The document discusses the efficiency of immutable data in functional programming, emphasizing the benefits of pure functions and the avoidance of shared state. It highlights the challenge of performance compared to mutable data structures and introduces persistent data structures as a solution through structural sharing. Key takeaways include that while functional data structures may not be as fast, their benefits in state management can compensate for performance losses.

1. How Efficient Immutable Data Enables Functional
Programming

2. How Efficient Immutable Data Enables Functional
Programming
or
Okasaki
For
Dummies

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Who Am I?

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Tom Faulhaber
➡ Planet OS CTO
➡ Background in
networking, Unix OS,
visualization, video
➡ Currently working mostly
in “Big Data”
➡ Contributor to the
Clojure programming
language

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Who Are YOU?

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What is functional programming?

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y = f(x)
Pure Functions:

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y = f(x)
Pure Functions:
y = f(x)

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y = f(x)
Pure Functions:
y = f(x)y = f(x)
Not modified
Not shared

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Higher-order Functions:
map(f, [x1, x2, ..., xn]) !
[f(x1), f(x2), ..., f(xn)]

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Higher-order Functions:
g = map(f)
Result is a new function

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Higher-order Functions:
g = map f

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Other Aspects:
➡Type inference
➡Laziness

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Functional is the opposite of
Object-oriented

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State is
managed
through
encapsulation
Object-oriented:
State is avoided
altogether
Functional:

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Why functional?

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Why functional?
➡ No shared state makes it easier to reason about
programs
➡ Concurrency problems simply go away (almost!)
➡ Undo and backtracking are trivial
➡ Algorithms are often more elegant
It is better to have 100 functions operate on one data
structure than 10 functions on 10 data structures. -
Alan Perlis

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Why functional?
A host of new languages support the functional model:
- ML, Haskell, Clojure, Scala, Idris
- All with different degrees of purity

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There’s a catch!

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There’s a catch!
f(5)
This is cheap:

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There’s a catch!
f({"type": "object",
"properties": {
"mesos": {
"description": "Mesos specific configuration properties",
"type": "object",
"properties": {
"master": { … }
… } … } … } … })
But this is expensive:

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There’s a catch!
f(<my whole database>)
And this is crazy:

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Persistent Data Structures
to the Rescue

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Persistent Data Structures
The goal: Approximate the performance of mutable
data structures: CPU and memory.
The big secret: Use structural sharing!
There are lots of little secrets, too. We won’t cover
them today.

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Persistent Data Structures - History
1990 2000 2010
Persistant
Arrays
(Dietz)
ML Language
(1973)
Catenable
Queues
(Buchsbaum/
Tarjan)
Okasaki
Haskell
Language
Clojure
CollectionsFinger Trees
(1977)
Zipper
(Huet)
Data.Map
in Haskell
Priority
Search
Queues
(Hinze)
Fast And
Space Efficient
Trie Searches
(Bagwell)
Ideal Hash
Trees
(Bagwell)
RRB
Trees
(Bagwell/
Rompf)

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The quick brown dog jumps over
6
Example: Vector
➡ In Java/C# ArrayList; in C++ std::vector.
➡ A list with constant access and update and amortized
constant append.
The quick brown fox jumps over
6 a[3] =“dog”dog

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Example: Vector
➡ In Java/C# ArrayList; in C++ std::vector.
➡ A list with constant access and update and amortized
constant append.
The quick brown dog jumps over
6 a.push_back(“the”)
The quick brown dog jumps over
7
the
the
The quick brown dog jumps over
7
the

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Example: Vector
➡ To build a persistent vector, we start with a tree:
Persistent
^
depth =
dlog ne
Data is in
the leaves
6
The quick brown fox jumps over

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The quick brown fox jumps over
6
0 1 2 3 4 5
000 001 010 011 100 101
LLL LLR LRL LRR RLL RLR
The quick brown fox jumps over
6
0 1 2 3 4 5
000 001 010 011 100 101
LLL LLR LRL LRR RLL RLR
The quick brown fox jumps over
6
0 1 2 3 4 5
000 001 010 011 100 101
LLL LLR LRL LRR RLL RLR
x = a[3]
The quick brown fox jumps over
6
0 1 2 3 4 5
000 001 010 011 100 101
LLL LLR LRL LRR RLL RLR
The quick brown fox jumps over
6
0 1 2 3 4 5
000 001 010 011 100 101
LLL LLR LRL LRR RLL RLR

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The quick brown fox jumps over
6 7
The quick brown fox jumps over
6 7
The quick brown fox jumps over
6 7
The quick brown fox jumps over
6
b = a.add(“the”)
7
The quick brown fox jumps over
6
the

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7
The quick brown fox jumps over the

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The quick brown fox jumps over
6

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7
The quick brown fox jumps over
6
the

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But, wait…

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But, wait…
O(1) 6= O(log n)
This isn’t what you promised!

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2
4
6
8
10
0 250 500 750 1000
Number of elements
Treedepth
2
4
6
8
10
0 250 500 750 1000
Number of elements
Treedepth
2
4
6
8
10
0 250 500 750 1000
Number of elements
Treedepth
d = 1
d = dlog2 ne

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The answer:
Use 32-way trees

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x = a[7022896]x = a[7022896]
00110 10110 01010 01001 10000
6 22 10 9 16

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6
apple
22
10
9
16

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O(1) ' O(log32 n)

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2
4
6
8
10
0 250 500 750 1000
Number of elements
Treedepth
d = 1
d = dlog2 ne
2
4
6
8
10
0 250 500 750 1000
Number of elements
Treedepth
d = dlog32 ne

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Example: Tree Walking
➡ The functional equivalent of the visitor pattern

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Clojure code to implement the walker:
(postwalk
(fn [node]
(if (= :blue (:color node))
(assoc node :color :green)
node))
tree)
Example: Tree Walking

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Example: Zippers
➡ Allow you to navigate and update a tree across many
operations by “unzipping” it.

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Takeaways
➡ Functional data structures can approximate the
performance of mutable data structures, but will
usually won’t be quite as fast.
➡ … but not having to do state management often
wins back the difference
➡ We need to choose data structures carefully
depending on how they’re going to be used.
➡ This doesn’t solve shared state, just reduces it. (but
see message passing, software transactional
memory, etc.)

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References
Chris Okasaki, Purely Functional Data Structures, Doctoral dissertation, Carnegie Mellon University, 1996.
Rich Hickey, “Are We There Yet?” Presentation at the JVM Languages SUmmit, 2009. http://www.infoq.com/
presentations/Are-We-There-Yet-Rich-Hickey
Gerard Huet, "Functional Pearl: The Zipper". Journal of Functional Programming 7 (5): 549–554. doi:10.1017/
s0956796897002864
Jean Niklas L’orange, “Understanding Clojure's Persistent Vectors” Blog post at http://hypirion.com/musings/
understanding-persistent-vector-pt-1.

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Discussion