# Symbolic Programming. Dr. Zoran Duric () Symbolic Programming 1/ 89 August 28, / 89

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1 Symbolic Programming Symbols: +, -, 1, 2 etc. Symbolic expressions: (+ 1 2), (+ (* 3 4) 2) Symbolic programs are programs that manipulate symbolic expressions. Symbolic manipulation: you do it all the time; now you ll write programs to do it. Dr. Zoran Duric () Symbolic Programming 1/ 89 August 28, / 89

2 Example Logical rules can be represented as symbolic expressions of the form, antecedent implies consequent. The following rule states that the relation of being inside something is transitive, x is inside y and y is inside z implies x is inside z. In lisp notation, we would represent this rule as (SETF rule (implies (and (inside x y) (inside y z)) (inside x z))) Dr. Zoran Duric () Symbolic Programming 2/ 89 August 28, / 89

3 Manipulating symbolic expressions (first rule) ;; The expression is a rule. ;; (FIRST RULE) IMPLIES (second rule) ;; The antecedent of the rule. ;; (SECOND RULE) (AND (INSIDE X Y) (INSIDE Y Z)) (third rule) ;; The consequent of the rule. ;; (THIRD RULE) (INSIDE X Z) (first (second rule)) ;; The antecedent is a conjunction. ;; (FIRST (SECOND RULE)) AND (second (second rule)) ;; The first conjunct of the antecedent. ;; (SECOND (SECOND RULE)) (INSIDE X Y) Dr. Zoran Duric () Symbolic Programming 3/ 89 August 28, / 89

4 Lisp and Common Lisp What are you looking for in a programming language? primitive data types: strings, numbers, arrays operators: +, -, +, /, etc. flow of control: if, or, and, while, for input/output: file handling, loading, compiling programs Dr. Zoran Duric () Symbolic Programming 4/ 89 August 28, / 89

5 Lisp has all of this and more. developed by John McCarthy at MIT second oldest programming language still in use (FORTRAN is oldest) specifically designed for symbolic programming We use a dialect of Lisp called Common Lisp. Common Lisp is the standard dialect We use a subset of Common Lisp. Dr. Zoran Duric () Symbolic Programming 5/ 89 August 28, / 89

6 Basic Data Types and Syntax Numbers: 1, 2, 2.72, 3.14, 2/3 (integers, floating point, rationals) Strings: abc, FOO, this is also a string Characters: - characters: a,b,...,z,a,b,...,z,0,1,2,...,9,,-,+,* - alpha characters: a,b,...,z,a,b,...,z - numeric characters: 0,1,2,...,9 sequence of characters including one or more alpha characters its actually more complicated than this but this will suffice Symbols: Dr. Zoran Duric () Symbolic Programming 6/ 89 August 28, / 89

7 Examples foo, my-foo, your foo, 1foo, foo2, FOO, FOO2 Lisp programs and data are represented by expressions. Expressions - (inductive definition) any instance of a primitive data type: numbers, strings, symbols a list of zero or more expressions Dr. Zoran Duric () Symbolic Programming 7/ 89 August 28, / 89

8 List open paren ( zero or more Lisp objects separated by white space close paren ) Examples 1, foo, BAR (primitive data types) (), (1), (1 foo BAR) (flat list structures) (1 (1 foo BAR) biz 3.14) (nested list structure) Dr. Zoran Duric () Symbolic Programming 8/ 89 August 28, / 89

9 Comment character ; Lisp ignores anything to the right of a comment character. Lisp is case insensitive with regard to symbols. FOO, Foo, foo, foo designate the same symbol, but FOO, Foo, foo, foo designate different strings. Dr. Zoran Duric () Symbolic Programming 9/ 89 August 28, / 89

10 Interacting with the Lisp Interpreter Instead of 1. Write program 2. Compile program 3. Execute program you can simply type expressions to the Lisp interpreter. EVAL compiles, and executes symbolic expressions interpreted as programs. The READ-EVAL-PRINT loop reads, EVALs, and prints the result of executing symbolic expressions. Instances of simple data types EVALuate to themselves. string 3.14 t nil Dr. Zoran Duric () Symbolic Programming 10/ 89August 28, / 89

11 sym ;; Would cause an error if typed to the interpreter. ;; Interpreter errors look like ;; > sym ;; Error: The symbol SYM has no global value EVAL expression expression is a string return the expression expression is a number return the expression expression is a symbol look up the value of the expression You will learn how symbols get values later Dr. Zoran Duric () Symbolic Programming 11/ 89August 28, / 89

