COMS W4115 Programming Languages & Translators Maria Ayako Taku COMS W PLT Columbia University 1 April 24, 2013 Functional Programming Languages and the Influence of Lambda Calculus Lecture 23

Why Functional Programming? COMS W PLT Columbia University 2 April 24, 2013 You may have heard that: (1)functional programs are very succinct and elegant, but… (2) they take forever to write and understand let xor p = match p with (false, x) -> x | (true, x) -> not x;; let xor p = match p with (false, x) -> x | (true, x) -> not x;; Simple XOR program:

Outline COMS W PLT Columbia University 3 April 24, 2013 I.What is Functional Programming? II.Lambda Calculus' Influence on Functional Programming III.Benefits of Functional Programming IV.OCaml in Action: An Entire Interpreter in 3 slides

What is Functional Programming? COMS W PLT Columbia University 4 April 24, 2013 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)) let f = let a = 1*2 in let b = 4-3 in a + b;; let f = let a = 1*2 in let b = 4-3 in a + b;; In OCaml:

What is Functional Programming? COMS W PLT Columbia University 5 April 24, 2013 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; }

What is Functional Programming? COMS W PLT Columbia University 6 April 24, 2013 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?

Outline COMS W PLT Columbia University 7 April 24, 2013 I.What is Functional Programming? II.Lambda Calculus' Influence on Functional Programming III.Benefits of Functional Programming IV.OCaml in Action: An Entire Interpreter in 3 slides

Lambda Calculus' Influence COMS W PLT Columbia University 8 April 24, 2013 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…

Lambda Calculus' Influence Function Abstraction COMS W PLT Columbia University 9 April 24, 2013 Lambda Calculus Recap A function abstraction consists of four parts: 1.a lambda followed by 2.a single variable, 3.a period, and then 4.an expression λx.expr

Lambda Calculus' Influence Function Abstraction COMS W PLT Columbia University 10 April 24, 2013 λx.expr Lambda Calculus: fun x -> expr;; OCaml: f(x) = expr Algebra:

Lambda Calculus' Influence Function Abstraction COMS W PLT Columbia University 11 April 24, 2013 is equivalent to 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;; let myFunc x = expr;; The Let Command

Lambda Calculus' Influence Function Abstraction COMS W PLT Columbia University 12 April 24, 2013 # let fToc temp = (temp )/. 1.8;; # fToc 98.6;; - : float = # let fToc temp = (temp )/. 1.8;; # fToc 98.6;; - : float = double fToc (double temp) { return (temp-32)/1.8; } fToc(98.6); double fToc (double temp) { return (temp-32)/1.8; } fToc(98.6); An OCaml "let" example Similar code in Java

Lambda Calculus' Influence Beta Reductions COMS W PLT Columbia University 13 April 24, 2013 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 → = 8 Layman's Terms: (λx.expr1)expr2 means "replace every instance of x in expr1 with expr2"

Lambda Calculus' Influence Beta Reductions COMS W PLT Columbia University 14 April 24, 2013 (λx.expr1)expr2 Lambda Calculus: (fun x ->expr1)expr2;; OCaml: (fun x ->x*x)5;; (* Evaluates to 5*5 = 25 *) (fun x ->x*x)5;; (* Evaluates to 5*5 = 25 *) Example Usage:

Lambda Calculus' Influence Beta Reductions COMS W PLT Columbia University 15 April 24, 2013 (fun x ->expr1)expr2;; let x = 5 in x*x;; (* Evaluates to 5*5=25*) let x = 5 in x*x;; (* Evaluates to 5*5=25*) Example Usage: The Let Command let x = expr2 in expr1;; Is semantically equivalent to: The "let" command can once again be used to perform similar functionality to the "fun" command.

Outline COMS W PLT Columbia University 16 April 24, 2013 I.What is Functional Programming? II.Lambda Calculus' Influence on Functional Programming III.Benefits of Functional Programming IV.OCaml in Action: An Entire Interpreter in 3 slides

Benefits of Functional Programming COMS W PLT Columbia University 17 April 24, 2013 A few benefits in a nutshell: 1.Succinct Code 2.Encourages disciplined and logical thinking 3.Lazy Evaluation 4.Higher Level Functions Example: List.fold_left (fun s e ->s + e) 0 [42; 17; 120];; 5.No Side Effects & Referential Transparency

Benefits of Functional Programming No Side Effects COMS W PLT Columbia University 18 April 24, 2013 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.

Benefits of Functional Programming No Side Effects COMS W PLT Columbia University 19 April 24, 2013 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 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

Benefits of Functional Programming Referential Transparency COMS W PLT Columbia University 20 April 24, 2013 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.

Benefits of Functional Programming Referential Transparency COMS W PLT Columbia University 21 April 24, 2013 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! 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!

