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• 1. Control in Sequential Languages + some discussion of functional programming John Mitchell CS 242 Reading: Chapter 8, Sections 8.1 – 8.3 (only) Chapter 4, Section 4.4 (only) Fall 2008
• 2. JavaScript blocks and scopes
• { } groups JavaScript statements
• Does not provide a separate scope
• Blocks w/scope can be expressed using function
• (function(){ … })() - create function of no args and call
• Example
• var y=0;
• (function () { // begin block
• var x=2; // local variable x
• y = y+x;
• }) (); // end block
RECAP
• 3. Homework 1, Problem 6
• var x = 5;
• function f(y) {return (x+y)-2};
• function g(h){var x = 7; return h(x)};
• {var x = 10; g(f)};
• var x = 5;
• function f(y) {return (x+y)-2};
• function g(h){var x = 7; return h(x)};
• {var x = 10; g(f)};
• (function (){
• var x = 5;
• (function (){
• function f(y) {return (x+y)-2};
• (function (){
• function g(h){var x = 7; return h(x)};
• (function (){
• var x = 10; g(f);
• })()
• })()
• })()
• })()
• 4. Topics
• Structured Programming
• Go to considered harmful
• Exceptions
• “ structured” jumps that may return a value
• dynamic scoping of exception handler
• Continuations
• Function representing the rest of the program
• Generalized form of tail recursion
• Discussion of functional programming
• Relevant to Haskell, section 4.4 of text
• 5. Fortran Control Structure
• 10 IF (X .GT. 0.000001) GO TO 20
• 11 X = -X
• IF (X .LT. 0.000001) GO TO 50
• 20 IF (X*Y .LT. 0.00001) GO TO 30
• X = X-Y-Y
• 30 X = X+Y
• ...
• 50 CONTINUE
• X = A
• Y = B-A
• GO TO 11
Similar structure may occur in assembly code
• 6. Historical Debate
• Dijkstra, Go To Statement Considered Harmful
• Letter to Editor, C ACM , March 1968
• Link on CS242 web site
• Knuth, Structured Prog. with go to Statements
• You can use goto, but do so in structured way …
• Continued discussion
• Welch, “GOTO (Considered Harmful) n , n is Odd”
• General questions
• Do syntactic rules force good programming style?
• Can they help?
• 7. Advance in Computer Science
• Standard constructs that structure jumps
• if … then … else … end
• while … do … end
• for … { … }
• case …
• Modern style
• Group code in logical blocks
• Avoid explicit jumps except for function return
• Cannot jump into middle of block or function body
• 8. Exceptions: Structured Exit
• Terminate part of computation
• Jump out of construct
• Pass data as part of jump
• Return to most recent site set up to handle exception
• Unnecessary activation records may be deallocated
• May need to free heap space, other resources
• Two main language constructs
• Declaration to establish exception handler
• Statement or expression to raise or throw exception
Often used for unusual or exceptional condition; other uses too
• 9. JavaScript Exceptions
• throw e //jump to catch, passing exception object as parameter
• try { … //code to try
• } catch (e if e == …) { … //catch if first condition true
• } catch (e if e == …) { … //catch if second condition true
• } catch (e if e == …) { … //catch if third condition true
• } catch (e){ … // catch any exception
• } finally { … //code to execute after everything else
• }
http://developer.mozilla.org/En/Core_JavaScript_1.5_Guide/ Exception_Handling_Statements
• 10. JavaScript Example
• function invert(matrix) {
• if … throw “Determinant”;
• };
• try { … invert(myMatrix); …
• }
• catch (e) { …
• // recover from error
• }
• 11. ML Example (book discusses ML)
• exception Determinant; (* declare exception name *)
• fun invert (M) = (* function to invert matrix *)
• if …
• then raise Determinant (* exit if Det=0 *)
• else …
• end;
• ...
• invert (myMatrix) handle Determinant => … ;
Value for expression if determinant of myMatrix is 0 try catch
• 12. C++ Example
• Matrix invert(Matrix m) {
• if … throw Determinant;
• };
• try { … invert(myMatrix); …
• }
• catch (Determinant) { …
• // recover from error
• }
• 13. ML Exceptions (cover briefly so book is useful to you)
• Declaration
• exception  name  of  type 
• gives name of exception and type of data passed when raised
• Raise
• raise  name   parameters 
• expression form to raise and exception and pass data
• Handler
•  exp1  handle  pattern  =>  exp2 
• evaluate first expression
• if exception that matches pattern is raised,
• then evaluate second expression instead
• General form allows multiple patterns.
