techtangents

My PL Shopping List
===================

- static types
- lightweight syntax for lambda expressions
- type annotations on any expression
- higher-kinded types
- monad comprehensions (for/do)
- applicative comprehensions (applicative do, idiom brackets)
- functor comprehensions

techtangents

package demo.maps;

import java.util.HashMap;
import java.util.Map;

import static demo.maps.MapUtils.P.p;

public class MapUtils {

    private MapUtils() {

techtangents

type Pos2D = Pos2D { x : Int, y : Int }

area : Pos2D -> Int
area (Pos2D {x,y}) = x * y

techtangents

module Namespacing2 where


type Pos2DU = { x :: Number, y :: Number }

area :: Pos2DU -> Number
area {x = x, y = y} = x * y

data Pos2DT = Pos2DT { x :: Number, y :: Number }

techtangents

https://wiki.haskell.org/Typeclassopedia

Functor -> Applicative -> Monad
Apply -----^


https://github.com/purescript/purescript-control

Functor -> Apply -> Applicative -> Monad
                 -> Bind ----------^

techtangents

package com.example;

public abstract class Either<A, B> {
    
    public abstract <T> T fold(final F<A, T> af, final F<B, T> bf);
    
    private Either(){}
    
    public static <A, B> Either<A, B> a(final A a) {
        return new Either<A, B>() {

techtangents

Higher-kinded types in Java
===========================

If we consider that types classify values, then kinds classify types. 
To use Haskell notation, simple java types are of kind * - the kind of types of values. 
Generic types (e.g. List) are of kind * -> * - this is essentially a type-level 
function - pass a type parameter A to the List type constructor and you get a List<A>.

Higher-kinded types are (basically) of kind (* -> *) -> *. 

techtangents

import java.util.function.Function;

public class Blah {

    private Blah() {
    }

    static class A {
    }

techtangents

Proof of the functor laws for the Maybe functor 

fmap :: (a -> b) -> Maybe a -> Maybe b
fmap f (Just x) = Just (f x)
fmap f Nothing  = Nothing

Prove:
fmap id = id

Case 1: Just x

techtangents

module FreeDom where

import Control.Monad.Free
import Control.Monad.Free.Trans
import DOM
import DOM.HTML
import DOM.HTML.Window
import DOM.Node.Node
import DOM.Node.Types
import Data.Array