12 Invoking Functions (Procedures) in Lisp Function names are symbols: +, -, *, sort, merge, concatenate Lisp uses prefix notation (function argument 1... argument n ) (+ 1 2) ;; + is the function, 1 and 2 are the arguments ( ) ;; + takes any number of arguments What happens when EVAL encounters a list? Lists (with the exception of special forms) are assumed to signal the invocation of a function. APPLY handles function invocation Dr. Zoran Duric () Symbolic Programming 12/ 89August 28, / 89

13 EVAL expression expression is a string or a number return the expression expression is a symbol look up the value of the expression it is of the form (function name expression 1... expression n ) APPLY function name to expression 1... expression n Dr. Zoran Duric () Symbolic Programming 13/ 89August 28, / 89

14 APPLY function name to expression 1... expression n EVAL expression 1 result 1... EVAL expression n result n function name better have a definition; look it up! the definition for function name should look something like function name formal parameter 1... formal parameter n expression involving formal parameter 1... formal parameter n substitute result i for formal parameter i in the expression EVAL the resulting expression Dr. Zoran Duric () Symbolic Programming 14/ 89August 28, / 89

15 Example function name: WEIRD formal parameters: X1 X2 X3 definition: X2 > (WEIRD 1 one 1.0) EVAL (WEIRD 1 one 1.0) APPLY WEIRD to 1 one 1.0 EVAL 1 1 EVAL one one EVAL substitute 1 for X1 substitute one for X2 substitute 1.0 for X3 EVAL one Dr. Zoran Duric () Symbolic Programming 15/ 89August 28, / 89

16 > (WEIRD 1st arg 1st call (weird 1st arg 2nd call 2nd arg 2nd call (weird 1st arg 3rd call 2nd arg 3rd call 3rd arg 3rd call )) 3rd arg 1st call ) 2nd arg 2nd call Dr. Zoran Duric () Symbolic Programming 16/ 89August 28, / 89

17 (+ (* (+ 1 2) 3) (/ 12 2)) (+ (* (+ 1 ;; Indenting helps to make nested 2) ;; function invocation clearer. 3) (/ 12 ;; What is the order of evaluation 2)) ;; in this nested list expression? (+ (* (+ 1 2) 3) (/ 12 2)) [9] / \ (* (+ 1 2) 3) [5] (/ 12 2) [8] / \ / \ (+ 1 2) [3] 3 [4] 12 [6] 2 [7] / \ 1 [1] 2 [2] Dr. Zoran Duric () Symbolic Programming 17/ 89August 28, / 89

18 Defining Functions (Procedures) in Lisp (defun function name list of formal parameters function definition) The function name is a symbol. The formal parameters are symbols. The function definition is one or more expressions. Examples (defun weird (x y z) y) function name list of three formal parameters function definition consisting of one expression Dr. Zoran Duric () Symbolic Programming 18/ 89August 28, / 89

19 Examples of Functions (defun square (x) (* x x)) (defun hypotenuse (a b) (sqrt (+ (square a) (square b))) How would these functions appear in a text file? Dr. Zoran Duric () Symbolic Programming 19/ 89August 28, / 89

20 Functions Documented ;; HYPOTENUSE takes two arguments corresponding ;; to the length of the two legs of a right triangle and returns ;; length of the hypotenuse of the triangle. (defun hypotenuse (a b) ;; SQRT is a built-in function that ;; computes the square root of a number. (sqrt (+ (square a) (square b))) ;; SQUARE computes the square of its single argument. (defun square (x) (* x x)) Dr. Zoran Duric () Symbolic Programming 20/ 89August 28, / 89

21 Boolean Functions and Predicates In Lisp, NIL is boolean false and any expression that evaluates to anything other than NIL is interpreted as boolean true. nil T is the default boolean true. T evaluates to itself. t Boolean predicates return T or NIL. (oddp 3) (evenp 3) (< 2 3) (= 1 2) Dr. Zoran Duric () Symbolic Programming 21/ 89August 28, / 89

22 Boolean Functions and Predicates Boolean functions return non-nil or NIL An OR expression evaluates to non-nil if at least one of its arguments must evaluate to non-nil. (or t nil) Degenerate case of no arguments: (or) An AND expression evaluates to non-nil if All of its arguments must evaluate to non-nil. (and t nil) Degenerate case of no arguments: (and) A NOT expression evaluates to non-nil if its only argument evaluates to NIL. (not t) Any expression can be interpreted as a boolean value. (and 3.14 this string is interpreted as boolean true ) Dr. Zoran Duric () Symbolic Programming 22/ 89August 28, / 89

