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Lecture 2: Schreme

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  1. Lecture 2: Schreme Available within the network will be functions and services to which you subscribe on a regular basis and others that you call for when you need them. In the former group will be investment guidance, tax counseling, selective dissemination of information in your field of specialization, announcement of cultural, sport, and entertainment events that fit your interests, etc. In the latter group will be dictionaries, encyclopedias, indexes, catalogues, editing programs, teaching programs, testing programs, programming systems, data bases, and – most important – communication, display, and modeling programs. All these will be – at some late date in the history of networking - systematized and coherent; you will be able to get along in one basic language up to the point at which you choose a specialized language for its power or terseness. J. C. R. Licklider and Robert W. Taylor, The Computer as a Communication Device, April 1968 CS655: Programming Languages University of Virginia Computer Science David Evans http://www.cs.virginia.edu/~evans

  2. Menu • Registration Survey Results • My Answers • Universal Languages • Stuff Languages are Made Of • Scheme • Infinitely many different functions CS 655: Lecture 2

  3. Favorite Programming Languages C 41/3 C++ 21/3 Java 21/3 Perl 1 My answer: • For getting work done: C (with LCLint) • For reading other people’s code: CLU • For fun: FL, Scheme CS 655: Lecture 2

  4. Most Hated PL COBOL 2 Perl 2 (also favorite) Java 1 Lisp 1 None 4 My answer: For asthetics, readability: APL For teaching intro CS courses: C++ For writing big systems: Lisp CS 655: Lecture 2

  5. Experience of Students in this Class C++ (38 years), C (36), BASIC (29), Pascal (21), various assemblies (12), Java (9), Perl (5), FORTRAN (4), Python(2½), Ada (2), Lisp dialects (1½), COBOL (1), Smalltalk (½) • Algol60 direct successors = 106 • Pre-Algol languages = 46 • Completely object-oriented languages = ½ • But O-O doesn’t really mean anything • Pure functional languages = 0 • Python is close (but has globals and state) CS 655: Lecture 2

  6. Partner Preference Assigned Randomly 4 Choose Your Own 4 No Clear Preference 2 CS 655: Lecture 2

  7. Can class go over time? No problem 10 Problem 0 One said, “but if I am bored and you keep me there I will be really annoyed and glare at you”. CS 655: Lecture 2

  8. Technical Questions • Used higher-order procedures: • No: 4 A little: 3 Yes: 3 • Wrote function that returned infinitely many possible different functions • No: 10 (some used tables of function pointers) • Fixed points: find x where f(x) = x • Gets really interesting when x is a function! CS 655: Lecture 2

  9. Why taking this class? CS 655: Lecture 2

  10. Next: Computability and Universal Programming Languages CS 655: Lecture 2

  11. Computability • A programming language is universal if it can express all computable functions. • A function is “computable” if there exists an algorithm that computes it. • An algorithm is a computational procedure that takes a finite number of steps. • What’s a computational procedure? CS 655: Lecture 2

  12. Turing Machine • Tape head can: • Read symbol from tape • Write symbol on tape • Move tape left or right one square • Change its own state (finite state machine)   Infinitely long tape CS 655: Lecture 2

  13. Universal Turing Machine • Universal Turing Machine is a Turing machine that can simulate any other Turing machine • Input (start state on tape) contains both a description of a Turing Machine (i.e., a program) and its input • Yes, there really are such things • Hopefully you will see it in CS660 CS 655: Lecture 2

  14. Computability • A computational procedure is something that can be described by a Turing Machine • A language is universal if it can express: all algorithms = all finite computational procedures = all Turing machines = one Universal Turing Machine CS 655: Lecture 2

  15. Not everything is computable • Halting Problem – will a Turing Machine halt? • Suppose we could compute it: (define (halts? P) ...) returns true if P halts, false otherwise. CS 655: Lecture 2

  16. Based on Duane Boning, http://sicp.ai.mit.edu/Fall-1999/lectures/lec25/6001-12-9-99-computability.ppt (define contradicts-halts (if (halts? contradict-halts) (loop-forever) #t)) If contradict-halts halts, it loops forever; If contradict-halts doesn’t halt, value is true. Yikes! halts? must not exisit! Note: this is not a proof. (proof in 650) Perhaps it is if that doesn’t exist. CS 655: Lecture 2

  17. Is a language universal? • How can we prove a language is universal? • Produce a program that implements a Universal Turing Machine in the language (usually this is pretty easy) • How can we prove a language is not universal? • Prove that it cannot express the function of some Turing Machine CS 655: Lecture 2

  18. Elements of Language CS 655: Lecture 2

  19. Elements of Language • (Almost?) All Languages have: • Primitives • Means of combination • English: • Primitives = words (?) • e.g., “Floccipoccinihilipilification” (the act of rendering useless) • Means of combination • e.g., Sentence = Subject Verb Object CS 655: Lecture 2

