Functional Programming Past Present Future

Functional ProgrammingPast, Present and

FuturePushkar N Kulkarni

IBM RuntimesIBM India Software Lab

Functional Programming - today’s special …

• Timeline – parallel to the imperative timeline

• Languages• Concepts

Goal: Bootstrapping for functional programming

The beginning of all creation …

Theory of Computation <- Math + Logic

Alonzo ChurchLambda Calculus

Alan TuringTuring Machine

Stephen KleeneRecursive Function

Theory

Lambda Calculus

It’s a formal system in mathematical logic for expressing computation based on function abstraction and application using variable binding and substitution. ~ Wikipedia

Lambda Calculus – Fundamental Idea

x //variable

t //lambda term

Λx.t //lambda abstraction

Λx. x2+1 // x is bound in t by Λx

Λx. x2+1(2) = 22+1 = 5 //application

Note: A lambda abstraction has no name

LISP - 1958

LIST Processor

Influenced by Church’s lambda calculus notation

Multi-paradigm, pre-fix notation

John McCarthy

LISP;;Employee compensation

(defun total (bonus-calc base) (+ (funcall bonus-calc base) base))

;; Good month

(total #'(lambda (x)(* 0.8 x)) 10000)

;; Bad month

(total #'(lambda (x)(+ (* 0.2 x) 10)) 10000)

LISP – Well known dialects

• Scheme – 1970• Common Lisp – 1984• Racket – 1984• Clojure – 2007• Lisp Flavoured Erlang (LFE) – 2008 (v1

March 2016)

Academic Research (1960 – 1985)

• ISWIM – If You See What I Mean – 1966• SASL – St. Andrews Static Language – 1972• ML – MetaLanguage – 1973 => Ocaml, F#• Miranda – 1985 => Haskell

Back to some Lambda Calculus

F(x) = x3+4x //F(x) id a first-order function

//maps values to values

dF(x)/dx = 3x2 + 4

//d/dx maps functions to functions

d/dx is an example of higher-order functions

Higher-order Functions

A function is a higher-order function if:• It takes at least one function as an argument OR• It returns a function

All other functions are first–order functions!

Erlang - 1984

Designed for massive scalable soft real time systems

Fault-tolerance and concurrency

Erlang

Multi-paradigm, but has a functional core•First-class functionsFunctions can be passed to functionsFirst-class citizens=> Higher-order functions•Immutable valuesImmutable “variables” – creating new values insteadMinimizing moving parts has benefits

Erlang – Higher-order functions%base salaries

S = [10000, 30000, 40000, 15000].

%The Bonus calculator

Bonus = fun(X)-> X + X*0.2 + 1500 end.

%Total salaries

T = lists:map(Bonus, S)

>> [13500, 37500, 49500, 19500]

Erlang – Higher-order functions

%find total salaries exceeding 30000

MoreThan30K = fun(Y) -> Y > 30000 end.

lists:filter(MoreThan30K,T).

>> [37500, 49500]

You just learnt “map” and “filter”. Let them sink in!

Haskell - 1990

• Full blown functional language• Algebraic data types and type classes• No statements – the entire program is an

”expression”• Pattern matching• Lazy evaluation• Purely functional – functions have no side effect

Haskell – Algebraic Data Types (ADT)

• Derived from Type Theory• A composite type - formed by combining

other types

data List a = Nil | Cons a (List a)

data Tree a = Node a (Tree a) (Tree a) | Nil

Haskell – Pattern Matching

-- construct a List from an list

makeList (x:xs) = Cons x (makeList xs)

makeList [] = Nil

-- construct an list from a List

makeArr (Cons x (xs)) = x:(makeArr xs)

makeArr Nil = []

Quiz

Why was the language named Haskell?

Haskell Curry (1900 – 1982)

Currying

Introduced by Shönfinkel

Lambda calculus deals with single argument functionsWhat about multiple argument functions then?

If F(X, Y, Z) -> N, then

curry(F): X -> (Y -> (Z -> N))

Lambda Calculus - Currying

F(X, Y, Z) = X + Y + Z

F(1, 2, 3) = Fcurried(1)(2)(3)

//apply only one argument at a time

Fcurried (1) = F’curried

F’curried(2) = F”curried

F”curried(3) = 6

OCaml - 1996

• Multi-paradigm• Derived from ML• Static type system helps eliminate runtime

problems• Emphasis on performance – good

optimizing compiler

Currying in OCaml# let plus x y z = x + y + z;;

# plus 1 2 3;;

- : int = 6

# let x = plus 1;;

val x : int -> int -> int = <fun>

Currying in OCaml# let y = x 2;;

val y : int -> int = <fun>

# y 3;;

- : int = 6

Cool, but what’s the use of all this?

Currying in OCamlFunction to add 2 to all numbers of a listlet add2 x = x + 2

List.map add2 [1;2;3;4;5];;

Function to add 3 to all numbers of a listlet add3 x = x + 3

List.map add3 [1;2;3;4;5];;

Currying in OCaml

With currying:let add x y = x + y

List.map (add 2) [1;2;3;4;5]

List.map (add 3) [1;2;3;4;5]

•Better reuse of code•Improved readability

Quiz

What significant event occurred around 1995 in the Programming

Languages space?

