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CSCI 2210: Programming in Lisp
ANSI Common Lisp, Chapters 5-10 CSCI Programming in Lisp; Instructor: Alok Mehta; 4.ppt CSCI Programming in Lisp; Instructor: Alok Mehta
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Progn Progn Prog1 Creates a block of code
Expressions in body are evaluated Value of last is returned (if (< x 0) (progn (format t "X is less than zero ") (format t "and more than one statement ") (format t "needs to be executed in the IF") (- x) ) Prog1 Same as progn, except value of first expression is returned CSCI Programming in Lisp; Instructor: Alok Mehta; 4.ppt
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Block Like a progn with A name An "emergency exit" Examples
return-from - Returns from a named block return - Returns from a block named NIL Examples > (block head (format t "Here we go") (return-from head 'idea) (format t "We'll never see this")) Here we go. IDEA > (block nil (return 27)) 27 CSCI Programming in Lisp; Instructor: Alok Mehta; 4.ppt
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Implicit use of Blocks Some Lisp constructs implicitly use blocks
All iteration constructs use a block named NIL (note return) > (dolist (x '(a b c d e)) (format t "~A " x) (if (eql x 'c) (return 'done))) A B C DONE Defun uses a block with same name as the function > (defun foo () (return-from foo 27)) CSCI Programming in Lisp; Instructor: Alok Mehta; 4.ppt
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Iteration DOTIMES (Review) DOLIST Example
(dotimes (<counter> <upper-bound> <final-result>) <body>) Example (dotimes (i 5) (print i)) ;; prints DOLIST (dolist (<element> <list-of-elements> <final-result>) (dolist (elem '(a b c d)) (print elem)) ;; prints a b c d CSCI Programming in Lisp; Instructor: Alok Mehta; 4.ppt
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Example of DOLIST Given a list of ages of people, how many adults?
> (setf ages '( )) Adult defined as: >= 21 years old > (defun adultp (age) (>= age 21)) Using Count-if (defun count-adult (ages) (count-if #'adultp ages)) Using dolist (defun count-adult (ages &aux (nadult 0)) (dolist (age ages nadult) (if (adultp age) (setf nadult (+ 1 nadult))))) CSCI Programming in Lisp; Instructor: Alok Mehta; 4.ppt
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Example (cont.) Get the ages of the first two adults Notes
(defun first-two-adults (ages &aux (nadult 0) (adults nil)) (dolist (age ages) (if (adultp age) (progn (setf nadult (+ nadult 1)) (push age adults) (if (= nadult 2) (return adults)))))) Notes PROGN (and PROG1) are like C/C++ Blocks { … } > (prog1 (setf a 'x) (setf b 'y) (setf c 'z)) X > (progn (setf a 'x) (setf b 'y) (setf c 'z)) Z RETURN exits the DOLIST block Note: does not necessarily return from the procedure! Takes an optional return value CSCI Programming in Lisp; Instructor: Alok Mehta; 4.ppt
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DO DO is more general than DOLIST or DOTIMES Example
(defun do-expt (m n) ;; Return M^N (do ((result 1) ;; Bind variable ‘Result’ to 1 (exponent n)) ;; Bind variable ‘Exponent’ to N ((zerop exponent) result) ;; test and return value (setf result (* m result)) ;; Body (setf exponent (- exponent 1)) ;; Body Equivalent C/C++ definition int do_expt (int m, int n) { int result, exponent; for (result=1,exponent=n; (exponent != 0); ) { result = m * result; exponent = exponent - 1; } return result; CSCI Programming in Lisp; Instructor: Alok Mehta; 4.ppt
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DO Template Full DO Template (There is also a DO*)
(DO ( (<p1> <i1> <u1>) (<p2> <i2> <u2>) … (<pN> <iN> <uN>) ) ( <term-test> <a1> <a2> … <aN> <result> ) <body> ) Rough equivalent in C/C++ for ( <p1>=<i1>, <p2>=<i2>,…,<pN>=<iN>; //Note: Lisp=parallel !(<term-test>); // C/C++ has a “continuation-test” <p1>=<u1>, <p2>=<u2>,…,<pN>=<uN>) { <body> } <a1>; <a2>; … ; <aN>; <result>; // Note: (DO…) in Lisp evaluates to <result> // Note: <p1>,<p2>,…,<pN> are now restored to original values CSCI Programming in Lisp; Instructor: Alok Mehta; 4.ppt
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Do-expt, Loop Here is another (equivalent) definition of do-expt Loop