23 Conditional Statements and Flow of Control Any expression can be used as a test in a conditional statement. Simple conditional statements (if test expression consequent expression alternative expression) Formatted differently using automatic indentation. (if test expression consequent expression alternative expression) Dr. Zoran Duric () Symbolic Programming 23/ 89August 28, / 89

24 Examples (if t consequent alternative ) (if nil consequent alternative ) You do not need to include the alternative. (if t consequent ) The default alternative is NIL. (if nil consequent ) Dr. Zoran Duric () Symbolic Programming 24/ 89August 28, / 89

25 General CONDitional statement (cond conditional clause 1... conditional clause n ) Conditional clause (test expression expression 1... expression m ) Examples (cond ((and t nil) 1) ((or (not t)) 2) ((and) 3)) (cond (t nil)) (if t nil) (defun classify (x) (cond ((= x 0) zero ) ((evenp x) even ) ((oddp x) odd ))) Dr. Zoran Duric () Symbolic Programming 25/ 89August 28, / 89

26 Examples (cont.) (defun classify again (x) (cond ((= x 0) zero ) ((evenp x) even ) (t odd ))) ;; Good programming practice! (classify again 0) (defun classify once more (x) (cond ((= x 0) waste of time zero ) ((evenp x) who cares even ) (t (+ x x) what a waste odd ))) (classify once more 2) Dr. Zoran Duric () Symbolic Programming 26/ 89August 28, / 89

27 Examples (cont.) (defun classify for the last time (x) (cond ((= x 0) (princ so far our lisp is pure ) zero ) ((evenp x) (princ side effects simplify coding ) even ) (t (+ x x) (princ side effects complicate understanding ) odd ))) (classify for the last time 3) Dr. Zoran Duric () Symbolic Programming 27/ 89August 28, / 89

28 Recursive functions Recursion works by reducing problems to simpler problems and then combining the results. (defun raise (x n) (if (= n 0) ;; We can handle this case since x 0 is just 1. 1 (* x ;; Reduce the problem using x n = x x n 1. (raise x (- n 1))))) Dr. Zoran Duric () Symbolic Programming 28/ 89August 28, / 89

29 Example Order Level call RAISE 3 2 first time 1 call RAISE 3 1 second time 2 call RAISE 3 0 third time 3 return 1 from RAISE from the third call return 3 from RAISE from the second call return 9 from RAISE from the first call Dr. Zoran Duric () Symbolic Programming 29/ 89August 28, / 89

30 APPLY and EVAL work together recursively Order Level call EVAL (+ (* 2 3) 4) first time 1 call APPLY + with (* 2 3) and 4 call EVAL (* 2 3) second time 2 call APPLY * with 2 and 3 call EVAL 2 third time 3 return 2 from EVAL by the third call call EVAL 3 fourth time 3 return 3 from EVAL by the fourth call return 6 from APPLY Dr. Zoran Duric () Symbolic Programming 30/ 89August 28, / 89

31 Evaluating Functions in Files > (load one.lisp ) or just > (load one ) if the extension is.lisp. Dr. Zoran Duric () Symbolic Programming 31/ 89August 28, / 89

32 Symbols can be assigned Values The global environment is just a big table that EVAL uses to look up or change the value of symbols. There are other environments beside the global environment. SETF changes values of symbols in environments. Changing the value of a symbol is one example of a side effect. Assign the symbol FOO the value 1 in the global environment (SETF foo 1) (SETF bar 2) (SETF baz (+ foo bar)) Dr. Zoran Duric () Symbolic Programming 32/ 89August 28, / 89

33 Symbols assigned values in the global environment are global variables (SETF sym 3) (defun double (x) (+ x x)) (double sym) We use the terms variable and symbol interchangeably. Global variables can be referenced inside function definitions. (SETF factor 3) (defun scale (x) (* x factor)) (scale sym) From a structured programming perspective, global variables are discouraged. Dr. Zoran Duric () Symbolic Programming 33/ 89August 28, / 89

34 Function Invocation Revisited New environments are created during function invocation. (defun local (x) (SETF x (+ x 1)) (* x x)) In the following example, the symbol X is assigned 2 in the global environment prior to invoking LOCAL on (+ X 1). (SETF x 2) Dr. Zoran Duric () Symbolic Programming 34/ 89August 28, / 89

35 Function Invocation Revisited (cont.) In APPLYing LOCAL to (+ X 1), the single argument expression (+ X 1) EVALuates to 3. Before EVALuating the definition of LOCAL, APPLY creates a new environment that points to the global environment. In this new environment, the formal parameter X is assigned the value 3 of the argument expression. In looking up the value of a symbol while EVALuating the definition of LOCAL, EVAL looks first in the new environment and, if it can t find the symbol listed there, then it looks in the global environment. (local (+ x 1)) In general, function invocation builds a sequence of environments that EVAL searches through. Dr. Zoran Duric () Symbolic Programming 35/ 89August 28, / 89

