// Scala Lecture 5

//=================

// (Immutable)

// Object Oriented Programming in Scala

// =====================================

abstract class Animal 

case class Bird(name: String) extends Animal {

   override def toString = name

}

case class Mammal(name: String) extends Animal

case class Reptile(name: String) extends Animal

Mammal("Zebra")

println(Mammal("Zebra"))

println(Mammal("Zebra").toString)

Bird("Sparrow")

println(Bird("Sparrow"))

println(Bird("Sparrow").toString)

Bird("Sparrow").copy(name = "House Sparrow")

def group(a : Animal) = a match {

  case Bird(_) => "It's a bird"

  case Mammal(_) => "It's a mammal"

}

// There is a very convenient short-hand notation

// for constructors:

class Fraction(x: Int, y: Int) {

  def numer = x

  def denom = y

}

val half = new Fraction(1, 2)

half.numer

case class Fraction(numer: Int, denom: Int)

val half = Fraction(1, 2)

half.numer

half.denom

// In mandelbrot.scala I used complex (imaginary) numbers 

// and implemented the usual arithmetic operations for complex 

// numbers.

case class Complex(re: Double, im: Double) { 

  // represents the complex number re + im * i

  def -(that: Complex) = Complex(this.re - that.re, this.im - that.im)

  def *(that: Complex) = Complex(this.re * that.re - this.im * that.im,

                                 this.re * that.im + that.re * this.im)

  def *(that: Double) = Complex(this.re * that, this.im * that)

  def abs = Math.sqrt(this.re * this.re + this.im * this.im)

}

val test = Complex(1, 2) + Complex (3, 4)

import scala.language.postfixOps

// this could have equally been written as

val test = Complex(1, 2).+(Complex (3, 4))

// this applies to all methods, but requires

import scala.language.postfixOps

List(5, 2, 3, 4).sorted

List(5, 2, 3, 4) sorted

// ...to allow the notation n + m * i

import scala.language.implicitConversions   

val i = Complex(0, 1)

implicit def double2complex(re: Double) = Complex(re, 0)

val inum1 = -2.0 + -1.5 * i

val inum2 =  1.0 +  1.5 * i

// All is public by default....so no public is needed.

// You can have the usual restrictions about private 

// values and methods, if you are MUTABLE !!!

case class BankAccount(init: Int) {

  private var balance = init

  def deposit(amount: Int): Unit = {

    if (amount > 0) balance = balance + amount

  }

  def withdraw(amount: Int): Int =

    if (0 < amount && amount <= balance) {

      balance = balance - amount

      balance

    } else throw new Error("insufficient funds")

}

// BUT since we are completely IMMUTABLE, this is 

// virtually of no concern to us.

// another example about Fractions

import scala.language.implicitConversions

import scala.language.reflectiveCalls

case class Fraction(numer: Int, denom: Int) {

  override def toString = numer.toString + "/" + denom.toString

  def +(other: Fraction) = 

    Fraction(numer * other.denom + other.numer * denom, 

             denom * other.denom)

  def *(other: Fraction) = Fraction(numer * other.numer, denom * other.denom)

 }

implicit def Int2Fraction(x: Int) = Fraction(x, 1)

val half = Fraction(1, 2)

val third = Fraction (1, 3)

half + third

half * third

1 + half

// DFAs in Scala  

//===============

import scala.util.Try

// A is the state type

// C is the input (usually characters)

case class DFA[A, C](start: A,              // starting state

                     delta: (A, C) => A,    // transition function

                     fins:  A => Boolean) { // final states (Set)

  def deltas(q: A, s: List[C]) : A = s match {

    case Nil => q

    case c::cs => deltas(delta(q, c), cs)

  }

  def accepts(s: List[C]) : Boolean = 

    Try(fins(deltas(start, s))).getOrElse(false)