Functional Programming on the JVM

(2004 – date)• Groovy - 2003• Scala - 2004• Clojure - 2007• Java 8 - 2014

Scala

• Seamless integration with Java

• Combines object oriented programming and functional programming

• Type inference• Higher order functions• Pattern matchingMartin

Odersky

Scala

Simple functional code to find the length of a list:(no loops in functional programming!)def listLength (list: List[_]): Int = list match { case Nil => 0 case _ => 1 + listLength(list.tail)}

Any problems here?

Scala

listLength(List.Range(0, 100000))

>> StackOverflow

Are loops better than recursive calls then?Has functional programming hit a barrier here?

Scala - TCONo! You have tail recursion and tail-recursion optimization (TCO)def length(as: List[_]): Int = { @tailrec def length0(as: List[_], count: Int = 0): Int = as match { case Nil => count case head :: tail => length0(tail, count+ 1)

} length0(as)

}

Scala - TCOSimplistic essence of tail-call optimization

Execution state

Single, reusablestack frame

Clojure - 2007Our fascination with LISP is never ending!

Rich Hickey

• LISP for the JVM

• Java-Clojure interoperability

• Other implementations – ClojureScript, ClojureCLR

• Used in creative computing!

Clojure(defn fib[n](condp = n 0 1 1 1 (+ (fib (- n 1)) (fib (- n 2)))))

user=> (time (fib 40))

"Elapsed time: 2946.136757 msecs"

165580141

user=> (time (fib 40))

"Elapsed time: 2882.10746 msecs"

165580141

Clojure

Pure functions•Referential Transparency•No side effects – stateless programs•Given an argument, the function must return the same value! (fib 4) is always 3, for example. => Values (fib K) can be reused for all KSpeed up? Caching?

Clojure - Memoization

(def m-fib(memoize (fn [n] (condp = n

0 1

1 1

(+ (m-fib (- n 1)) (m-fib (- n 2)))))))

Clojure - Memoization

user=> (time (m-fib 40))

"Elapsed time: 0.823773 msecs"

165580141

user=> (time (m-fib 40))

"Elapsed time: 0.082013 msecs"

165580141

Java 8 - 2014

The exciting times begin!•Lambdas•Stream Interface – lazy evaluation!•Functional Interfaces•Default methods – for backward compatibilityA mammoth like Java embracing the functional paradigm is a big cue about the times to come.

Lazy Evaluation

Laziness is not always bad

Lazy Evaluation

• Evaluate an expression only when it’s use is encountered

• Values are created only when needed• Reduction in memory footprint• Fast• In combination with memoization, results in

very efficient functional code

Problem

Find the number of first deliveries of overs, when a batsman who scored at least five centuries and hit at least 100 sixes, was out.

Java 8 – Lazy EvaluationallDeliveries.stream()

.filter(d -> d.deliveryNumber() == 1)

.filter(d -> d.wicket())

.map(d -> d.getBatsman())

.filter(b -> b.totalCenturies() >= 5)

.filter(b -> b.totalSixes >= 100)

.count() //terminal operation

•Lambdas•Immutability•Lazy evaluation, terminal operation•Map/filter

Java 8 - ParallelismParallel execution. Almost zero change to your code.allDeliveries.parallelStream()

.filter(d -> d.deliveryNumber() == 1)

.filter(d -> d.wicket())

.map(d -> d.getBatsman())

.filter(b -> b.totalCenturies() >= 5)

.filter(b -> b.totalSixes >= 100)

.count() //terminal operation

Java 8• No intentions of becoming a full blown

functional language• Lambdas and lazy evaluation provide a big

boost• Readability improved – anonymous classes

not needed• Reusability improved – lambdas, functional

interfaces• Java 9 – better Stream interface expected

Idris – A peek into the future

• Data types are first class objects!• You can generate data types, store them, pass

them around• Dependent types were developed by Haskell

Curry to deepen the connection between programming and logic (Curry-Howard correspondence)

• Dependent types – types that depend on values!• Influenced by Agda

Idris – dependent typesListType : (singleton : Bool) -> Type

ListType False = List Nat

ListType True = Nat

sumList : (singleton : Bool)->ListType singleton->Nat

sumList False (x :: xs) = x + sumList False xs

sumList False [] = 0

sumList True x = x

Why Functional Programming• Higher levels of behavioural abstraction –

tell what is to be done, not how to do it• Agile Methodologies - Code reuse,

readability• Correctness• Exploiting massively parallel hardware

Challenges• Paradigm shift in thinking needed• Newer design patterns – no imperative

design patterns • Performance evaluation difficult – recursive

data structures, recursive functions• Runtime performance – garbage collection

critical

Recap

• Lambda Calculus• Lambdas• First-class functions, higher order functions• Algebraic data types• Pattern matching• Currying

Recap

• Tail-call recursion and TCO• Pure functions, referential transparency• Memoization• Lazy evaluation• Parallelism• Dependent data types

A programming language that does not change the way you think is not worth knowing ~ Alan Perlis

Functional programming changes the way you think.

It’s worth knowing!

(Thank you!)

(twitter @pushkar_nk)(github pushkarnk)