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1 a little more on macros 1 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 as uninterpreted data structures: binary trees -- 'dot' at the root of every sub-tree -- atoms at the leaves 2

2 2-step macro evaluation takes two steps s-expression expansion evaluation value MACROEXPAND EVAL >(MACROEXPAND '(COND ((NULL x) 1) ((NULL y) 2) (:OTHERWISE 3))) (IF (NULL X) 1 (IF (NULL Y) 2 (IF :OTHERWISE 3 NIL))) 3 one last buildrec version (DEFUN buildrec2(main initial terminal reduce build) (LET (( helper (GENSYM "helper"))) (EVAL (PPRINT (LIST 'DEFUN main (LIST initial) (LIST helper initial terminal)))) (EVAL (PPRINT (LIST 'DEFUN helper (LIST initial 'result) (LIST 'IF (LIST 'EQUAL initial terminal) 'result (LIST helper (LIST 'FUNCALL reduce initial) (LIST 'FUNCALL build initial 'result)))))) )) (DEFMACRO buildrec3(main initial terminal reduce build) (LET (( helper (GENSYM "helper"))) (PPRINT `(DEFUN,main (,initial) (helper,initial,terminal))) (PPRINT `(DEFUN helper (,initial result) (IF (EQUAL,initial,terminal) result (helper (FUNCALL,reduce,initial) )) ; where are all the EVALs gone?? (FUNCALL,build,initial result))))) 4

3 destructuring Macro parameters can be "destructured" shown as lists with named parts: >(DEFMACRO cross ((a b) (c d)) `((,a,d) (,b,c))) >(MACROEXPAND '(cross (one two) (three four))) '((ONE FOUR) (TWO THREE)) ; T why the term "de-structuring"? 5 fancier example: >(DEFMACRO crossdot ((a. b) (c. d)) `'((,a,d) (,b,c))) >(crossdot (one two three) (four five six)) ((ONE (FIVE SIX)) ((TWO THREE) FOUR) what's happening? what are a, b, c & d bound to? 6

4 how similar are macros & functions? macro is treated as a function with 1 argument fundamental difference: order of evaluation cf. nested CONDs expansion of the outer macro arg requires expansion of the inner but it works outside-in, rather than the usual inside-out 7 change of pace & of programming language time to reread Ch. 1, and Ch. 16: Prolog 8

5 terms are basic Prolog statements express logical relationships among terms a term = generalization of a functional expression it looks like this: functor(arg1, arg2) no evaluation implied used to represent both objects and facts 9 facts, rules, queries facts = statements taken to be true e. g, Ottawa is the capital of Canada. rules = facts with conditions C is a city if C is a capital of a country. query = "yes" if a fact or an instance of a general fact or rule ("Is Ottawa a city?"), otherwise "no" 10

6 objects objects are labelled tree-stuctures: composer(name('berlioz'), nationality(french)) Names begin with lower-case or are quoted; Variables begin with upper-case 11 facts facts instantiate relations among objects the sun & planets are instance of a 'solar system' relation: solar_system(sun, planets(mercury, venus, earth)) can facts include variables? times(x,1,x). variables used in general or universal facts 12

7 naming the parts root label of a term = functor sometimes "principal functor" to distinguish root label from functors of sub-terms sub-trees of the root = arguments number of arguments = arity symbolic atoms are terms with arity 0. Example: times(x,1,x) is a term of arity 3, with functor times. 13 what we can build from terms facts: capital('canada', 'Ottawa'). queries:?- capital(country, 'Ottawa'). Country = 'Canada' rules: city(x) :- capital(country, X).?-city('Ottawa'). Yes ; assuming capital('canada', 'Ottawa') is asserted as a fact 14

8 syntax issues All functors are symbolic-atoms (can't be numbers) normally alphanumeric (including _) begin with lower case letter Edinburgh Prolog implementations are case-sensitive Prolog more restricted than Lisp in symbolic-atom names: x-y is OK in Lisp as an atom, but not in Prolog syntax. 15 lists lists are special kind of object-terms: [a, b] = a.b.[] = '.'(a, '.'(b, [])) only way to write empty list: [] the functor. builds binary trees just as in Lisp 16

9 % pl examples?- X = a(term). % solve the equation for X. % (Find an X which makes the = relation true. X = a(term)?- X =.(a,[]). % This is equivalent to cons-ing 'a' with []. X = [a] % Prolog uses list notation in the output, where % possible.?- X =.(a, b, c). X = '.'(a,b,c) % '.' is not the. functor of arity 2, since it has % arity 3 here. 17 more dots & cons?- X =.(a, b). X = [a b] % [first rest] is a handy notation for constructing dotted pairs, or more commonly, lists.?- X = [a []]. % [H T] = list whose 'first' is H and whose 'rest' is T. (So if [H T] is a list, then T must be a list.) X = [a] 18

10 pattern-matching destructuring is built-in?- [H T] = [[a, b], a, 22]. H = [a,b] T = [a,22] Lisp's EQUAL compares lists, returns T or NIL Prolog's = compares terms and binds variables to data 19

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