• 14. C++ vs ML Exceptions
• C++ exceptions
• Can throw any type
• Stroustrup: “I prefer to define types with no other purpose than exception handling. This minimizes confusion about their purpose. In particular, I never use a built-in type, such as int, as an exception.” -- The C++ Programming Language, 3 rd ed.
• ML exceptions
• Exceptions are a different kind of entity than types.
• Declare exceptions before use
• Similar, but ML requires the recommended C++ style.
• 15. Which handler is used?
• Dynamic scoping of handlers
• First call handles exception one way
• Second call handles exception another
• General dynamic scoping rule
• Jump to most recently established handler on run-time stack
• Dynamic scoping is not an accident
• User knows how to handler error
• Author of library function does not
• exception Ovflw;
• fun reciprocal(x) =
• if x<min then raise Ovflw else 1/x;
• (reciprocal(x) handle Ovflw=>0) / (reciprocal(y) handle Ovflw=>1);
try try catch catch throw
• 16. Exception for Error Condition
• - datatype ‘a tree = LF of ‘a | ND of (‘a tree)*(‘a tree)
• - exception No_Subtree;
• - fun lsub (LF x) = raise No_Subtree
• | lsub (ND(x,y)) = x;
• > val lsub = fn : ‘a tree -> ‘a tree
• This function raises an exception when there is no reasonable value to return
• We’ll look at typing later.
• 17. Exception for Efficiency
• Function to multiply values of tree leaves
• fun prod(LF x) = x
• | prod(ND(x,y)) = prod(x) * prod(y);
• Optimize using exception
• fun prod(tree) =
• let exception Zero
• fun p(LF x) = if x=0 then (raise Zero) else x
• | p(ND(x,y)) = p(x) * p(y)
• in
• p(tree) handle Zero=>0
• end;
• 18. Dynamic Scope of Handler
• exception X;
• (let fun f(y) = raise X
• and g(h) = h(1) handle X => 2
• in
• g(f) handle X => 4
• end) handle X => 6;
Which handler is used? See JavaScript next slide scope handler
• 19. Dynamic Scope of Handler
• try{
• function f(y) { throw “exn”};
• function g(h){ try {h(1)} catch(e){return 2} };
• try {
• g(f)
• } catch(e){4};
• } catch(e){6};
Which catch catches the throw?
• 20. Dynamic Scope of Handler
• try{
• function f(y) { throw “exn”};
• function g(h){ try {h(1)}
• catch(e){return 2}
• };
• try {
• g(f)
• } catch(e){4};
• } catch(e){6};
g(f) f(1) Dynamic scope: find first handler, going up the dynamic call chain JavaScript version catch(e) 6 formal h catch(e) 2 access link formal y 1 access link fun f access link access link fun g catch(e) 4 access link
• 21. Dynamic Scope of Handler
• exception X;
• (let fun f(y) = raise X
• and g(h) = h(1) handle X => 2
• in
• g(f) handle X => 4
• end) handle X => 6;
g(f) f(1) Dynamic scope: find first X handler, going up the dynamic call chain leading to raise X. Book version (ML) handler X 6 formal h handler X 2 access link formal y 1 access link fun f access link access link fun g handler X 4 access link
• 22. Compare to static scope of variables
• exception X;
• (let fun f(y) = raise X
• and g(h) = h(1)
• handle X => 2
• in
• g(f) handle X => 4
• end) handle X => 6;
• val x=6;
• (let fun f(y) = x
• and g(h) = let val x=2 in
• h(1)
• in
• let val x=4 in g(f)
• end);
Book version (ML)
• 23. Compare to static scope of variables
• try{
• function f(y) { throw “exn”};
• function g(h){ try {h(1)}
• catch(e){return 2}
• };
• try {
• g(f)
• } catch(e){4};
• } catch(e){6};
• var x=6;
• function f(y) { return x};
• function g(h){ var x=2;
• return h(1)
• };
• (function (y) {
• var x=4;
• g(f)
• })(0);
JavaScript version declaration declaration
• 24. Static Scope of Declarations
• var x=6;
• function f(y) { return x};
• function g(h){
• var x=2; return h(1) };
• (function (y) {
• var x=4; g(f)
• })(0);
g(f) f(1) Static scope: find first x, following access links from the reference to X. JavaScript version var x 6 formal h var x 2 access link formal y 1 access link function f access link access link function g var x 4 access link
• 25. Static Scope of Declarations
• val x=6;
• (let fun f(y) = x
• and g(h) = let val x=2 in
• h(1)
• in
• let val x=4 in g(f)
• end);
g(f) f(1) Static scope: find first x, following access links from the reference to X. Book version (ML) val x 6 formal h val x 2 access link formal y 1 access link fun f access link access link fun g val x 4 access link
• 26. Typing of Exceptions
• Typing of raise  exn 
• Recall definition of typing
• Expression e has type t if normal termination of e
• produces value of type t
• Raising exception is not normal termination
• Example: 1 + raise X
• Typing of handle  exn  =>  value 
• Converts exception to normal termination
• Need type agreement
• Examples
• 1 + ((raise X) handle X => e) Type of e must be int
• 1 + (e 1 handle X => e 2 ) Type of e 1, e 2 must be int
• 27. Exceptions and Resource Allocation
• exception X;
• (let
• val x = ref [1,2,3]
• in
• let
• val y = ref [4,5,6]
• in
• … raise X
• end
• end); handle X => ...