}

// the example shown in the handout 

abstract class State

case object Q0 extends State

case object Q1 extends State

case object Q2 extends State

case object Q3 extends State

case object Q4 extends State

val delta : (State, Char) => State = 

  { case (Q0, 'a') => Q1

    case (Q0, 'b') => Q2

    case (Q1, 'a') => Q4

    case (Q1, 'b') => Q2

    case (Q2, 'a') => Q3

    case (Q2, 'b') => Q2

    case (Q3, 'a') => Q4

    case (Q3, 'b') => Q0

    case (Q4, 'a') => Q4

    case (Q4, 'b') => Q4 

    case _ => throw new Exception("Undefined") }

val dfa = DFA(Q0, delta, Set[State](Q4))

dfa.accepts("abaaa".toList)     // true

dfa.accepts("bbabaab".toList)   // true

dfa.accepts("baba".toList)      // false

dfa.accepts("abc".toList)       // false

// NFAs (Nondeterministic Finite Automata)

case class NFA[A, C](starts: Set[A],          // starting states

                     delta: (A, C) => Set[A], // transition function

                     fins:  A => Boolean) {   // final states 

  // given a state and a character, what is the set of 

  // next states? if there is none => empty set

  def next(q: A, c: C) : Set[A] = 

    Try(delta(q, c)).getOrElse(Set[A]()) 

  def nexts(qs: Set[A], c: C) : Set[A] =

    qs.flatMap(next(_, c))

  // depth-first version of accepts

  def search(q: A, s: List[C]) : Boolean = s match {

    case Nil => fins(q)

    case c::cs => next(q, c).exists(search(_, cs))

  }

  def accepts(s: List[C]) : Boolean =

    starts.exists(search(_, s))

}

// NFA examples

val nfa_trans1 : (State, Char) => Set[State] = 

  { case (Q0, 'a') => Set(Q0, Q1) 

    case (Q0, 'b') => Set(Q2) 

    case (Q1, 'a') => Set(Q1) 

    case (Q2, 'b') => Set(Q2) }

val nfa = NFA(Set[State](Q0), nfa_trans1, Set[State](Q2))

nfa.accepts("aa".toList)             // false

nfa.accepts("aaaaa".toList)          // false

nfa.accepts("aaaaab".toList)         // true

nfa.accepts("aaaaabbb".toList)       // true

nfa.accepts("aaaaabbbaaa".toList)    // false

nfa.accepts("ac".toList)             // false

// Q: Why the kerfuffle about the polymorphic types in DFAs/NFAs?

// A: Subset construction. Here the state type for the DFA is

//    sets of states.

def subset[A, C](nfa: NFA[A, C]) : DFA[Set[A], C] = {

  DFA(nfa.starts, 

      { case (qs, c) => nfa.nexts(qs, c) }, 

      _.exists(nfa.fins))

}

subset(nfa).accepts("aa".toList)             // false

subset(nfa).accepts("aaaaa".toList)          // false

subset(nfa).accepts("aaaaab".toList)         // true

subset(nfa).accepts("aaaaabbb".toList)       // true

subset(nfa).accepts("aaaaabbbaaa".toList)    // false

subset(nfa).accepts("ac".toList)             // false

import scala.math.pow

// The End ... Almost Christmas

//===============================

// I hope you had fun!

// A function should do one thing, and only one thing.

// Make your variables immutable, unless there's a good 

// reason not to. Usually there is not.

// I did it once, but this is actually not a good reason:

// generating new labels:

var counter = -1

def Fresh(x: String) = {

  counter += 1

  x ++ "_" ++ counter.toString()

}

Fresh("x")

Fresh("x")

// I think you can be productive on Day 1, but the 

// language is deep.

//

// http://scalapuzzlers.com

//

// http://www.latkin.org/blog/2017/05/02/when-the-scala-compiler-doesnt-help/

val two   = 0.2

val one   = 0.1

val eight = 0.8

val six   = 0.6

two - one == one

eight - six == two

eight - six

// problems about equality and type-errors

List(1, 2, 3).contains("your cup")   // should not compile, but retruns false

List(1, 2, 3) == Vector(1, 2, 3)     // again should not compile, but returns true