36 Reconsider the roles of EVAL and APPLY EVAL expression in ENV expression is a string return the expression expression is a number return the expression expression is a symbol look up the value of expression in ENV expression is a special form do something special! expression has form (function name arg expression 1... arg expression n ) APPLY function name to arg expression 1... arg expression n in ENV Dr. Zoran Duric () Symbolic Programming 36/ 89August 28, / 89

37 Reconsider the roles of EVAL and APPLY (cont.) Note that now that we have side effects, order of evaluation is important. Now it makes sense for COND clauses to have more than one expression besides the test and for function definitions to consist of more than one expression. (SETF x 1) (SETF x (+ x x)) (SETF x (* x x)) ;; x 4 (SETF x 1) (SETF x (* x x)) (SETF x (+ x x)) ;; x 2 Dr. Zoran Duric () Symbolic Programming 37/ 89August 28, / 89

38 Reconsider the roles of EVAL and APPLY (cont.) APPLY function name to arg expression 1... arg expression n in ENV evaluate the arguments in left to right order EVAL arg expression 1 in ENV arg result 1... EVAL arg expression n in ENV arg result n look up the definition of function name: function name formal parameter 1... formal parameter n definition = def expression 1... def expression m create a new environment ENV in which for each i formal parameter i is assigned the value arg result i evaluate the expressions in the definition in left to right order EVAL def expression 1 in ENV def result 1... EVAL def expression m in ENV def result m return def result m Dr. Zoran Duric () Symbolic Programming 38/ 89August 28, / 89

39 Question: How is ENV constructed? Environments can be described as sequences (linked lists) of tables where each table assigns symbols to values. Each function is associated with (maintains a pointer to) the environment that was in place at the time the function was defined. In many cases, this is just the global environment, but there are exceptions as you will soon see. ENV is constructed by creating a new table in which the symbols corresponding to formal parameters are assigned the values of the arguments. This table then points to the environment associated with the function. APPLY creates a new environment from the environment associated with the function being applied. Dr. Zoran Duric () Symbolic Programming 39/ 89August 28, / 89

40 Environments created during recursive function invocation. (defun raise (x n) (if (= n 0) 1 (* x (raise x (- n 1))))) > (raise 3 2) Dr. Zoran Duric () Symbolic Programming 40/ 89August 28, / 89

41 Local Variables As noted above, you can change the value of symbols in environments In the following function definition, the formal parameters X and Y are treated as variables whose values are determined locally with respect to the function in which the formal parameters are introduced. (defun sqrt-sum-squares (x y) (SETF x (* x x)) (SETF y (* y y)) (sqrt (+ x y))) Dr. Zoran Duric () Symbolic Programming 41/ 89August 28, / 89

42 You can also introduce additional local variables using LET LET is a special form meaning it handled specially by EVAL. (let ((var 1 var expression 1 )... (var n expression n )) body expression 1... body expression m ) (let ((x (+ 1 2))) (sqrt x)) (let (var 1... var n ) body expression 1... body expression m ) (let (x) (SETF x (+ 1 2)) (sqrt x)) (defun sqrt-sum-squares-let (x y) (let ((p (* x x)) (q (* y y))) (sqrt (+ p q)))) Dr. Zoran Duric () Symbolic Programming 42/ 89August 28, / 89

43 LET statements improve readability LET statements are not strictly necessary but they can dramatically improve the readability of code. Environments created using nested LET statements. Dr. Zoran Duric () Symbolic Programming 43/ 89August 28, / 89

44 Example of nested LET statements (let ((x 1)) (let ((x 2)) (let ((x 3)) (princ x)) (princ x)) (princ x)) Note that the scope of local variables is determined lexically by the text and specifically by the nesting of expressions. Dr. Zoran Duric () Symbolic Programming 44/ 89August 28, / 89

45 Functions with Local State Environments persist over time. State information (local memory) for a specific function or set of functions. (let ((sum 0)) (defun give (x) (SETF sum (- sum x))) (defun take (x) (SETF sum (+ sum x))) (defun report () sum)) > (take 5) > (take 10) > (report) > (give 7) > (report) Dr. Zoran Duric () Symbolic Programming 45/ 89August 28, / 89

