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COMS W4115 Programming Languages & Translators Maria Ayako Taku [email protected]

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Lecture 23

Functional Programming Languagesand the Influence of Lambda Calculus

COMS W4115

Programming Languages & Translators

Maria Ayako Taku

COMS W4115 - PLT Columbia University 1 April 24, 2013

Why Functional Programming?

You may have heard that:

- functional programs are very succinct and elegant,

but…

(2) they take forever to write and understand

Simple XOR program:

let xor p = match p

with (false, x) -> x

| (true, x) -> not x;;

COMS W4115 - PLT Columbia University 2 April 24, 2013

Outline

What is Functional Programming?

Lambda Calculus' Influence on Functional Programming

Benefits of Functional Programming

OCaml in Action: An Entire Interpreter in 3 slides

COMS W4115 - PLT Columbia University 3 April 24, 2013

What is Functional Programming?

- A "programming paradigm" that focuses on the evaluation of functions
- Programs are defined as recursive functions, where each takes a single input and outputs a single result.
- Recall lambda calculus nests functions in this manner. Ex: (+ (* 1 2) (- 4 3))

In OCaml:

let f =

let a = 1*2 in

let b = 4-3 in

a + b;;

COMS W4115 - PLT Columbia University 4 April 24, 2013

What is Functional Programming?

- One important trademark of Functional Programming:

It avoids both changes in state and mutable data

These expressions are

not equal.

Conceptually, they

are more like this.

//F# //C#

let a=42; int a=42;

//F# //C#

let a=42; static int a(){

return 42;

}

http://johnnycoder.com/blog/2009/04/20/functional-programming-part-1/

COMS W4115 - PLT Columbia University 5 April 24, 2013

What is Functional Programming?

Some Common (more or less) FP Languages:

- LISP
- OCaml
- Haskell
- Erlang
- F# (multi-paradigm)

So what's the value in functional programming?

Are its benefits worth taking the time to learn it and overcoming the (possibly) steep learning curve?

COMS W4115 - PLT Columbia University 6 April 24, 2013

Outline

- What is Functional Programming?
- Lambda Calculus' Influence on Functional Programming
- Benefits of Functional Programming
- OCaml in Action: An Entire Interpreter in 3 slides

COMS W4115 - PLT Columbia University 7 April 24, 2013

Lambda Calculus' Influence

- The syntax and theory of Functional Programming is highly influenced by lambda calculus.
- Knowledge of lambda calculus means that FP is easier to learn, understand, and use efficiently.

You might recognize some of the following FP syntax traits from lambda calculus…

COMS W4115 - PLT Columbia University 8 April 24, 2013

Lambda Calculus' InfluenceFunction Abstraction

λx.expr

Lambda Calculus Recap

A function abstraction consists of four parts:

- a lambda followed by
- a single variable,
- a period, and then
- an expression

COMS W4115 - PLT Columbia University 9 April 24, 2013

Lambda Calculus' InfluenceFunction Abstraction

OCaml:

Lambda Calculus:

fun x -> expr;;

λx.expr

Algebra:

f(x) = expr

COMS W4115 - PLT Columbia University 10 April 24, 2013

Lambda Calculus' InfluenceFunction Abstraction

The Let Command

- Named Functions: OCaml strays from pure functional programming at times.
- The "let" command can be used to allow one to create named functions

fun x -> expr;;

is equivalent to

let myFunc x = expr;;

COMS W4115 - PLT Columbia University 11 April 24, 2013

Lambda Calculus' InfluenceFunction Abstraction

# let fToc temp =

(temp -. 32.0)/. 1.8;;

# fToc 98.6;;

- : float = 36.99999999

An OCaml "let" example

doublefToc (double temp) {

return (temp-32)/1.8;

}

fToc(98.6);

Similar code

in Java

COMS W4115 - PLT Columbia University 12 April 24, 2013

Lambda Calculus' InfluenceBeta Reductions

Lambda Calculus Recap

A function application is evaluated via a beta reduction

Which occurs when an actual value is substituted for a variable

Examples:

(λx.xzx)y → [y/x]xzx = yzy

(λx.+ 1 x)7 → + 1 7 = 8

Layman's Terms: (λx.expr1)expr2 means "replace every instance of x in expr1 with expr2"

COMS W4115 - PLT Columbia University 13 April 24, 2013

Lambda Calculus' InfluenceBeta Reductions

OCaml:

Lambda Calculus:

(fun x ->expr1)expr2;;

(λx.expr1)expr2

Example Usage:

(fun x ->x*x)5;;

(* Evaluates to 5*5 = 25 *)

COMS W4115 - PLT Columbia University 14 April 24, 2013

Lambda Calculus' InfluenceBeta Reductions

The Let Command

(fun x ->expr1)expr2;;

The "let" command can once again be used to perform similar functionality to the "fun" command.

Is semantically equivalent to:

let x = expr2 in expr1;;

Example Usage:

let x = 5 in x*x;;

(* Evaluates to 5*5=25*)

COMS W4115 - PLT Columbia University 15 April 24, 2013

Outline

- What is Functional Programming?
- Lambda Calculus' Influence on Functional Programming
- Benefits of Functional Programming
- OCaml in Action: An Entire Interpreter in 3 slides

COMS W4115 - PLT Columbia University 16 April 24, 2013

Benefits of Functional Programming

A few benefits in a nutshell:

- Succinct Code
- Encourages disciplined and logical thinking
- Lazy Evaluation
- Higher Level FunctionsExample:List.fold_left(fun s e ->s + e) 0 [42; 17; 120];;
- No Side Effects & Referential Transparency

COMS W4115 - PLT Columbia University 17 April 24, 2013

Benefits of Functional ProgrammingNo Side Effects

Side Effect:

a function or expression has a side effect if it modifies state or has an observable interaction with the "outside world."

Examples:

- Modify global/static variables
- Modify arguments
- Write data to a display or file

Functional programs contain no assignment statements. So variables, once given a value, never change.

COMS W4115 - PLT Columbia University 18 April 24, 2013

Benefits of Functional ProgrammingNo Side Effects

Simple Side Effect Example in Java

static int x = 5;

static void changeX (int a){

x = a;

}

changeX(4); // This function has the side effect

// of changing the value of global var x

COMS W4115 - PLT Columbia University 19 April 24, 2013

Benefits of Functional ProgrammingReferential Transparency

Referential Transparency:An expression (e.g., function) is referentially transparent if it always produces the same output for the same input.

Lack of side effects results in referential transparency.

Because of this behavior, a variable/expression can always be replaced with its value without changing the behavior of a program if that language has Referential Transparency.

COMS W4115 - PLT Columbia University 20 April 24, 2013

Benefits of Functional ProgrammingReferential Transparency

Lack of Referential Transparency in Java

static int x = 10;

static int add(int a){

return a + x;

}

add(1); // returns 11

x = 0;

add(1); // returns 10, even though same input. NOT RT!

COMS W4115 - PLT Columbia University 21 April 24, 2013

Why are Referential Transparency and Lack of Side Effects Good?

- Elimination of bugs
- Debugging in general is easier
- Independence of evaluation order
- Safe reuse of subprograms
- Safe multithreading

COMS W4115 - PLT Columbia University 22 April 24, 2013

Why are Referential Transparency and Lack of Side Effects Good?

Easier and Better Compiling

Easier to Compile – It's not only people that benefit from being able to better predict and understand a program's behavior

Better Compiling – optimization via:

- Memoization
- Parallelization
- Common Subexpression Elimination

COMS W4115 - PLT Columbia University 23 April 24, 2013

Outline

- What is Functional Programming?
- Lambda Calculus' Influence on Functional Programming
- Benefits of Functional Programming
- OCaml in Action: An Entire Interpreter in 3 slides

COMS W4115 - PLT Columbia University 24 April 24, 2013

Implementing an Interpreter in OCaml

- We will build a simple desk calculator to perform integer arithmetic.
- You recall the basic block diagram of a simple interpreter:

tokens

AST

Lexer

Parser

AST Walker

Input

(arithmetic expression)

Output

(evaluated arithmetic expression)

