Purely Functional Data StructuresJean-Baptiste MazonRiviera Func 2013-05-21

OHAI

Jean-Baptiste Mazon@jbmazon

Sophia-AntipolisPL

(Google Docs)

Purely Functional Data Structures

About — What — Why — How

Persistence

● ephemeral● partially persistent● fully persistent● confluently persistent

immutable data ⇒ fully persistent structures

Persistence: linked lists

Persistence: concatenated lists

Persistence: binary search tree

Persistence: insertion

Amortization

Mutable textbook example: autosized vector

Okasaki examples:● queues● binomial heaps● splay heaps● pairing heaps

Okasaki examples:● queues● binomial heaps● splay heaps● pairing heaps

Naive queue

1 2 3 n-2 n-1 n

Amortized queue

...breaks with persistence

1 2 3

n-2n-1n

Persistence and Amortization

execution traceexpensive operation

call-by-valuecall-by-namecall-by-need

stream

Lazy Evaluation

1 2 3

321

f

r

Persistent Amortized Queue

1 1f r

better than amortized?

Realtime Queue

problem with reverse

rotate(f,r,a) = f ++ reverse(r) ++ arotate(f|fs,r|rs,a) = f | rotate(fs,rs,r|a)

“scheduling”

Numerics

Lists

List =● Empty● Cons(e,List)

Peano arithmetic

Nat =● Zero● Succ(Nat)

Numerics: random access list

… but cons, head, tail are O(lg N)

0 1 2 3 4 5 6, ,

Numerics: zeroless

how

consequence on listconsequence on first tree

head O(1)tail and cons O(1)?

Numerics: redundancy

22222111111011111

Numerics: quaternary

But wait, there's more!

● not only queues● skew binary● bootstrapping● implicit recursive

slowdown

KTHXBYE

Image Credits

Alexberlioz [CC-BY-SA-3.0], from Wikimedia CommonsMarc NL [Public domain], from Wikimedia CommonsJ.J. [CC-BY-SA-3.0], from Wikimedia Commons