Collection Builders and Quanti ers vs Streams

Transcript

1. Collection Builders and Quantifiers vs Streams Michael Wiedeking (michael.wiedeking@mathema.de) 4th Virtual Machine Meetup – Prague 29. September 2017
2. Motivation
3. In Java, what are the advantages of streams over loops?
4. Streams … have a more declarative style … are often terser … have a strong affinity with functions … encourage less mutability … encourage looser coupling … can succinctly express quite sophisticated behaviour … provide scope for future efficiency gains But: – Performance – Familiarity – Cognitive overhead – Debugging https://stackoverflow.com/questions/44180101/in-java-what-are-the-advantages-of-streams-over-loops#44180875
5. return students.stream() .filter(s –> s.age() < 18) .collect(toList()) ;
6. List<Student> filtered = new ArrayList<>(); for (Student s : students) { if (s.age() < 18) { filtered.add(s); } } return filtered;
7. return ⟨s ∈ students ∣ s.age < 18⟩
8. return ⟨s ∣ s ∈ students, s.age < 18⟩
9. students.stream() .filter(x –> x.age() < 18) .findFirst() ;
10. students.stream() .filter(x –> x.age() < 18) .findFirst() ; students.stream() .filter(x –> x.age() < 18) .limit(1) ;
11. List<Integer> a = Arrays.asList(3, 1, 7, 4, 2, 5, 9, 8, 6); Stream<Integer> s = a.stream() .filter(x –> x < 5) .sorted() ; System.out.println(s.limit(3).collect(Collectors.toList())); System.out.println(s.count());
12. List<Integer> a = Arrays.asList(3, 1, 7, 4, 2, 5, 9, 8, 6); Stream<Integer> s = a.stream() .filter(x –> x < 5) .sorted() ; System.out.println(s.limit(3).collect(Collectors.toList())); System.out.println(s.count()); [1, 2, 3] Exception in thread "main" java.lang.IllegalStateException: stream has already been operated upon or closed
13. Point of View
14. s.stream().foreach(f);
15. s.stream().foreach(f); for x ∈ s do f(x) end
16. sum = 0; s.stream() .foreach(x –> sum += x) ; println(sum); sum ← 0 for x ∈ s do sum ← sum + x end printLine(sum)
17. sum = 0; s.stream() .foreach(x –> sum += x) ; println(sum); sum ← 0 for x ∈ s do sum ← sum + x end printLine(sum)
18. a = new int[1]; s.stream() .foreach(x –> a[0] += x) ; println(a[0]); sum ← 0 for x ∈ s do sum ← sum + x end printLine(sum)
19. a = new int[1]; s.stream() .filter(x >= 0) .foreach(x –> a[0] += x) ; println(a[0]); sum ← 0 for x ∈ s, x ≥ 0 do sum ← sum + x end printLine(sum)
20. sum ← 0 for x ∈ s do sum ← sum + x if sum ≥ limit then break end end printLine(sum)
21. Collection Builders
22. • List.of(…) • Set.of(…) • Map.of(k 1 , v 1 , … , k 10 , v 10 ) • Map.ofEntries(entry(k 1 , v 1 ), … , entry(k 10 , v 10 ), …)
23. (1, 2, 2, 3) {1, 2, 3} {1 ↦ ‘a’, 2 ↦ ‘b’, 3 ↦ ‘c’} ⦃1, 2, 2, 3⦄ ⟨1, 2, 2, 3⟩ [1, 2, 2, 3] [1 2 3] [1 2; 3 4] Tuple Set Map Bag List Array Vector Matrix