• Resources may be allocated between handler and raise
• May be “garbage” after exception
• Examples
• Memory
• Lock on database
• Threads
General problem: no obvious solution
• 28. Continuations
• Idea:
• The continuation of an expression is “the remaining work to be done after evaluating the expression”
• Continuation of e is a function normally applied to e
• General programming technique
• Capture the continuation at some point in a program
• Use it later: “jump” or “exit” by function call
• Useful in
• Compiler optimization: make control flow explicit
• Operating system scheduling, multiprogramming
• Web site design, other applications
• 29. Example of Continuation Concept
• Expression
• 2*x + 3*y + 1/x + 2/y
• What is continuation of 1/x?
• Remaining computation after division
• var before = 2*x + 3*y;
• function cont(d) {return (before + d + 2/y)};
• cont (1/x);
JavaScript version
• 30. Example of Continuation Concept
• Expression
• 2*x + 3*y + 1/x + 2/y
• What is continuation of 1/x?
• Remaining computation after division
• let val before = 2*x + 3*y
• fun continue(d) = before + d + 2/y
• in
• continue (1/x)
• end
Book version (ML)
• 31. Example: Tail Recursive Factorial
• Standard recursive function
• fact(n) = if n=0 then 1 else n*fact(n-1)
• Tail recursive
• f(n,k) = if n=0 then k else f(n-1, n*k)
• fact(n) = f(n,1)
• How could we derive this?
• Transform to continuation-passing form
• Optimize continuation functions to single integer
• 32. Continuation view of factorial
• fact(n) = if n=0 then 1 else n*fact(n-1)
• fact(9)
• fact(8)
• fact(7)
• This invocation multiplies by 9 and returns
• Continuation of fact(8) is  x. 9*x
• Multiplies by 8 and returns
• Continuation of fact(7) is
•  y. (  x. 9*x) (8*y)
• Multiplies by 7 and returns
• Continuation of fact(6) is
•  z. (  y. (  x. 9*x) (8*y)) (7*z)
return n 9 ... return n 8 ... return n 7 ...
• 33. Derivation of tail recursive form
• Standard function
• fact(n) = if n=0 then 1 else n*fact(n-1)
• Continuation form
• fact(n, k) = if n=0 then k(1)
• else fact(n-1,  x.k ( n*x) )
• fact(n,  x.x) computes n!
• Example computation
• fact(3,  x.x) = fact(2,  y. ( (  x.x) ( 3*y) ) )
• = fact(1,  x. ( (  y.3*y)(2*x) ) )
• =  x. ( (  y.3*y)(2*x) ) 1 = 6
continuation
• 34. Tail Recursive Form
• Optimization of continuations
• fact(n,a) = if n=0 then a
• else fact(n-1, n*a )
• Each continuation is effectively  x.(a*x) for some a
• Example computation
• fact(3,1) = fact(2, 3) was fact(2,  y.3*y)
• = fact(1, 6) was fact(1,  x.6*x)
• = 6
• 35. Other uses for continuations
• Explicit control
• Normal termination -- call continuation
• Abnormal termination -- do something else
• Compilation techniques
• Call to continuation is functional form of “go to”
• Continuation-passing style makes control flow explicit
• MacQueen: “Callcc is the closest thing to a
• ‘ come-from’ statement I’ve ever seen.”