COMS W4115 - PLT Columbia University 25 April 24, 2013

Implementing an Interpreter in OCaml

{openParser }

ruletoken =

parse[’ ’ ’\t’ ’\r’ ’\n’]{token lexbuf}

|’+’ {PLUS }

| ’-’ {MINUS }

| ’*’ { TIMES }

|’/’ {DIVIDE }

|[’0’-’9’]+aslit { LITERAL (int_of_string lit)}

|eof{EOF }

scanner.mll

ast.mli

typeoperator = Add | Sub |Mul|Div

typeexpr=

Binopofexpr* operator *expr

| Lit ofint

Courtesy of Stephen Edwards' PLT Lecture Slides: http://www.cs.columbia.edu/~sedwards/classes/2012/w4115-fall/ocaml.pdf

COMS W4115 - PLT Columbia University 26 April 24, 2013

Implementing an Interpreter in OCaml

parser.mly

%{openAst%}

%token PLUS MINUS TIMES DIVIDE EOF

%token

%left PLUS MINUS

%left TIMES DIVIDE

%startexpr

%type

%%

expr:

exprPLUS expr{Binop($1,Add,$3)}

|expr MINUS expr{Binop($1, Sub,$3)}

|expr TIMES expr{Binop($1,Mul,$3)}

|expr DIVIDE expr{Binop($1,Div,$3)}

| LITERAL { Lit($1)}

COMS W4115 - PLT Columbia University 27 April 24, 2013

Implementing an Interpreter in OCaml

openAst

letreceval=function

Lit(x)-> x

|Binop(e1, op, e2)->

letv1 =eval e1 andv2 =eval e2 in

matchopwith

Add -> v1 + v2

| Sub -> v1 - v2

| Mul->v1 * v2

|Div-> v1 /v2

let_ =

letlexbuf=Lexing.from_channelstdinin

letexpr=Parser.exprScanner.tokenlexbufin

letresult =evalexprin

print_endline(string_of_int result)

AST Walker:

calc.ml

COMS W4115 - PLT Columbia University 28 April 24, 2013

Quick Side Note:Pattern Matching in OCaml

Pattern Matching a Parameter (function…)

Pattern Matching a Value (match…with)

function

param1 -> expr1

| param2 -> expr2

| param3 -> expr3

match exprwith

param1 -> expr1

| param2 -> expr2

| param3 -> expr3

Main difference is how the pattern matcher receives

its value to match

COMS W4115 - PLT Columbia University 29 April 24, 2013

Quick Side Note:Pattern Matching in OCaml

If you recall the XOR program from the beginning of this lecture, you should now be able to understand how this works.

Hint: Variables, such as "x" will match anything and are

bound to a value when the pattern matches.

let xor p = match p

with (false, x) -> x

| (true, x) -> not x;;

COMS W4115 - PLT Columbia University 30 April 24, 2013

Compiling the Interpreter

$ ocamllexscanner.mll # create scanner.ml

8 states, 267 transitions, table size 1116 bytes

$ ocamlyaccparser.mly # create parser.ml and parser.mli

$ ocamlc–c ast.mli # compile AST types

$ ocamlc–c parser.mli # compile parser types

$ ocamlc–c scanner.ml # compile the scanner

$ ocamlc–c parser.ml # compile the parser

$ ocamlc–c calc.ml # compile the interpreter

$ ocamlc–o calcparser.cmoscanner.cmocalc.cmo

$ ./calc

2 * 3 + 4 * 5

26

$

COMS W4115 - PLT Columbia University 31 April 24, 2013

So Why Functional Programming?

It's hard to get to compile, but once it compiles, it works

-Unknown PLT Student

COMS W4115 - PLT Columbia University 32 April 24, 2013

References

- Edwards, Stephen. “An Introduction to Objective Caml.” http://www.cs.columbia.edu/~sedwards/classes/2012/w4115-fall/ocaml.pdf
- Huges, John. “Why Functional Programming Matters.” Research Topics in Functional Programming, Addison-Wesley, 1990: pp 17-42
- “Advantages of Functional Programming.” http://c2.com/cgi/wiki?AdvantagesOfFunctionalProgramming

COMS W4115 - PLT Columbia University 33 April 24, 2013

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