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The mathematical model of computation that

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1. The mathematical model of computation that denotational semantics is based upon is called . 2. A(n) is a condition which is true upon entry to a loop every time the loop is entered, and is still true at the termination of the loop. 3. True or False. Denotational semantics is a method for defining the semantics of a programming language by giving an interpreter for that language. 4. Consider the following Lisp function: (defun update (store V n) (prog (currentenv newbinding newstore) (setq currentenv (cdaddr store))) (setq newbinding (cons (list ’eq ’V (list ’quote V)) (list n))) (setq newstore (list ’lambda (list ’V) (cons ’cond (cons newbinding currentenv)))) (return newstore)))) Note that the (prog (list of local variables) (exp-1) (exp-2) ... (exp-n) (return exp)) construction declares a list of local variables used in the expressions with exp being the value returned. Let S represent the Lisp expression (lambda (V) (cond ((eq V (quote x)) 4) (t (quote bottom)))) . What is the internal list representation that Lisp uses for S? What is (cdaddr S) ? Trace the execution of (update S ’x 5) , showing the values of currentenv , newbinding , and newstore . 5. Consider the Prolog program which solves the Towers of Hanoi problem. This problem is to move a stack of blocks from one location to another without ever changing the order in which blocks are placed on top of each other. A third stack may be used but only one block may be moved at a time. hanoi(N) :- move(N, left, center, right). move(0, X, Y, Z).

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