46 Functions as Arguments FUNCTION tells EVAL to interpret its single argument as a function. FUNCTION does not evaluate its single argument. (SETF foo (function oddp)) FUNCALL takes a FUNCTION and zero or more arguments for that function and applies the function to the arguments. (funcall foo 1) (funcall (function +) 1 2) There is a convenient abbreviation for FUNCTION. (funcall # + 1 2) Dr. Zoran Duric () Symbolic Programming 46/ 89August 28, / 89

47 What is FUNCALL good for? Generic functions add flexibility. (defun generic-function (x y test) (if (funcall test x y) do something positive do something negative )) (generic-function 1 2 # <) There are lots of generic functions built into Common Lisp. (sort ( ) # <) Ignore the ( ) for the time being. (sort ( ) # >) Dr. Zoran Duric () Symbolic Programming 47/ 89August 28, / 89

48 Lambda Functions (or what s in a name?) LAMBDA specifies a function without giving it a name. (SETF foo # (lambda (x) (* x x))) (funcall foo 3) (funcall # (lambda (x y) (+ x y)) 2 3) LAMBDA functions are convenient for specifying arguments to GENERIC functions. (sort ( ) # (lambda (x y) (< (mod x 3) (mod y 3)))) Dr. Zoran Duric () Symbolic Programming 48/ 89August 28, / 89

49 Lambda can have memory Lambda functions can have local memory just like named functions. (defun spawn (x) # (lambda (request) (cond ((= 1 request) (SETF x (+ x 1))) ((= 2 request) (SETF x (- x 1))) (t x)))) (SETF spawn1 (spawn 10) spawn2 (spawn 0)) (funcall spawn1 1) (funcall spawn1 1) (funcall spawn2 2) (funcall spawn2 2) (funcall spawn1 0) (funcall spawn2 0) Dr. Zoran Duric () Symbolic Programming 49/ 89August 28, / 89

50 Referring to Symbols Instead of their Values QUOTE causes EVAL to suspend evaluation. (quote foo) Quote works for arbitrary expressions not just symbols. (quote (foo bar)) There is a convenient abbreviation for QUOTE. foo (foo bar) Dr. Zoran Duric () Symbolic Programming 50/ 89August 28, / 89

51 Building Lists and Referring to List Elements Build a list with LIST. (SETF sym (list )) Refer to its components with FIRST, SECOND, REST, etc. (first sym) (second sym) (rest sym) LIST, FIRST, REST, etc provide a convenient abstraction for pointers. In fact, you don t have to know much at all about pointers to do list manipulation in Lisp. Dr. Zoran Duric () Symbolic Programming 51/ 89August 28, / 89

52 Put together a list with pieces of other lists (SETF new (list 7 sym)) What if you want a list that looks just like SYM but has 7 for its first element and you want to use the REST of SYM? Use CONS. (cons 7 (rest sym)) If you want a list L such that (FIRST L) = X and (REST L) = Y then (CONS X Y) does the trick. (cons 7 ()) Dr. Zoran Duric () Symbolic Programming 52/ 89August 28, / 89

53 Example Here is a simple (but not particularly useful) recursive function. (defun sanitize-list (x) (if (null x) x (cons element (sanitize-list (rest x))))) (sanitize-list (1 2 3)) (CONS 1 2) is perfectly legal, but it isn t a list. For the time being assume that we only use CONS to construct lists. What about nested lists? Dr. Zoran Duric () Symbolic Programming 53/ 89August 28, / 89

54 Nested lists correspond to trees (1 (2 3 (4)) (5 6 7)) Each nonterminal node / \ in the tree is a list. / \ / \ / \ The children of a node 1 (2 3 (4)) (5 6 7) corresponding to a list / \ / \ are the elements of the / \ / \ list. 2 3 (4) \ 4 Dr. Zoran Duric () Symbolic Programming 54/ 89August 28, / 89

55 How would you SANITIZE a tree? (defun sanitize-tree (x) (cond ((null x) x) ;; No more children. ((not (listp x)) element) ;; Terminal node. (t (cons (sanitize-tree (first x)) ;; Break the problem down into two subproblems. (sanitize-tree (rest x)))))) (sanitize-tree (1 2 (3 4) ((3)))) Dr. Zoran Duric () Symbolic Programming 55/ 89August 28, / 89

56 EQUAL determines structural equality (equal (list 1 2) (cons 1 (cons 2 nil))) Is there another kind of equality? Given (SETF X (LIST 1 2)) and (SETF Y (LIST 1 2)) what is the difference between X and Y? What s the different between (list 1 2) and (1 2)? It could be that you don t need to know! Dr. Zoran Duric () Symbolic Programming 56/ 89August 28, / 89

