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Data Abstraction Functional Programming

Data Abstraction Functional Programming. Academic Year 2005-2006 Alessandro Cimatti cimatti@itc.it. Interpreter Interaction. > 1 1 > 1.2 1.2 > a error: unbound variable - a if continued: try evaluating symbol again 1> [ back to top level ] >(a b c) error: unbound function - a

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Data Abstraction Functional Programming

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  1. Data AbstractionFunctional Programming Academic Year 2005-2006 Alessandro Cimatti cimatti@itc.it

  2. Interpreter Interaction > 1 1 > 1.2 1.2 > a error: unbound variable - a if continued: try evaluating symbol again 1> [ back to top level ] >(a b c) error: unbound function - a if continued: try evaluating symbol again 1> [ back to top level ] > '(a b c) (a b c)

  3. Interpreter Interaction > nil nil > t t > T t > '(a (b c) d) (a (b c) d) > (setq sam 'abc) abc > sam abc

  4. Interaction with the Interpreter > (load "file-name") ; load the content of the file > (compile-file "file-name") ; the compiled version is in file-name.o ; then load in file-name.o > (compile 'func-name) ; compile a particular function > (time (func-name arg1 ... argn)) ; print real and run time for executing ; func-name >(bye) or (quit) or <ctrl>-D ; exit the interpreter

  5. Trace and Untrace > (trace cnt-atom) (cnt-atom) > (cnt-atom '(a b)) Entering: CNT-ATOM, Argument list: ((a b)) Entering: CNT-ATOM, Argument list: (a) Exiting: CNT-ATOM, Value: 1 Entering: CNT-ATOM, Argument list: ((b)) Entering: CNT-ATOM, Argument list: (b) Exiting: CNT-ATOM, Value: 1 Entering: CNT-ATOM, Argument list: (nil) Exiting: CNT-ATOM, Value: 0 Exiting: CNT-ATOM, Value: 1 Exiting: CNT-ATOM, Value: 2 2 > (untrace cnt-atom) nil

  6. Some data abstraction

  7. Sets (defun set_in (el l) (cond ((null l) nil) ((equal el (first l)) t) (t (set_in el (rest l))))) (defun set_insert (el l) (cond ((null l) (cons el l)) ((equal el (first l)) l) (t (cons (first l) (set_insert el (rest l)))))) (defun set_union (l1 l2) (if (null l1) l2 (set_union (rest l1) (set_insert (first l1) l2)))) (defun set_remove (el l) (cond ((null l) l) ((equal el (first l)) (rest l)) (t (cons (first l) (set_remove el (rest l)))))) (defun set_equal (l1 l2) (cond ((null l1) (null l2)) ((set_in (first l1) l2) (set_equal (rest l1) (set_remove (first l1) l2))) (t nil))) (defun set_intersect (l1 l2) (set_intersect-iter l1 l2 nil)) (defun set_intersect-iter (l1 l2 res) (cond ((null l1) res) ((set_in (first l1) l2) (set_intersect-iter (rest l1) l2 (cons (first l1) res))) (t (set_intersect-iter (rest l1) l2 res))))

  8. Association Lists • An association list is a structure that associates a key to a value ((a1 v1) (a2 v2) … (an vn)) (defun al_assoc (key l) (cond ((null l) nil) ((equal key (car (first l))) (cdr (first l))) (t (al_assoc key (rest l))))) (defun al_setval (key val l) (cons (cons key val) l)) (defun al_erase (key l) (cond ((null l) l) ((equal key (car (first l))) (al_erase key (rest l))) (t (cons (first l) (al_erase key (rest l))))))

  9. Exercise: count and sum • Write a function that traverses a tree and prints • the number of symbols in the tree • the sum of the numbers in the tree > (countsum ‘(2 . b)) Sum: 2; Count: 1 > (countsum ‘(2 2 . 3)) Sum: 7; Count: 0 > (countsum ‘((a . b) c)) Sum: 0; Count: 3 > (countsum ‘(1 b 2 c)) Sum: 3; Count: 2