24. • {1, … , n} • {1, 3, … , n} • {a, a + Δ, … , b} • {a, a − Δ, … , b} • {a, …} • {a, a + Δ, … } • {…, −1, 0, +1, …} • {a, b, c, d, e, f, g} • {1, 2, 3, 4, 5, 6, 7} • {1, … , 5; 7, 8; 10, … , 15; 20, … , 25; 30, 31}
25. x_class := [ CA FE BA BE 00 00 00 35 00 05 07 00 03 07 00 04 01 00 01 58 01 00 10 6A 61 76 61 2F 6C 61 6E 67 2F 4F 62 6A 65 63 74 06 01 00 01 00 02 00 00 00 00 00 00 00 00 ] 16 x_class : Array⟦ 1 ⟧ = [ (CA) 16 , (FE) 16 , (BA) 16 , (BE) 16 , … ]
26. {(x 1 , x 2 , … , x n ) | x 1 ∈ C 1 , p 1 (x 1 ); x 2 ∈ C 2 (x 1 ), p 2 (x 1 , x 2 ); … ; x n–1 ∈ C n–1 (x 1 , x 2 , … , x n–2 ), p n–1 (x 1 , x 2 , … , x n–1 ); x n ∈ C n (x 1 , x 2 , … , x n ), p n (x 1 , x 2 , … , x n ) }
27. {(x, y, z) ∣ x ∈ S, y ∈ S, z ∈ S, x² + y² = z²} where S := {1, … , N}
28. {(x, y, z) ∣ x ∈ S, y ∈ S, z ∈ S, x² + y² = z²} where S := {1, … , N} ⟨(x, y, z) ∣ x ∈ {1, … , N}, y ∈ {x, … , N}, z ∈ {y, … , N}, x² + y² = z² ⟩
29. {(x, y, z) ∣ x ∈ S, y ∈ S, z ∈ S, x² + y² = z²} where S := {1, … , N} ⟨(x, y, z) ∣ x ∈ {1, … , N}, y ∈ {x, … , N}, z ∈ {y, … , N}, x + y ≤ z, x² + y² = z² ⟩
30. C 1 := {1, 2, 3} C 2 := {2, 3, 4} assert {x | x ∈ C 1 ∧ x ∈ C 2 } = {2, 3} assert {x | x ∈ C 1, x ∈ C 2 } = {2, 3} assert {x | x ∈ C 1, y ∈ C 2 } = {1, 2, 3} assert {(x, y) | x ∈ C 1, y ∈ C 2 } = {(1, 2), (1, 3), (1, 4), (2, 2), …} assert {x | x ∈ C 1 ∨ x ∈ C 2 } = {1, 2, 3, 4} assert ⟨x | x ∈ C 1 ∨ x ∈ C 2 ⟩ = ⟨1, 2, 3, 2, 3, 4⟩ assert ⟨x | x ∈ C 1 ∘ C 2 ⟩ = ⟨1, 2, 3, 2, 3, 4⟩ assert ⟨x | x ∈ C 1 ‡ C 2 ⟩ = ⟨1, 2, 2, 3, 3, 4⟩
31. s.map(t) {t(x) | x ∈ s}
32. assert {x² | x ∈ {1, … , 5}} = {1, 4, 9, 16, 25}
33. Quantifiers
34. … s.stream().allMatch(p) … s.stream().anyMatch(p) … s.stream().noneMatch(p)
35. … s.stream().allMatch(p) … s.stream().anyMatch(p) … s.stream().noneMatch(p) … ∀(x ∈ s) p(x) … ∃(x ∈ s) p(x) … ∄(x ∈ s) p(x)
36. o = s.filter(p).findAny(); if (o.isPresent()) { (o.get()); } if ∃(x ∈ s) p(x) then (x) end
37. Everything else
38. • s.count() • s.findAny() • s.findFirst() • s.min(c) • s.max(c) • s.skip(n) • s.dropWhile(p) • s.takeWhile(p) • s.reduce(…) • s.collect(…) • s.limit(n)
39. s.findAny() s.findFirst() s.count() arb s s.arb() s.first() |s| s.numberOfElements()
40. {1, 2, 3} ⦃1, 2, 2, 3⦄ ⟨1, 2, 2, 3⟩ [1, 2, 2, 3] • ordered skip(n) dropWhile(p) takeWhile(p) • others ⟪⟫❨❩❲❳⁅ ⁆⸦⸧⦅⦆⦇⦈⦉⦊⦋ ⦌⦍ ⦎⦏ ⦐⦑⦒⦓⦔⦕⦖⸢⸣⸤⸥⸨⸩⟬⟭⟮⟯⌈⌉⌊⌋ unordered, unique unordered ordered ordered
41. ∑[1 ≤ k ≤ n] 2k ∑{k | k ∈ {1, … , n}} 2k ∑⟨(i, j) | i ∈ ⟨1, … , n⟩, j ∈ ⟨1, … , m⟩⟩ a[i][j]
42. Examples
43. Pythagorean Quadruples a² + b² + c² = d²
44. S := {1, … , N} S ∖ {d ∣ a ∈ S, b ∈ S, c ∈ S, d ∈ S, a² + b² + c² = d²}
45. S := {1, … , N} S ∖ {d ∣ a ∈ S, b ∈ S, c ∈ S, d ∈ S, a² + b² + c² = d²} {d ∣ d ∈ S, ∄(a ∈ S) ∄(b ∈ S) ∄(c ∈ S) a² + b² + c² = d²}
