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Continuations and Control
Gul Agha
CS 421
CS 421 Spring 2005 2
Imperative Version of fact-iter
(define n-reg '*)
(define a-reg '*)
(define fact-iter
(lambda (n)
(set! n-reg n)
(set! a-reg 1)
(fact-iter-acc/reg)))
CS 421 Spring 2005 3
Imperative version (contd.)
(define fact-iter-acc/reg
(lambda ( )
(if (zero? n-reg)
a-reg
(begin (set! a-reg (* n-reg a-reg))
(set! n-reg (– n-reg 1))
(fact-iter-acc/reg)))))
CS 421 Spring 2005 4
Imperative Transform on
CPS style code
What environment will the continuation be
evaluated in?
CS 421 Spring 2005 5
CPS form of Remove
(define remove (lambda (s los k) (if (null? los) (k '( )) (if (eq? s (car los)) (remove s (cdr los) k) (remove s (cdr los) (lambda (v) (k (cons (car los) v))) )))))
CS 421 Spring 2005 6
Imperative Transform on
remove-cps
(define s-reg ’) (define los-reg ’) (define k-reg ’*) (define remove (lambda (s los k) (set! s-reg s) (set! los-reg los) (set! k-reg k) (remove/reg)))
CS 421 Spring 2005 7
(define remove/reg (lambda ( ) (if (null? los-reg) (k '( )) (if (eq? s-reg (car los-reg)) (begin (set! los-reg (cdr los-reg)) (remove/reg)) (begin (set! k (lambda (v) (k-reg (cons (car los-reg) v)))) (set! los-reg (cdr los-reg)) (remove/reg))))
Wrong!! Why?
CS 421 Spring 2005 8
Environment
- Continuations must save the bindings in
(part of) the current environment that they
need.
- Linked list of continuations
- Interpreters take care of storing the current
environment.
fun env fun env fun env
CS 421 Spring 2005 9
What cps does not achieve?
- Time complexity class of code is
unchanged.
- Time or space requirement may change
only by a constant factor.
CS 421 Spring 2005 10
Fibonacci
(define fib (lambda (n) (if (or (= n 0) (= n 1)) n (+ (fib (– n 1)) (fib (– n 2))))) (define fib (lambda (n k) (if (or (= n 0) (= n 1)) (k n) (fib (– n 1) (lambda (v) (k (+ v (fib (– n 2)))) )) )))
CS 421 Spring 2005 11
CPS Fib
(define fib (lambda (n k) (if (or (= n 0) (= n 1)) (k n) (fib (– n 1) (lambda (v) (fib (– n 2) (lambda (w) k (+ v w)))) )))
CS 421 Spring 2005 12
Linear Recursive Fib
(define fib (lambda (n) (car fib*(n))))
(define fib* (lambda (n) (cond ((= n 0) (cons 0 0)) ((= n 1) (cons 0 1)) (else (let ((x (fib* (– n 1)))) (cons (+ (car x) (cdr x)) (car x)))))))
Exercise: convert to cps form!
CS 421 Spring 2005 19
Co-routines
- Co-routines provide a symmetric control model.
- Used in simulations and games (Simula)
- Co-routine for each player or object.
- Master unit calls one co- routine.
- Co-routines yield to each other.
CS 421 Spring 2005 20
Co-routines
(define (make-coroutine (lambda (co-body) (letrec ((state (lambda ( ) (co-body resume))) (resume (lambda (that) (call/cc (lambda (this) (set! state this) (that))) ))) (lambda ( ) (state)) )))
CS 421 Spring 2005 21
Example Co-routine
(define A (make-coroutine (lambda (resume) (….) (resume B) (….) (resume B) (….) ‘finito)))
(define B (make-coroutine (lambda (resume) (….) (resume A) (….) (resume A) (….) ‘finito)))
CS 421 Spring 2005 22
Binding current continuation
(let/cc k body)
Is a macro for:
(call/cc (lambda (k) body))
- Can there be more than one continuation
stored?
- What is the extent of a continuation?
- What is (call/cc call/cc)?
CS 421 Spring 2005 23
What does this do?
(let ((cont #f)) (call/cc (lambda (k) (set! cont k))) (cont #f) )
- Initial value of cont unimportant
- Current continuation is bound to k
- cont is bound to k
- cont is invoked with an unimportant value
- We have a time warp
CS 421 Spring 2005 24
Lexically Scoped Exceptions
- Also called block/break exceptions.
- Lexically surrounding block must catch
exception.
- A structured form of labels and gotos
- Examples:
- return, break, continue in C have single point of return.
- Labeled break in Java.
CS 421 Spring 2005 25
True Exceptions
Also called catch/throw exceptions (define find-symbol (lambda (id tree) (letrec ((find (lambda (tree) (if (pair? tree) (or (find (car tree)) (find (cdr tree))) (if (eq? tree id) (throw 'find t) f ))) (catch 'find (find tree)) ) CS 421 Spring 2005 26
Escape in Common Lisp
(defun fact (n)
(prog (r)
(setq r 1)
loop (cond ((= n 1) (return r)))
(setq r (* n r))
(setq n (- n 1))
(go loop) ) )
CS 421 Spring 2005 27
Escape from Nested Context
in Common Lisp
(defun fact2 (n)
(prog (r)
(setq r 1)
loop (setq r (* (cond ((= n 1) (return r))
('else n) )
r ))
(setq n (– n 1))
(go loop) ) )
CS 421 Spring 2005 28
Continuations with
Indefinite Extent
(define (fact n)
(let ((r 1) (k 'void))
(call/cc (lambda (c) (set! k c) 'void))
(set! r (* r n))
(set! n (– n 1))
(if (= n 1)
r
(k 'recurse)) ) )
CS 421 Spring 2005 29
Continuations with Indefinite Extent
(define (fact n)
(let ((r 1))
(let ((k (call/cc (lambda (c) c))))
(set! r (* r n))
(set! n (– n 1))
(if (= n 1)
r
(k k)) ) ) )
