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COMS W4115 Programming Languages & Translators Maria Ayako Taku mat2185@columbia

Lecture 23. Functional Programming Languages and the Influence of Lambda Calculus. COMS W4115 Programming Languages & Translators Maria Ayako Taku mat2185@columbia.edu. COMS W4115 - PLT Columbia University 1 April 24, 2013. Why Functional Programming?.

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COMS W4115 Programming Languages & Translators Maria Ayako Taku mat2185@columbia

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  1. Lecture 23 Functional Programming Languagesand the Influence of Lambda Calculus COMS W4115 Programming Languages & Translators Maria Ayako Taku mat2185@columbia.edu COMS W4115 - PLT Columbia University 1 April 24, 2013

  2. 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

  3. 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

  4. 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

  5. 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

  6. 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

  7. 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

  8. 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

  9. 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

  10. 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

  11. 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

  12. 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

  13. 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

  14. 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

  15. 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

  16. 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

  17. 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

  18. 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

  19. 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

  20. 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

  21. 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

  22. 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

  23. 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

  24. 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

  25. 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

  26. 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

  27. Implementing an Interpreter in OCaml parser.mly %{openAst%} %token PLUS MINUS TIMES DIVIDE EOF %token <int> LITERAL %left PLUS MINUS %left TIMES DIVIDE %startexpr %type<Ast.expr>expr %% 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

  28. 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

  29. 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

  30. 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

  31. 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

  32. 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

  33. 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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