  10. Exercise: hints • To print, use the following construct (format t “control string” arg1 ... argn) > (setq sum 12.4) 12.4 > (setq count 5) 5 > (format t “Sum: ~A; Count: ~A~%” sum count) Sum: 12.4; Count: 5

  11. Exercise: hints • We don’t want two recursions • We want to compute both functions at the same time • We need a way to accumulate two partial results • the partial sum of the numbers seen so far • the number of symbols seen so fa • Pack the result in a cons cell! • car contains sum • cdr contains count

  12. Exercise: count and sum (defun countsum (x) (countsum-iter x (cons 0 0))) (defun countsum-iter (x res) (let ((cnt (car res)) (sum (cdr res))) (cond ((null x) res) ((symbolp x) (cons (+ cnt 1) sum)) ((numberp x) (cons cnt (+ sum x))) (t (countsum-iter (cdr x) (countsum-iter (car x) res))))))

  13. Exercise: count and sum >(trace countsum-iter) >(countsum '(a 1 b (2 . 3) (c . d))) 1> (COUNTSUM-ITER (A 1 B (2 . 3) (C . D)) (0 . 0)) 2> (COUNTSUM-ITER A (0 . 0)) <2 (COUNTSUM-ITER (0 . 1)) 2> (COUNTSUM-ITER (1 B (2 . 3) (C . D)) (0 . 1)) 3> (COUNTSUM-ITER 1 (0 . 1)) <3 (COUNTSUM-ITER (1 . 1)) 3> (COUNTSUM-ITER (B (2 . 3) (C . D)) (1 . 1)) 4> (COUNTSUM-ITER B (1 . 1)) <4 (COUNTSUM-ITER (1 . 2)) 4> (COUNTSUM-ITER ((2 . 3) (C . D)) (1 . 2)) 5> (COUNTSUM-ITER (2 . 3) (1 . 2)) 6> (COUNTSUM-ITER 2 (1 . 2)) <6 (COUNTSUM-ITER (3 . 2)) 6> (COUNTSUM-ITER 3 (3 . 2)) <6 (COUNTSUM-ITER (6 . 2)) <5 (COUNTSUM-ITER (6 . 2)) 5> (COUNTSUM-ITER ((C . D)) (6 . 2)) 6> (COUNTSUM-ITER (C . D) (6 . 2)) 7> (COUNTSUM-ITER C (6 . 2)) <7 (COUNTSUM-ITER (6 . 3)) 7> (COUNTSUM-ITER D (6 . 3)) <7 (COUNTSUM-ITER (6 . 4)) <6 (COUNTSUM-ITER (6 . 4)) 6> (COUNTSUM-ITER NIL (6 . 4)) <6 (COUNTSUM-ITER (6 . 4)) <5 (COUNTSUM-ITER (6 . 4)) <4 (COUNTSUM-ITER (6 . 4)) <3 (COUNTSUM-ITER (6 . 4)) <2 (COUNTSUM-ITER (6 . 4)) <1 (COUNTSUM-ITER (6 . 4)) (6 . 4)

  14. Exercise: count and sum (defun countsum (x) (let* ((res (countsum-iter x (cons 0 0))) (cnt (car res)) (sum (cdr res))) (format t “Symbols Count: ~A; Numbers Sum: ~A~%” cnt sum))) (defun countsum-iter (x res) (let ((cnt (car res)) (sum (cdr res))) (cond ((null x) res) ((symbolp x) (cons (+ cnt 1) sum)) ((numberp x) (cons cnt (+ sum x))) (t (countsum-iter (cdr x) (countsum-iter (car x) res))))))

  15. Homework • Write a program to normalize expressions for lambda calculus • Suggested steps: • Define the ADT for lambda terms • constructors • recognizers • Define substitution primitive • Define recognizer for redex’s • Define beta-reduction rule • Define the normalizer: • recursively traverse the term looking for redex, and reduce • careful with infinite looping!! • Some remarks • homework due by december 20 • homework is closely related to course project!!!

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