let flag: (Bool) -> String = { $0 ? "✅" : "❌" }

// ------------------------
// Predicative
// ------------------------

protocol Predicative {
  static func + (lhs: Self, rhs: Self) -> Self
  static func * (lhs: Self, rhs: Self) -> Self
  static func gt<P: PredicateLike>(_: P.Input) -> P where P.Input: Comparable, P.Output == Self
  static func lt<P: PredicateLike>(_: P.Input) -> P where P.Input: Comparable, P.Output == Self
  static func eq<P: PredicateLike>(_: P.Input) -> P where P.Input: Equatable, P.Output == Self
  static func or<P: PredicateLike>(_: P, _: P) -> P where P.Output == Self
  static func and<P: PredicateLike>(_: P, _: P) -> P where P.Output == Self
  static func run<P: PredicateLike>(_: P) -> (P.Input) -> Self where P.Output == Self
}

extension Predicative {

  static func or<P: PredicateLike>(_ p1: P, _ p2: P) -> P where P.Output == Self {
    return .init(p1, p2, *)
  }

  static func and<P: PredicateLike>(_ p1: P, _ p2: P) -> P where P.Output == Self {
    return .init(p1, p2, +)
  }

  static func run<P: PredicateLike>(_ p: P) -> (P.Input) -> Self where P.Output == Self {
    return p.run
  }
}

// ------------------------
// Predicate
// ------------------------

protocol PredicateLike {
  associatedtype Input
  associatedtype Output: Predicative

  init(_: Input, _: @escaping (Input, Input) -> Output)
  init(_: Self, _: Self, _: @escaping (Output, Output) -> Output)

  func run(_ i: Input) -> Output
}

extension PredicateLike {

  static func leaf<P>(_ i: P.Input, _ b: @escaping (P.Input, P.Input) -> P.Output) -> P where P: PredicateLike {
    return .init(i, b)
  }

  static func pred<P>(_ p1: P, _ p2: P, _ f: @escaping (P.Output, P.Output) -> P.Output) -> P where P: PredicateLike {
    return .init(p1, p2, f)
  }

  static func or<P: PredicateLike>(_ p1: P, _ p2: P) -> P {
    return P.Output.or(p1, p2)
  }

  static func and<P: PredicateLike>(_ p1: P, _ p2: P) -> P {
    return P.Output.and(p1, p2)
  }

  static func lt<P: PredicateLike>(_ i: P.Input) -> P where P.Input: Comparable {
    return P.Output.lt(i)
  }

  static func gt<P: PredicateLike>(_ i: P.Input) -> P where P.Input: Comparable {
    return P.Output.gt(i)
  }

  static func eq<P: PredicateLike>(_ i: P.Input) -> P where P.Input: Equatable {
    return P.Output.eq(i)
  }

}

func || <P>(lhs: P, rhs: P) -> P where P: PredicateLike {
  return .or(lhs, rhs)
}

func && <P>(lhs: P, rhs: P) -> P where P: PredicateLike {
  return .and(lhs, rhs)
}

func gt<P: PredicateLike>(_ j: P.Input) -> P where P.Input: Comparable {
  return .gt(j)
}

func lt<P: PredicateLike>(_ j: P.Input) -> P where P.Input: Comparable {
  return .lt(j)
}

func eq<P: PredicateLike>(_ j: P.Input) -> P where P.Input: Equatable {
  return .eq(j)
}

// ------------------------
// PRED
// ------------------------

enum Predicate<I, O: Predicative>: PredicateLike {
  typealias Input = I
  typealias Output = O

  case _reduceLeaf(I, (I, I) -> O)
  indirect case _reducePred(Predicate, Predicate, (O, O) -> O)

  init(_ i: Input, _ f: @escaping (Input, Input) -> Output) {
    self = ._reduceLeaf(i, f)
  }

  init(_ p1: Predicate<I, O>, _ p2: Predicate<I, O>, _ f: @escaping (O, O) -> O) {
    self = ._reducePred(p1, p2, f)
  }

  func run(_ i: I) -> O {
    switch self {
    case let ._reduceLeaf(j, reduce):
      return reduce(i, j)
    case let ._reducePred(p, q, reduce):
      return reduce(p.run(i), q.run(i))
    }
  }
}

// ------------------------
// Bool
// ------------------------

extension Bool: Predicative {

  static func + (lhs: Bool, rhs: Bool) -> Bool {
    return lhs && rhs
  }
  static func * (lhs: Bool, rhs: Bool) -> Bool {
    return lhs || rhs
  }

  static func gt<P>(_ i: P.Input) -> P where P: PredicateLike, P.Input: Comparable, P.Output == Bool {
    return .leaf(i, >)
  }

  static func lt<P>(_ i: P.Input) -> P where P: PredicateLike, P.Input: Comparable, P.Output == Bool {
    return .leaf(i, <)
  }

  static func eq<P>(_ i: P.Input) -> P where P: PredicateLike, P.Input: Equatable, P.Output == Bool {
    return .leaf(i, ==)
  }
}