  20. Means of Combination • Allow us to say infinitely many things with a finite number of primitives • In English, words aren’t really primitives (linguists call the primitives morphemes – smallest units of meaning) • Means of Combination work on word parts: Antifloccipoccinihilipilification (the act of not rendering useless) Antifloccipoccinihilipilificationator (one who does the act of not rendering useless) CS 655: Lecture 2

  21. Describing Means of Combination • BNF (Backus Naur Form) <non-terminal> ::= <replacement> Terminals are primitives in the language (don’t appear on left-hand side.) • Alternatives <non-terminal> ::= <replacement1> | <replacement2> short for: <non-terminal> ::= <replacement1> <non-terminal> ::= <replacement2> CS 655: Lecture 2

  22. BNF • John Backus • FORTRAN (manual described syntax using verbose English, not a formal notation) • Member of Algol60 committee, introduced formal notation for syntax • Influential in development of functional languages: FP, FL, Turing Lecture • Normal  Peter Naur (Donald Knuth’s suggestion) • Chair of Algol60 committee CS 655: Lecture 2

  23. BNF Example Sentence ::= NP VP NP ::= Noun VP ::= Verb Noun ::= Dave | Scheme Verb ::= rocks | sucks Could this language be a universal programming language? CS 655: Lecture 2

  24. BNF Example • Sentence ::= NP VP • NP ::= Noun • VP ::= Verb • Noun ::= Dave | Scheme • Verb ::= rocks | sucks | NounandNP We can express infinitely many things with a tiny language! With the right meaning function, this could be a universal programming language. CS 655: Lecture 2

  25. Scheme CS 655: Lecture 2

  26. Scheme • Like all (?) languages, Scheme has: • Primitives • Means of Combination • Also, like all (?) reasonable programming languages it has: • Means of Abstraction CS 655: Lecture 2

  27. Mini-Scheme Primitives Examples • Numerals 0 655 3.52 -58 • Functions + • Constants #f #t • You know what the primitives mean. • Numeral  Number 655  655 • Function  Function +  math addition CS 655: Lecture 2

  28. Means of Combination • Application Expression ::= (Expression) Expression ::= (Expression Expression) Expression ::= (Expression Expression Expression) ... Expression ::= (Expression*) (+ 655 58) (* (+ 0 (+ 2 2)) 6) “Evaluate all the expressions, then apply the first expression (a procedure) to all the other values.” CS 655: Lecture 2

  29. Means of Combination • Special Forms (ifExpression1 Expression2 Expression3 ) If the value of Expression1 is #f, the value of the if is the value of Expression3. Otherwise, it is the value of Expression2 . • A few others, but they are not necessary (note: neither is if!) CS 655: Lecture 2

  30. Means of Combination • Make Procedure Expression ::= (lambda (Variable) Expression) “A procedure that when applied to value, evaluates to Expression with all instances of Variable substituted for by value.” Note: “substitution” is complicated. CS 655: Lecture 2

  31. Mini-Scheme Expression ::= (Expression*) | (lambda (Variable) Expression) | (ifExpression1 Expression2 Expression3 ) | numeral | #f | #t | + Variable ::= identifier Is mini-scheme a Universal Programming Language? (Left as challenge problem.) CS 655: Lecture 2

  32. Means of Abstraction (define VariableExpression) Substitute Expression for Variable. (define two 2) 2 (+ two two) 4 CS 655: Lecture 2

  33. Abstracting Procedures (define square (lambda (x) (* x x)) proc (square two) 4 (define (Variable1Variable2) Expression) is just an abbreviation for: (define Variable1 (lambda (Variable2) Expression) CS 655: Lecture 2

  34. Multiple Arguments (define (Variable1Variable2 Variable3) Expression) is just an abbreviation for: (define Variable1 (lambda (Variable2) (lambda (Variable3) Expression))) This is called “currying”. CS 655: Lecture 2

  35. Currying (define add (lambda (x) (lambda (y) (+ x y)))) (add 5) proc ((add 5) 2) 7 CS 655: Lecture 2

  36. add • add is a procedure that returns infinitely many different procedures! (define add (lambda (x) (lambda (y) (+ x y)))) CS 655: Lecture 2

  37. triadd (define triadd (lambda (x) (lambda (y) (lambda (z) (+ x y z))))) • triadd is a procedure that returns infinitely many different procedures, each of which is a procedure that returns infinitely many different procedures! • So, after today your answer to survey question: “Yes, infinitely many!” CS 655: Lecture 2

  38. Charge • Problem Set 1 out today • Its not long but may be hard, start it soon • Question 0 think about: • Do we really need define? • What scheme expressions do not have values? • Next time: Higher-Order Functions, Intro to Metacircular Evaluators CS 655: Lecture 2