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generating functions, templates, and macros

generating functions, templates, and macros. Yves Lespérance Adapted from Peter Roosen-Runge. midterm October 20. bring photo ID closed book; no access to cellphones, PDAs, laptops, etc. test will be based on the material in the textbook (Ch. 2-8, 10-12, 14), lectures, and readings.

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generating functions, templates, and macros

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  1. generating functions, templates, and macros Yves Lespérance Adapted from Peter Roosen-Runge

  2. midterm October 20 • bring photo ID • closed book; no access to cellphones, PDAs, laptops, etc. • test will be based on the material in the textbook (Ch. 2-8, 10-12, 14), lectures, and readings

  3. constructing a pumper • Automating Ch. 11 pumper will create a tail-recursive function and a main function to call it, with arguments: • function name, the initial result, and a 'construction' function f • f constructs a new (partial) result from a previous (partial) result, • with the name of f = |HELP-name|

  4. pumper in action • Example: construct both • tail-recursive rev (reverse) • and its helper function • (pumper 'rev • NIL ; initial • 'CONS ; used to construct result ) • recall in rev2 • result -->(CONS (FIRST list) result)

  5. numerical example • sum of squares: (sumsq list) • slow version: (+ (* (FIRST list) (FIRST list)) (sumsq (REST list)) • or define sumsq and |Help-SUMSQ| (pumper 'sumsq 0 '(LAMBDA (x y) (+ (* x x) y)) )

  6. the main function • code to construct the main function (DEFUN makeMain (name helper initial) (EVAL (LIST 'DEFUN name '(arglist) (LIST helper 'arglist initial)) ) )

  7. make the helper (DEFUN makeHelp (helper f) (EVAL (LIST 'DEFUN helper '(arglist result) (LIST 'IF '(ENDP arglist) 'result (LIST helper '(REST arglist) (LIST’FUNCALL(LIST 'FUNCTION f) (LIST 'FIRST arglist) result))))) )

  8. demo >(makehelp 'helpfun 'CONS) (defun helpfun (arglist result) (if (endp arglist) result (helpfun (rest arglist) (FUNCALL (function CONS) (first arglist) result))))

  9. assembling the pieces (DEFUN pumper (name initial f) (LET ((helper (INTERN (FORMAT nil "Help-~a" name)))) (makeMain name helper initial) (makeHelp helper f) ) )

  10. using templates • use template for expressions involving substitutions of values for variables into a fixed structure • Lisp's substitution operators • backquote` : means don’t evaluate unless specified • comma , : ,expr means evaluate • see form-cons.html

  11. template example (DEFUN makeMain (name helper initial) (EVAL ‘(DEFUN ,name (arglist) (,helper arglist ,initial))) )

  12. the complete pumper (DEFUN pumper (name initial f) (LET ((helper (INTERN (FORMAT nil "Help-~a" name)))) (EVAL `(DEFUN ,name (arglist) (,helper arglist ,initial))) (EVAL `(DEFUN ,helper (arglist result) (IF (ENDP arglist) result (,helper (REST arglist) (FUNCALL (FUNCTION ,f) (FIRST arglist) result)))) ) )

  13. pumper demo • tail-recursive reverse >(pumper 'rev NIL 'CONS) • |Help-REV| • >(rev '(a b c)) • (C B A) • (symbol-function '|Help-REV|) = (LAMBDA-BLOCK |Help-REV| (ARGLIST RESULT) (IF (ENDP ARGLIST) RESULT (|Help-REV| (REST ARGLIST) (FUNCALL #'CONS (FIRST ARGLIST) RESULT))))

  14. closures • A function may be defined in one context and used in another. If it contains free variables, this may cause problems. • Lisp avoids this by keeping a record of the environment where the function was defined in a closure.

  15. closure e.g. (DEFUN gen_adder (n) (FUNCTION (LAMBDA (x) (+ x n)))) (DEFUN eg (n k) (FUNCALL (gen_adder k) n)) >(eg 5 7) 12

  16. macros

  17. sort of like functions, but . . • one of the most interesting but tricky aspects of Lisp. • unlike functions, macros don't evaluate their arguments • they compute on unevaluated expressions • just uninterpreted data structures: • binary trees • 'dot' at the root of every sub-tree • atoms at the leaves • macros can be expanded once when function that uses macros is defined or compiled

  18. COND is an example >(DESCRIBE ’COND) … special operator with macro definition, has 1 property SYSTEM::MACRO. For more information, evaluate (SYMBOL-PLIST ’COND)… >(SYMBOL-PLIST ’COND) (SYSTEM::MACRO #<COMPILED-CLOSURE COND>)

  19. 2-step macro evaluation takes two steps s-expression value expansion evaluation MACROEXPAND EVAL >(MACROEXPAND '(COND ((NULL x) 1) ((NULL y) 2) (:OTHERWISE 3))) (IF (NULL X) 1 (IF (NULL Y) 2 (IF :OTHERWISE 3 NIL)))

  20. e.g. flambda • often write (FUNCTION (LAMBDA …)); define a macro flambda that abbreviates this. (DEFMACRO flambda (&REST args) (LIST ’FUNCTION (CONS 'LAMBDA args))) ; args will be a list (MACROEXPAND ’(FLAMBDA (X Y) (CONS X Y))) #’(LAMBDA (X Y) (CONS X Y))

  21. using a template (DEFMACRO flambda (&REST args) `(FUNCTION (LAMBDA ,args)))

  22. e.g. 2+ (DEFMACRO 2+ (ARG) `(1+ (1+ ,arg))) >(MACROEXPAND ’(2+ x)) (1+ (1+ x)) T >(2+ (+ 3 5)) 10

  23. destructuring • Macros often destructure their arguments, i.e. extract some of their parts; this is easier if we use structured parameters, lists with named parts >(DEFMACRO cross ((a b) (c d)) `((,a ,d) (,b ,c))) (MACROEXPAND '(cross (one two) (three four))) ((one four) (two three))

  24. fancier example: (DEFMACRO crossdot ((a . b) (c . d)) `((,a ,d) (,b ,c))) (MACROEXPAND '(crossdot (one two three) (four five six))) ((one (five six)) ((two three) four) • what's happening? what are a, b, c & d bound to?

  25. use of macros • support abstraction at little cost, e.g. get-state-field • can add abbreviations that make programming easier, e.g. COND, AND for more than 2 arguments, loop constructs, etc. • can define embedded languages within Lisp with little execution cost • caveat: user must learn the syntax expected by the macros

  26. macros vs. functions • a macro is treated internally as a function of one argument • order of evaluation is different, outside-in rather than inside-out, e.g. >(MACROEXPAND ’(2+ (2+ 5)) (1+ (1+ (2+ 5))) T >(2+ (2+ 5)) 9

  27. more examples see http://www.cs.yorku.ca/course/3401/MacroExamples.html

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