57 List Structures in Memory CONS creates dotted pairs also called cons cells. (SETF pair (cons 1 2)) CONSP checks for dotted pairs. (consp pair) CAR and CDR are the archaic names for FIRST and REST (car pair) (cdr pair) Dr. Zoran Duric () Symbolic Programming 57/ 89August 28, / 89

58 EQ compares memory locations EQ checks to see if two pointers (memory locations) are equivalent. (eq (list 1 2) (list 1 2)) (SETF point pair) (eq point pair) Integers point to unique locations in memory. (eq 1 1) (SETF one 1) (eq 1 one) Floating numbers are not uniquely represented. (eq ) Dr. Zoran Duric () Symbolic Programming 58/ 89August 28, / 89

59 Destructive Modification of List Structures SETF allows us to modify structures in memory. The first argument to SETF must reference a location in memory. Change the first element of the pair from 1 to 3. (setf (first pair) 3) Create a nested list structure. (SETF nest (list 1 2 (list 3 4) 5)) Change the first element of the embedded list from 3 to 7. (setf (first (third nest)) 7) Dr. Zoran Duric () Symbolic Programming 59/ 89August 28, / 89

60 Why would we destructively modify memory? To maintain consistency in data structures that share memory. (SETF mom (person (name Lynn) (status employed))) (SETF dad (person (name Fred) (status employed))) (SETF relation (list married mom dad)) (setf (second (third dad)) retired) dad relation Dr. Zoran Duric () Symbolic Programming 60/ 89August 28, / 89

61 Difference between list and quote can be critical (defun mem1 () (let ((x (list 1 2))) x)) (defun mem2 () (let ((x (1 2))) x)) (SETF xmem1 (mem1)) (setf (first xmem1) 3) (SETF xmem2 (mem2)) (setf (first xmem2) 3) (mem1) (mem2) Dr. Zoran Duric () Symbolic Programming 61/ 89August 28, / 89

62 Predicates and Builtin Lisp Processing Functions (SETF x (list 1 2 3)) (SETF y (list 4 5)) LAST returns the last CONS cell in an expression. (last x) ;; (3) (defun alt last (x) (if (consp (rest x)) (alt last (rest x)) x)) (alt last x) Dr. Zoran Duric () Symbolic Programming 62/ 89August 28, / 89

63 APPEND two or more lists together APPEND uses new CONS cells. (append x y) x (defun alt append (x y) (if (null x) y (cons (first x) (alt append (rest x) y)))) (alt append x y) Dr. Zoran Duric () Symbolic Programming 63/ 89August 28, / 89

64 NCONC (destructive append) NCONC is like APPEND except that it modifies structures in memory. NCONC does not use any new cons cells. (nconc x y) x (defun alt nconc (x y) (setf (rest (last x)) y) x) (alt nconc x y) Dr. Zoran Duric () Symbolic Programming 64/ 89August 28, / 89

65 MEMBER If X is an element of Y then MEMBER returns the list corresponding to that sublist of Y starting with X, otherwise MEMBER returns NIL. (member 1 ( )) (defun alt member (x y) (cond ((null y) nil) ((eq x (first y)) y) (t (alt member x (rest y))))) (alt member 1 ( )) Dr. Zoran Duric () Symbolic Programming 65/ 89August 28, / 89

66 Check if X is EQ to Y or any subpart of Y (defun subexpressionp (x y) (cond ((eq x y) t) ((not (consp y)) nil) ((subexpressionp x (first y)) t) ((subexpressionp x (rest y)) t) (t nil))) (SETF z (list 1 2 (list 3 4 (list 5)) 6)) (subexpressionp 5 z) ;; T This is a typical function. Dr. Zoran Duric () Symbolic Programming 66/ 89August 28, / 89

67 An alternate definition of SUBEXPRESSIONP (defun alt subexpressionp (x y) (or (eq x y) (and (consp y) (or (alt subexpressionp x (first y)) (alt subexpressionp x (rest y)))))) (alt subexpressionp 4 z) Dr. Zoran Duric () Symbolic Programming 67/ 89August 28, / 89

68 Functions with Optional Arguments (member (3 4) ((1 2) (3 4) (5 6))) (member (3 4) ((1 2) (3 4) (5 6)) :test # equal) (member (3 4) ((1 2) (3 4) (5 6)) :test # (lambda (x y) (= (+ (first x) (second x)) (+ (first y) (second y))))) (member (3 4) ((1 2) (3 4) (5 6)) :test # (lambda (x y) (= (apply # + x) (apply # + y)))) Dr. Zoran Duric () Symbolic Programming 68/ 89August 28, / 89

