Purely Functional Data Structures
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The document discusses purely functional data structures, focusing on persistence types including ephemeral, partially persistent, and fully persistent structures. It covers various data structures like linked lists, binary search trees, and examples of queues and heaps, highlighting the implications of persistence on performance and operations. Additionally, it touches on concepts of amortization, lazy evaluation, and numerics related to data structures.
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Alexberlioz [CC-BY-SA-3.0], from Wikimedia
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Marc NL [Public domain], from Wikimedia
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J.J. [CC-BY-SA-3.0], from Wikimedia Commons](https://image.slidesharecdn.com/purelyfunctionaldatastructures-aswas-140901083634-phpapp02/85/Purely-Functional-Data-Structures-23-320.jpg)
Purely Functional Data Structures
- 1. Purely Functional Data Structures Jean-Baptiste Mazon Riviera Func 2013-05-21
- 2. OHAI Jean-Baptiste Mazon @jbmazon Sophia-Antipolis PL (Google Docs)
- 3. Purely Functional Data Structures About — What — Why — How
- 4. Persistence ● ephemeral ● partially persistent ● fully persistent ● confluently persistent immutable data ⇒ fully persistent structures
- 7. Persistence: binary search tree
- 9. Amortization Mutable textbook example: autosized vector Okasaki examples: ● queues ● binomial heaps ● splay heaps ● pairing heaps
- 10. Naive queue 1 2 3 n-2 n-1 n
- 11. Amortized queue 1 2 3 n n-1 n-2 ...breaks with persistence
- 12. Persistence and Amortization execution trace expensive operation call-by-value call-by-name call-by-need stream
- 13. Lazy Evaluation 1 2 3 1 2 3 f r
- 14. Persistent Amortized Queue 1 f r 1 better than amortized?
- 15. Realtime Queue problem with reverse rotate(f,r,a) = f ++ reverse(r) ++ a rotate(f|fs,r|rs,a) = f | rotate(fs,rs,r|a) “scheduling”
- 16. Numerics Lists List = ● Empty ● Cons(e,List) Peano arithmetic Nat = ● Zero ● Succ(Nat)
- 17. Numerics: random access list 0 1 2 3 4 5 6 , , … but cons, head, tail are O(lg N)
- 18. Numerics: zeroless how consequence on list consequence on first tree head O(1) tail and cons O(1)?
- 19. Numerics: redundancy 22222 111111 011111
- 21. But wait, there's more! ● not only queues ● skew binary ● bootstrapping ● implicit recursive slowdown
- 22. KTHXBYE
- 23. Image Credits Alexberlioz [CC-BY-SA-3.0], from Wikimedia Commons Marc NL [Public domain], from Wikimedia Commons J.J. [CC-BY-SA-3.0], from Wikimedia Commons