• 36. Theme Song: Charlie on the MTA
• Let me tell you the story Of a man named Charlie On a tragic and fateful day He put ten cents in his pocket, Kissed his wife and family Went to ride on the MTA
• Charlie handed in his dime At the Kendall Square Station And he changed for Jamaica Plain When he got there the conductor told him, &quot;One more nickel.&quot; Charlie could not get off that train.
• Chorus:                         Did he ever return,                         No he never returned                         And his fate is still unlearn'd                         He may ride forever                         'neath the streets of Boston                         He's the man who never returned.
• 37. Capturing Current Continuation
• Language feature (use open SMLofNJ; on Leland)
• callcc : call a function with current continuation
• Can be used to abort subcomputation and go on
• Examples
• callcc (fn k => 1);
• > val it = 1 : int
• Current continuation is “fn x => print x”
• Continuation is not used in expression
• 1 + callcc(fn k => 5 + throw k 2);
• > val it = 3 : int
• Current continuation is “fn x => print 1+x”
• Subexpression throw k 2 applies continuation to 2
skip callcc, at least for now
• 38. More with callcc
• Example
• 1 + callcc(fn k1=> …
• callcc(fn k2 => …
• if … then (throw k1 0)
• else (throw k2 “stuck”)
• ))
• Intuition
• Callcc lets you mark a point in program that you can return to
• Throw lets you jump to that point and continue from there
• 39. Example
• Pass two continuations and choose one
• fun f(x,k1,k2) = 3 + (if x>0 then throw k1(x)
• else throw k2(x));
• fun g(y,k1) = 2 + callcc(fn k2 => f(y,k1,k2));
• fun h(z) = 1 + callcc(fn k1 => g(z+1,k1));
• h(1);
• h(~2);
Answers: h(1)  3 h(~2)  2
• 40. Continuations in Mach OS
• OS kernel schedules multiple threads
• Each thread may have a separate stack
• Stack of blocked thread is stored within the kernel
• Mach “continuation” approach
• Blocked thread represented as
• Pointer to a continuation function, list of arguments
• Stack is discarded when thread blocks
• Programming implications
• Sys call such as msg_recv can block
• Kernel code calls msg_recv with continuation passed as arg
• Advantage/Disadvantage
• Saves a lot of space, need to write “continuation” functions
• 41. “ Continuations” in Web programming
• XMLHttpRequest similar to callcc:
• function callcc(url) {
• var xhr = new XMLHttpRequest();
• xhr.open('GET', url, false );
• xhr.send(null);
• return xhr.responseText;
• }
• Usage: alert(callcc('http://a.com/describe?id=10'));
• Server invokes continuation by sending a response
• Unfortunately, this pauses client while server runs
• 42. “ Continuations” in Web programming
• Asynchronous XHR also similar to continuations:
• function callWithContinuation(url, k ) {
• var xhr = new XMLHttpRequest();
• xhr.open('GET', url, true );
• xhr.onreadystatechange = function () {
• if (xhr.readyState == 4)
• k (xhr.responseText);
• }
• xhr.send(null);
• }
• Usage: callWithContinuation('http://a.com/describe?id=10', alert);
• Client continues while server runs
• Basis of AJAX Web programming paradigm
• 43. Continuations in compilation
• SML continuation-based compiler [Appel, Steele]
• 1) Lexical analysis, parsing, type checking
• 2) Translation to  -calculus form
• 3) Conversion to continuation-passing style (CPS)
• 4) Optimization of CPS
• 5) Closure conversion – eliminate free variables
• 6) Elimination of nested scopes
• 7) Register spilling – no expression with >n free vars
• 8) Generation of target assembly language program
• 9) Assembly to produce target-machine program
• 44. Coroutines (this is complicated…)
• datatype tree = leaf of int | node of tree*tree;
• datatype coA = A of (int* coB) cont (* searchA wants int and B-cont*)
• and coB = B of coA cont; (* searchB wants an A-continuation *)
• fun resumeA(x, A k) = callcc(fn k' => throw k (x, B k'));
• fun resumeB( B k) = callcc(fn k' => throw k (A k'));
• exception DISAGREE; exception DONE;
• fun searchA(leaf(x),(y, other: coB)) =
• if x=y then resumeB(other) else raise DISAGREE
• | searchA(node(t1,t2), other) = searchA(t2, searchA(t1, other));
• fun searchB(leaf(x), other : coA) = resumeA(x,other)
• | searchB(node(t1,t2), other) = searchB(t2, searchB(t1, other));
• fun startB(t: tree) = callcc(fn k => (searchB(t, A k); raise DONE));
• fun compare(t1,t2) = searchA(t1, startB(t2));
skip callcc, at least for now
• 45. Summary
• Structured Programming
• Go to considered harmful
• Exceptions
• “ structured” jumps that may return a value
• dynamic scoping of exception handler
• Continuations
• Function representing the rest of the program
• Generalized form of tail recursion
• Used in Lisp and ML compilation, some OS projects, web application development, …
• 46. What is a functional language ?