69 Data Abstraction A data abstraction for input/output pairs. Constructor for PAIRs. (defun make-pair (input output) (list PAIR input output)) Type tester for pairs. (defun is-pair (x) (and (listp x) (eq PAIR (first x)))) Access for PAIRs. (defun PAIR-input (pair) (second pair)) (defun PAIR-output (pair) (third pair)) Modifying PAIRs. (defun set-pair-input (pair new) (setf (second pair) new)) (defun set-pair-output (pair new) (setf (third pair) new)) Dr. Zoran Duric () Symbolic Programming 69/ 89August 28, / 89

70 Using the data abstraction (SETF pairs (list (make-pair 3 8) (make-pair 2 4) (make-pair 3 1) (make-pair 4 16))) (defun monotonic increasingp (pairs) (cond ((null pairs) t) ((> (PAIR-input (first pairs)) (PAIR-output (first pairs))) nil) (t (monotonic increasingp (rest pairs))))) (monotonic increasingp pairs) ;; NIL Dr. Zoran Duric () Symbolic Programming 70/ 89August 28, / 89

71 Using the data abstraction (cont.) (SETF increasing (list (make-pair 1 2) (make-pair 2 3) (make-pair 3 4) (make-pair 4 5))) (monotonic increasingp increasing) ;; T Dr. Zoran Duric () Symbolic Programming 71/ 89August 28, / 89

72 Using the data abstraction (cont.) (defun funapply (input fun) (cond ((null fun) nil) ((= input (PAIR-input (first fun))) (PAIR-output (first fun))) (t (funapply input (rest fun))))) (funapply 2 increasing) ;; 3 (defun alt funapply (input fun) (let ((pairs (member input fun :test # (lambda (x y) (= x (PAIR-input y)))))) (if pairs (PAIR-output (first pairs))))) (alt funapply 2 increasing) ;; 3 Dr. Zoran Duric () Symbolic Programming 72/ 89August 28, / 89

73 Mapping Functions MAPCAR (mapcar # first ((1 2) (3 4) (5 6))) (mapcar # (lambda (x y) (list x y)) ( ) ( )) MAPCAN (splice the results together using NCONC) (mapcan # (lambda (x) (if (oddp x) (list x) nil)) ( )) Dr. Zoran Duric () Symbolic Programming 73/ 89August 28, / 89

74 Mapping Functions (cont.) EVERY SOME APPLY (every # oddp ( )) (some # evenp (1 2 3)) (apply # + (1 2 3)) (apply # + (mapcar # (lambda (x) (if (oddp x) x 0)) ( ))) Dr. Zoran Duric () Symbolic Programming 74/ 89August 28, / 89

75 Alternative Forms of Iteration DO for general iteration The general form is (do index variable specification (end test result expression) body) where index variable specification is a list specs of the form (step variable initial value step value) Dr. Zoran Duric () Symbolic Programming 75/ 89August 28, / 89

76 Alternative Forms of Iteration (cont.) (do ((i 0 (+ i 1)) (nums nil)) ((= i 10) nums) (SETF nums (cons (random 1.0) nums))) We could have done everything in the variable specs. Notice the body of the DO in this case is empty. (do ((i 0 (+ i 1)) (nums nil (cons (random 1.0) nums))) ((= i 10) nums)) Dr. Zoran Duric () Symbolic Programming 76/ 89August 28, / 89

77 Alternative Forms of Iteration (cont.) DOLIST for iteration over lists (dolist (x ( )) (princ x)) DOTIMES for iterating i = 1 to n (dotimes (i 10) (princ i)) Which form of iteration should you use? Which ever one you want, but you should practice using the less familiar methods. In particular, we expect you to be able to understand code written using recursion and mapping functions. Dr. Zoran Duric () Symbolic Programming 77/ 89August 28, / 89

78 Tracing and Stepping Functions (defun raise (x n) (if (= n 0) 1 (* x (raise x (- n 1))))) Tell Lisp to TRACE the function RAISE. (trace raise) (raise 3 2) Dr. Zoran Duric () Symbolic Programming 78/ 89August 28, / 89

79 Tracing and Stepping Functions (cont.) Tell Lisp to stop tracing the function RAISE. (untrace raise) (raise 3 1) STEP a function Use :n to step through evaluation. :h lists options. (step (raise 3 2)) Dr. Zoran Duric () Symbolic Programming 79/ 89August 28, / 89

