klgraham

uniform.mean() // Approximately 0.5

uniform.prob({ $0 > 0.7 })   // Approximately 0.3
 
dice.prob({ $0 == 7 })   // Approximately 1/6

klgraham

let dice = die6.flatMap({
  (d1: Int) in return die6.map({ (d2: Int) in return d1 + d2 })
})

dice.sample(10)

klgraham

func nextInt(min min: Int, max: Int) -> ((Void) -> Int) {
     assert(max > min)
     return { () in return Int(arc4random_uniform(UInt32((max - min) + 1))) + min }
 }
  
 let die6 = Distribution<Int>(get: nextInt(min: 1, max: 6))
 die6.sample(10)

klgraham

let tf = uniform.map({ $0 < 0.7 })
tf.sample(10)

let bernoulli = tf.map({ $0 ? 1 : 0 })
bernoulli.sample(10)

klgraham

func lessThan(p: Double) -> (Double -> Bool) {
  return { x in return x < p }
}

klgraham

func randomDouble() -> Double {
  return Double(arc4random()) / Double(UInt32.max)
}

let uniform = Distribution<Double>(get: randomDouble)
uniform.sample(5)

klgraham

struct Distribution<A> {
    var get: () -> A?
    
    func sample(n: Int) -> [A] {
        return (1...n).map { x in get()! }
    }
    
    func map<B>(f: A -> B) -> Distribution<B> {
        var d = Distribution<B>(get: {() -> Optional<B> in return nil})
        d.get = {

klgraham

struct UniformDoubleDist: Stochastic {
    // Returns a uniform double on [0,1]
    func get() -> Double {
        return drand48()
    }
    
    func sample(n: Int) -> [Double] {
        return (1...n).map { x in get() }
    }
}

klgraham

protocol Parameterized {
    associatedtype ParameterType
    var p: ParameterType { get }
}

klgraham

protocol Stochastic {
    // the type of value stored in the distribution
    associatedtype ValueType
    
    // Sample a single value from the distribution
    func get() -> ValueType
    
    // Sample n values from the distribution
    func sample(n: Int) -> [ValueType]
}