Purely functional data structures demystified
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I spoke about 'Purely Functional Data structures' at Functional Conference 2014 in Bangalore. These are my slides with an extra section on further study. This talk is based on Chris Okasaki's book title Purely Functional Data Structures. The gist is that immutable and persistent data structures can be designed without sacrificing performance.
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Purely functional data structures demystified
- 1. Purely Functional Data Structures Demystified Mohit Thatte Functional Conf 2014, Bangalore
- 2. About Me Work The great outdoors @mohitthatte github.com/pastafari
- 5. Programs that use Maps Towers of Abstraction Map as ADT Map implementation Primitives…
- 7. Any sufficiently advanced data structure is indistinguishable from magic With apologies to Arthur C. Clarke!
- 10. AbstractionsData
- 11. Abstract Data Type Invariants Stack push, pop LIFO Name Operations ADT
- 13. Change perspective Think like a data structure designer
- 14. The ADT Challenge Given an ADT, give a correct implementation of all operations.
- 16. “You can program in any language you want… as long as it is imperative”
- 17. make it easier to reason about code Why Functional? Immutability Persistence
- 18. x = 5 y = x + 1 pr!nt x x = [1,2] y = x << 3 pr!nt x 5 is immutable [1,2] is NOT!
- 19. x = [1,2] foo(x) x ("et [x [1 2]] (foo x) x) What is x now? What is x now?
- 20. The ADT Challenge Given an ADT, give a correct and functional implementation of all operations.
- 21. Performance matters too. A lot.
- 23. The ADT Challenge Given an ADT, give a correct, functional and performant implementation of all operations.
- 26. 3 -2 3 -2 The Pair cons (def x (cons 3 -2)) (head x) (ta!" x) 3 -2 head ta!"
- 27. Cons, the Magnificent (defn ta!" [z] (z (fn [p q] q))) (defn head [z] (z (fn [p q] p))) (defn cons [x y] (fn [m] (m x y)))
- 28. Voila, a list! 3 2 1 nil (cons 3 (cons 2 (cons 1 n!")))
- 29. And so it goes… Pair List Sets …
- 31. 3 2 1 nil 3 4 Structural Sharing
- 32. Queue ADT enqueue peek dequeue append an e"ement f!rst e"ement rema!n!ng e"ements Invar!ant FIFO Operat!ons
- 33. Queue ADT
- 36. Pattern Matching
- 39. Use 2 lists… Be clever!
- 42. Amortized Analysis Care about a sequence of operations rather than worst case Earn credits each time you don’t do an expensive operation, spend credits when you do
- 44. Map ADT put get assoc!ate a key w!th va"ue "ookup key, return va"ue de"ete remove key & va"ue Invar!ant Operat!ons what you put !s what you get
- 45. Map ADT
- 46. Ideas?
- 47. Use a list? Nope. Too slow.
- 48. Use a Tree Yep!
- 52. 13 … until this happens 15 17 21
- 53. स"तuलन का होना ब,त ज़.री 1 !
- 55. Red Black Tree No red node can have a red child Every path from root to an empty node contains the same number of black nodes Guibas, Sedgewick 1978 Each node is colored Red or Black
- 56. Red Black Tree Source: Wikipedia
- 57. Red Black Tree Source: Wikipedia 7
- 58. Red Black Tree Source: Wikipedia 7
- 59. Red Black Tree Source: Wikipedia 7
- 60. Red Black Tree Source: Wikipedia 7
- 61. Red Black Tree Source: Wikipedia 7
- 62. Red Black Tree Source: Wikipedia 7
- 63. z a b c d a b y x y x z c d y x z x y z a b c d a b c d a b c d y z x
- 64. Pattern Matching is awesome!
- 65. Persistent Bit-Partitioned Vector Trie Phil Bagwell, Rich Hickey
- 67. Image: Jean Niklas L’orange http://hypirion.com/musings/understanding-persistent-vector-pt-1
- 74. Further study
- 75. Persistent vectors in Clojure http://hypirion.com/musings/understanding-persistent-vector-pt-1
- 76. Red Black Trees http://www.eternallyconfuzzled.com/tuts/datastructures/jsw_tut_rbtree.aspx Julienne Walker