46. S := {1, … , N} S ∖ {d ∣ a ∈ S, b ∈ S, c ∈ S, d ∈ S, a² + b² + c² = d²} {d ∣ d ∈ S, ∄(a ∈ S) ∄(b ∈ S) ∄(c ∈ S) a² + b² + c² = d²} {d ∣ d ∈ S, ∀(a ∈ S) ∀(b ∈ S) ∀(c ∈ S) a² + b² + c² ≠ d²}
47. S := {1, … , N} S ∖ {d ∣ a ∈ S, b ∈ S, c ∈ S, d ∈ S, a² + b² + c² = d²} {d ∣ d ∈ S, ∄(a ∈ S) ∄(b ∈ S) ∄(c ∈ S) a² + b² + c² = d²} {d ∣ d ∈ S, ∀(a ∈ S) ∀(b ∈ S) ∀(c ∈ S) a² + b² + c² ≠ d²} {d ∈ S ∣ ∀(a ∈ S) ∀(b ∈ S) ∀(c ∈ S) a² + b² + c² ≠ d²}
48. 100 % println( IntStream.rangeClosed(1, N).filter(d –> IntStream.range(1, d).allMatch(a –> IntStream.range(a, d).allMatch(b –> IntStream.range(b, d).allMatch(c –> a * a + b * b + c * c != d * d; ) ) ) ) .collect(toList()) );
49. 100 % println( IntStream.rangeClosed(1, N).filter(d –> { return IntStream.range(1, d).allMatch(a –> { return IntStream.range(a, d).allMatch(b –> { return IntStream.range(b, d).allMatch(c –> { return a * a + b * b + c * c != d * d; }); }); }); }) .collect(toList()) );
50. ~70 % println( IntStream.rangeClosed(1, N).filter(d –> { int dd = d * d; return IntStream.range(1, d).allMatch(a –> { int aa = a * a; return IntStream.range(a, d).allMatch(b –> { int aa_bb = aa + b * b; return IntStream.range(b, d).allMatch(c –> { return aa_bb + c * c != dd; }); }); }); }) .collect(toList()) );
51. {d ∈ S ∣ ∀(a ∈ S) ∀(b ∈ S) ∀(c ∈ S) a² + b² + c² ≠ d²} where S := {1, … , N}
52. ~7 % {d ∈ {1, … , N} ∣ ∀(a ∈ {1, … , d}) ∀(b ∈ {a, … , d}) ∀(c ∈ {b, … , d}) a² + b² + c² ≠ d² }
53. ~6 % {d ∈ {1, … , N} ∣ ∀(a ∈ {1, … , d} where dd := d²) ∀(b ∈ {a, … , d} where aa := a²) ∀(c ∈ {b, … , d} where aa_bb := aa + b²) aa_bb + c² ≠ dd }
54. Poker
55. public static boolean isFlush(Hand hand) { return hand.stream() .allMatch( c –> hand.stream() .filter(cc –> cc != c) .allMatch(cc –> cc.suit == c.suit) ) ; }
56. public static boolean isFlush(Hand hand) { Card arb = hand.stream().findAny().get(); return hand.stream() .filter(c –> c != arb) .allMatch(c –> c.suit == arb.suit) ; }
57. public static boolean isFlush(Hand hand) { Card arb = hand.stream().findAny().get(); Suit suit = arb.suit; return hand.stream() .filter(c –> c != arb) .allMatch(c –> c.suit == suit) ; }
58. function isFlush(Hand hand) → is return ∀(c ∈ hand) ∀(cc ∈ hand, cc ≠ c) ( cc.suit = c.suit ) end
59. function isFlush(Hand hand) → is return ( ∀(cc ∈ hand where c := arb(hand), cc ≠ c) cc.suit = c.suit ) end
60. function isFlush(Hand hand) → is return ( ∀( cc ∈ hand where (c := arb(hand); suit := c.suit), cc ≠ c ) cc.suit = suit ) end
61. function isFlush(Hand hand) → is return ( ∀( cc ∈ hand where c := arb(hand), suit := c.suit, cc ≠ c ) cc.suit = suit ) end
63. function fourOfAKind(Hand hand) → is return ( ∃(s ∈ ℘₄(hand)) ∀(c ∈ s where r := arb(s).rank) (c.rank = r) ) end
64. Quintessence
65. ∃(x ∈ s) (∃x ∈ s)
66. Questions?
67. Thank You! For more information about quantifiers in Aalgola see aalgola.org