

• and basic test

  Reader<BigDecimal, Integer> toInteger = BigDecimal::intValue;
  Reader<BigDecimal, String> mapped = toInteger.map(String::valueOf);
  
  assertThat(mapped.apply(BigDecimal.TEN), is("10"));
  

additional info

1. Reader could be extended to monad: https://github.com/aol/cyclops/blob/master/cyclops-pure/src/main/java/cyclops/control/Reader.java
2. and used for dependency injection: https://github.com/aol/cyclops/wiki/Reader-:-functional-dependency-injection