80 Association Lists An association list associates pairs of expressions. ((name Lynn) (age 29) (profession lawyer) (status employed)) ASSOC (assoc b ((a 1) (b 2) (c 3))) (SETF features ((name Lynn) (profession lawyer) (status employed))) (assoc status features) Dr. Zoran Duric () Symbolic Programming 80/ 89August 28, / 89

81 FIND is more general than ASSOC (find b (a b c)) (find b ((a 1) (b 2) (c 3)) :test # (lambda (x y) (eq x (car y)))) (SETF mom (person (name Lynn) (status employed))) (SETF dad (person (name Fred) (status employed))) (SETF parents (list mom dad)) (find Fred parents :test # (lambda (x y) (eq x (second (assoc name (rest y)))))) Dr. Zoran Duric () Symbolic Programming 81/ 89August 28, / 89

82 Writing your own READ-EVAL-PRINT Loop (defun alt read eval print () (format t %my prompt > ) (format t % A (alt eval (read))) (alt read eval print)) Dr. Zoran Duric () Symbolic Programming 82/ 89August 28, / 89

83 let ((history ()) (max 3)) (defun alt eval (expression) (if (and (listp expression) (eq (first expression) h) (integerp (second expression))) (if (and (>= (second expression) 0) (< (second expression) max)) (eval (nth (second expression) history)) No such history expression! ) (progn (SETF history (cons expression history)) (if (> (length history) max) (setf (rest (nthcdr (- max 1) history)) nil)) (eval expression))))) PROGN specifies a sequence of expressions as a block; PROGN returns the value of the last expresion in the sequence. Dr. Zoran Duric () Symbolic Programming 83/ 89August 28, / 89

84 Search (defun srch (nodes goal next insert) (let ((visited nil)) ;; add the predecessor to each node in nodes (SETF nodes (mapcar # (lambda(x) (list x nil)) nodes)) (loop ;; if there are no more nodes to visit or visitedmax. # of nodes, ;; return NIL as failure signal and the number of visited nodes. (if (or (null nodes) (>= (length visited) *visited max*)) (return (list nil nil (length visited)))) ;; if goal has been reached, return T as success signal, ;; the solution path, and the number of visited nodes. (if (funcall goal (first (first nodes))) (return (list t (return-path (first nodes) visited) (+ 1 (length visited))))) ;; else, add first node to visited, put its children on the list & iterate (SETF visited (cons (first nodes) visited)) (SETF nodes (funcall insert (funcall next (first (first nodes))) (rest nodes) visited)) ))) Dr. Zoran Duric () Symbolic Programming 84/ 89August 28, / 89

85 Insertion ;; eql-vis checks if the first elements of the two pairs are equalp (defun eql-vis (x y) (equalp (first x) (first y))) ; dfs insertion puts new chidren on the front of the list (defun dfs (children nodes visited) (append (remove-if # (lambda (x) (or (member x visited :test # eql-vis) (member x nodes :test # eql-vis))) children) nodes)) Dr. Zoran Duric () Symbolic Programming 85/ 89August 28, / 89

86 next & goal (defun children (graph) # (lambda (node) (mapcar # (lambda(x) (list x node)) (second (assoc node graph))))) (defun find-node (goal-node) # (lambda (node) (equalp node goal-node))) (defun print-list (l) (dolist (elt l t) (format t A % elt))) (SETF graph1 ((a (b e g)) (b (c d f)) (c nil) (d (c f)) (e (b f)) (f nil) (g (h i)) (h (b d)) (i (b e h)))) Dr. Zoran Duric () Symbolic Programming 86/ 89August 28, / 89

87 Using SRCH function (SETF *visited max* 100) (SETF *init-pos* a) (SETF *final-pos* f) (SETF result (srch (list *init-pos*) (find-node *final-pos*) (children graph1) # dfs)) (format t %Graph search - dfs: A % (first result)) (format t %Initial position: A % *init-pos*) (format t Final position: A (format t %Visited A nodes % (third result)) (format t Path: % ) (print-list (second result)) (format t % % ) Dr. Zoran Duric () Symbolic Programming 87/ 89August 28, / 89

88 Results CL-USER 66 > (load "srch.lsp") ; Loading text file srch.lsp #P"/home/u2/zduric/cs580/srch.lsp" CL-USER 67 > (load "proj.skel") ; Loading text file proj.skel #P"/home/u2/zduric/cs580/proj.skel" Dr. Zoran Duric () Symbolic Programming 88/ 89August 28, / 89

89 Results (cont.) CL-USER 68 > (proj) Graph search - dfs: T Initial position: A Final position: F Visited 5 nodes Path: A B F Dr. Zoran Duric () Symbolic Programming 89/ 89August 28, / 89

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