Why are Referential Transparency and Lack of Side Effects Good? COMS W PLT Columbia University 22 April 24, 2013 Elimination of bugs Debugging in general is easier Independence of evaluation order Safe reuse of subprograms Safe multithreading

Why are Referential Transparency and Lack of Side Effects Good? COMS W PLT Columbia University 23 April 24, 2013 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 Easier and Better Compiling

Outline COMS W PLT Columbia University 24 April 24, 2013 I.What is Functional Programming? II.Lambda Calculus' Influence on Functional Programming III.Benefits of Functional Programming IV.OCaml in Action: An Entire Interpreter in 3 slides

Implementing an Interpreter in OCaml COMS W PLT Columbia University 25 April 24, 2013 We will build a simple desk calculator to perform integer arithmetic. You recall the basic block diagram of a simple interpreter: Lexer Parser AST Walker tokensAST Input (arithmetic expression) Output (evaluated arithmetic expression)

Implementing an Interpreter in OCaml COMS W PLT Columbia University 26 April 24, 2013 Courtesy of Stephen Edwards' PLT Lecture Slides: { open Parser } rule token = parse [’ ’ ’\t’ ’\r’ ’\n’] { token lexbuf } | ’+’ { PLUS } | ’-’{ MINUS } | ’*’ { TIMES } | ’/’ { DIVIDE } | [’0’-’9’]+ as lit { LITERAL (int_of_string lit) } | eof{ EOF } { open Parser } rule token = parse [’ ’ ’\t’ ’\r’ ’\n’] { token lexbuf } | ’+’ { PLUS } | ’-’{ MINUS } | ’*’ { TIMES } | ’/’ { DIVIDE } | [’0’-’9’]+ as lit { LITERAL (int_of_string lit) } | eof{ EOF } type operator = Add | Sub | Mul | Div type expr = Binop of expr * operator * expr | Lit of int type operator = Add | Sub | Mul | Div type expr = Binop of expr * operator * expr | Lit of int scanner.mll ast.mli

Implementing an Interpreter in OCaml COMS W PLT Columbia University 27 April 24, 2013 parser.mly %{ open Ast %} %token PLUS MINUS TIMES DIVIDE EOF %token LITERAL %left PLUS MINUS %left TIMES DIVIDE %start expr %type expr % %{ open Ast %} %token PLUS MINUS TIMES DIVIDE EOF %token LITERAL %left PLUS MINUS %left TIMES DIVIDE %start expr %type expr % expr: expr PLUS 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) } expr: expr PLUS 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) }

Implementing an Interpreter in OCaml COMS W PLT Columbia University 28 April 24, 2013 AST Walker: calc.ml open Ast let rec eval = function Lit(x) -> x | Binop (e1, op, e2) -> let v1 = eval e1 and v2 = eval e2 in match op with Add -> v1 + v2 | Sub -> v1 - v2 | Mul ->v1 * v2 | Div -> v1 / v2 let _ = let lexbuf = Lexing.from_channel stdin in let expr = Parser.expr Scanner.token lexbuf in let result = eval expr in print_endline (string_of_int result) open Ast let rec eval = function Lit(x) -> x | Binop (e1, op, e2) -> let v1 = eval e1 and v2 = eval e2 in match op with Add -> v1 + v2 | Sub -> v1 - v2 | Mul ->v1 * v2 | Div -> v1 / v2 let _ = let lexbuf = Lexing.from_channel stdin in let expr = Parser.expr Scanner.token lexbuf in let result = eval expr in print_endline (string_of_int result)

Quick Side Note: Pattern Matching in OCaml COMS W PLT Columbia University 29 April 24, 2013 Pattern Matching a Parameter (function…) Pattern Matching a Value (match…with) Main difference is how the pattern matcher receives its value to match function param1 -> expr1 | param2 -> expr2 | param3 -> expr3 function param1 -> expr1 | param2 -> expr2 | param3 -> expr3 match expr with param1 -> expr1 | param2 -> expr2 | param3 -> expr3 match expr with param1 -> expr1 | param2 -> expr2 | param3 -> expr3

Quick Side Note: Pattern Matching in OCaml COMS W PLT Columbia University 30 April 24, 2013 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;; let xor p = match p with (false, x) -> x | (true, x) -> not x;;

Compiling the Interpreter COMS W PLT Columbia University 31 April 24, 2013 $ ocamllex scanner.mll # create scanner.ml 8 states, 267 transitions, table size 1116 bytes $ ocamlyacc parser.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 calc parser.cmo scanner.cmo calc.cmo $./calc 2 * * 5 26 $ $ ocamllex scanner.mll # create scanner.ml 8 states, 267 transitions, table size 1116 bytes $ ocamlyacc parser.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 calc parser.cmo scanner.cmo calc.cmo $./calc 2 * * 5 26 $

So Why Functional Programming? COMS W PLT Columbia University 32 April 24, 2013 It's hard to get to compile, but once it compiles, it works -Unknown PLT Student

References COMS W PLT Columbia University 33 April 24, 2013 Edwards, Stephen. “An Introduction to Objective Caml.” fall/ocaml.pdf Huges, John. “Why Functional Programming Matters.” Research Topics in Functional Programming, Addison- Wesley, 1990: pp “Advantages of Functional Programming.” ming