• “ No side effects”
• OK, we have side effects, but we also have higher-order functions…
• We will use pure functional language to mean
• “ a language with functions, but without side effects
• or other imperative features.”
• 47. No-side-effects language test
• Within the scope of specific declarations of x 1 ,x 2 , …, x n , all occurrences of an expression e containing only variables x 1 ,x 2 , …, x n , must have the same value.
• Example
• begin
• integer x=3; integer y=4;
• 5*(x+y)-3
• … // no new declaration of x or y //
• 4*(x+y)+1
• end
?
• 48. Example languages
• Pure Lisp
• atom, eq, car, cdr, cons, lambda, define
• Impure Lisp: rplaca, rplacd
• lambda (x) (cons
• (car x)
• (… (rplaca (… x …) ...) ... (car x) … )
• ))
• Cannot just evaluate (car x) once
• Common procedural languages are not functional
• Pascal, C, Ada, C++, Java, Modula, …
• Example functional programs in a couple of slides
• 49. Backus’ Turing Award
• John Backus was designer of Fortran, BNF, etc.
• Turing Award in 1977
• Turing Award Lecture
• Functional prog better than imperative programming
• Easier to reason about functional programs
• More efficient due to parallelism
• Algebraic laws
• Reason about programs
• Optimizing compilers
• 50. Reasoning about programs
• To prove a program correct,
• must consider everything a program depends on
• In functional programs,
• dependence on any data structure is explicit
• Therefore,
• easier to reason about functional programs
• Do you believe this?
• This thesis must be tested in practice
• Many who prove properties of programs believe this
• Not many people really prove their code correct
• 51. Haskell Quicksort
• Very succinct program
• qsort [] = []
• qsort (x:xs) = qsort elts_lt_x ++ [x]
• ++ qsort elts_greq_x
• where elts_lt_x = [y | y <- xs, y < x]
• elts_greq_x = [y | y <- xs, y >= x]
• This is the whole thing
• No assignment – just write expression for sorted list
• No array indices, no pointers, no memory management, …
• 52. Compare: C quicksort
• qsort( a, lo, hi ) int a[], hi, lo;
• { int h, l, p, t;
• if (lo < hi) {
• l = lo; h = hi; p = a[hi];
• do {
• while ((l < h) && (a[l] <= p)) l = l+1;
• while ((h > l) && (a[h] >= p)) h = h-1;
• if (l < h) { t = a[l]; a[l] = a[h]; a[h] = t; }
• } while (l < h);
• t = a[l]; a[l] = a[hi]; a[hi] = t;
• qsort( a, lo, l-1 );
• qsort( a, l+1, hi );
• }
• }
• 53. Interesting case study
• Naval Center programming experiment
• Separate teams worked on separate languages
• Surprising differences
• Some programs were incomplete or did not run
• Many evaluators didn’t understand, when shown the code, that the Haskell program was complete. They thought it was a high level partial specification.
Hudak and Jones, Haskell vs Ada vs C++ vs Awk vs …, Yale University Tech Report, 1994
• 54. Disadvantages of Functional Prog
• Functional programs often less efficient. Why?
• Change 3rd element of list x to y
• (cons (car x) (cons (cadr x) (cons y (cdddr x))))
• Build new cells for first three elements of list
• (rplaca (cddr x) y)
• Change contents of third cell of list directly
• However, many optimizations are possible
A B C D
• 55. Von Neumann bottleneck
• Von Neumann
• Mathematician responsible for idea of stored program
• Von Neumann Bottleneck
• Backus’ term for limitation in CPU-memory transfer
• Related to sequentiality of imperative languages
• Code must be executed in specific order
• function f(x) { if (x<y) then y = x; else x = y; }
• g( f(i), f(j) );
• 56. Eliminating VN Bottleneck
• No side effects
• Evaluate subexpressions independently
• Example
• function f(x) { return x<y ? 1 : 2; }
• g(f(i), f(j), f(k), … );
• Does this work in practice? Good idea but ...
• Too much parallelism
• Little help in allocation of processors to processes
• ...
• David Shaw promised to build the non-Von ...
• Effective, easy concurrency is a hard problem