// ------------------------
// String
// ------------------------

extension String: Predicative {

  static func * (lhs: String, rhs: String) -> String {
    return lhs + " || " + rhs
  }

  static func gt<P>(_ i: P.Input) -> P where P: PredicateLike, P.Input: Comparable, P.Output == String {
    return .leaf(i, { "\($0) > \($1)" })
  }

  static func lt<P>(_ i: P.Input) -> P where P: PredicateLike, P.Input: Comparable, P.Output == String {
    return .leaf(i, { "\($0) < \($1)" })
  }

  static func eq<P>(_ i: P.Input) -> P where P: PredicateLike, P.Input: Equatable, P.Output == String {
    return .leaf(i, { "\($0) == \($1)" })
  }
}

// ------------------------
// N
// ------------------------

struct N: Predicative {

  let s: String
  let b: Bool

  static func + (lhs: N, rhs: N) -> N {
    return N(s: lhs.s + rhs.s, b: lhs.b + rhs.b)
  }
  static func * (lhs: N, rhs: N) -> N {
    return N(s: lhs.s * rhs.s, b: lhs.b * rhs.b)
  }

  static func gt<P>(_ i: P.Input) -> P where P: PredicateLike, P.Input: Comparable, P.Output == N {
    return .leaf(i, { N(s:"(\($0) > \($1) [\(flag($0 > $1))])", b: $0 > $1) })
  }

  static func lt<P>(_ i: P.Input) -> P where P: PredicateLike, P.Input: Comparable, P.Output == N {
    return .leaf(i, { N(s:"(\($0) < \($1) [\(flag($0 < $1))])", b: $0 < $1) })
  }

  static func eq<P>(_ i: P.Input) -> P where P: PredicateLike, P.Input: Equatable, P.Output == N {
    return .leaf(i, { N(s:"(\($0) == \($1) [\(flag($0 == $1))])", b: $0 == $1) })
  }
}

// ------------------------
// Sequence
// ------------------------

extension Sequence {

  func filter(by: IPredicate<Element, Bool>) -> [Element] {
    return filter(by.run)
  }

  func filter(by: IPredicate<Element, N>) -> String {
    return map { e in
      let n = by.run(e)
      return "\(flag(n.b)) \(e): \n " + n.s
      }.joined(separator: "\n ")
  }
}

// ------------------------
// IPredicate
// ------------------------

struct IPredicate<I, O: Predicative> {
  let run: (I) -> O

  init(_ f: @escaping (I) -> O) {
    self.run = f
  }

  init<P>(_ target: KeyPath<I, P>, _ predicate: Predicate<P, O>) {
    run = { i in O.run(predicate)(i[keyPath: target]) }
  }

  func liftD(_ ip: IPredicate<I, O>, _ f: @escaping (O, O) -> O) -> IPredicate<I, O> {
    return IPredicate { i in f(self.run(i), ip.run(i)) }
  }
}

func == <R, I, P>(lhs: KeyPath<R, I>, rhs: Predicate<I, P>) -> IPredicate<R, P> where I: Comparable {
  return IPredicate(lhs, rhs)
}

func && <I, O>(lhs: IPredicate<I, O>, rhs: IPredicate<I, O>) -> IPredicate<I, O> {
  return lhs.liftD(rhs, +)
}

func || <I, O>(lhs: IPredicate<I, O>, rhs: IPredicate<I, O>) -> IPredicate<I, O> {
  return lhs.liftD(rhs, *)
}

//// ------------------------
//// Example
//// ------------------------

struct P: CustomStringConvertible {
  let name: String
  let age: Int
  let address: A
  var description: String {
    return "P(name: \(name), age: \(age))"
  }
}

struct A {
  let country: String
}

let allPersons = [
  P(name: "a", age: 40, address: A(country: "🇨🇦")),
  P(name: "a", age: 31, address: A(country: "🇬🇧")),
  P(name: "b", age: 21, address: A(country: "🇩🇪")),
  P(name: "b", age: 50, address: A(country: "🇫🇷")),
  P(name: "c", age: 60, address: A(country: "🇯🇵"))
]

let result1: [P] = allPersons.filter(by:
  \.age == eq(40) || \.name == eq("a")
)

let result2: String = allPersons.filter(by:
  \.age == eq(40) || \.name == eq("a")
)

print(result2)