(defun do-expt (m n) (do ((result 1 (* m result)) (exponent n (- exponent 1))) ((zerop exponent) result) ;; Note that there is no body! )) Loop An infinite loop, terminated only by a (return) (loop (print '(Say uncle)) (if (equal (read) 'uncle) (return))) CSCI Programming in Lisp; Instructor: Alok Mehta; 4.ppt
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Multiple Values We said each lisp expression returns a value
Actually, can return zero or more values (i.e. multiple values) > (round 7.6) ; Round returns two values 8 -0.4 > (setf a (round 7.6)) 8 ; Setf expects only one value, so it takes the first (8) > a How can you get all values? > (multiple-value-list (round 7.6)) (8 -0.4) > (multiple-value-setq (intpart dif) (round 7.6)) > intpart > dif CSCI Programming in Lisp; Instructor: Alok Mehta; 4.ppt
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Generating Multiple Values
How? Use values > (values 1 2 3) ; Generates 3 return values 1 2 3 > (defun uncons (aList) (values (first aList) (rest aList))) UNCONS > (uncons '(A B C)) A (B C) > (format t "Hello World") "Hello World" NIL > (defun format-without-return (out str &rest args) (apply #'format out str args) (values)) ; A function with no return value! FORMAT-WITHOUT-RETURN > (format-without-return t "Hello") Hello > CSCI Programming in Lisp; Instructor: Alok Mehta; 4.ppt
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Functions about functions
FBOUNDP - Is a symbol the name of a function? > (fboundp '+) T SYMBOL-FUNCTION - returns function > (symbol-function '+) #<Compiled-Function + 17B4E> > (setf (symbol-function 'sqr) #'(lambda (x) (* x x))) #<Interpreted-Function SQR> > (defun sqr (x) (* x x)) ; this is equivalent to above SQR Defun and symbol-function define global functions Local functions can be defined using LABELS > (defun add3 (x) (labels ((add1 (x) (+ x 1)) (add2 (x) (+ x 2))) (add1 (add2 x)))) CSCI Programming in Lisp; Instructor: Alok Mehta; 4.ppt
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Closures Want a function that can save some values for future access/update Can use global variables for this > (setf *number-of-hits* 0) ; Global variable > (defun increment-hits () (incf *number-of-hits*)) INCREMENT-HITS > (increment-hits) 1 2 But, what if someone clobbers the variable? > (setf *number-of-hits* "This variable is now a string") "This variable is now a string" Error: '*number-of-hits*' is not of the expected type: NUMBER Want something like "static" variables in C/C++. CSCI Programming in Lisp; Instructor: Alok Mehta; 4.ppt
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Closures (continued) One use of closures is to implement 'static' variables safely Closure -- Combination of a function and environment Environment can include values of variables > (let ((number-of-hits 0)) (defun increment-hits () (incf number-of-hits))) INCREMENT-HITS number-of-hits is a free variable It is a lexical variable (has scope) A function that refers to a free lexical variable is called a closure Multiple functions can share the same environment (defun increment-hits() (incf number-of-hits)) (defun reset-hit-counter() (setf number-of-hits 0)) CSCI Programming in Lisp; Instructor: Alok Mehta; 4.ppt
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Closures (cont) Example 1 Example 2 - Returns an "opposite" function
> (defun make-adder (n) ; returns function to add n to x #'(lambda (x) (+ x n))) > (setf add3 (make-adder 3)) ; returns function to add 3 #<Interpreted function C0EBF6> > (funcall add3 2) ; Call function add3 with argument 2 5 > (setf (symbol-function 'add3-b) (make-adder 3)) > (add3-b 5) 8 Example 2 - Returns an "opposite" function > (defun our-complement (f) #(lambda (&rest args) (not (apply f args)))) > (mapcar (our-complement #'oddp) '( )) (NIL T NIL T) Tip of the iceberg in terms of possibilities CSCI Programming in Lisp; Instructor: Alok Mehta; 4.ppt
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Trace Format (trace <procedure-name>) Example > (defun factorial (x) (if (<= x 1) 1 (factorial (- x 1)))) > (trace factorial) Causes entry, exit, parameter, and return values to be printed For EACH procedure being traced > (factorial 3) ; 1> FACTORIAL called with arg: ; | 2> FACTORIAL called with arg: | ; | | 3> FACTORIAL called with arg: | | ; | |3< FACTORIAL returns value: | | ; | 2< FACTORIAL returns value: | ; 1< FACTORIAL returns value: 6 Untrace stops tracing a procedure: (untrace <procedure-name>) CSCI Programming in Lisp; Instructor: Alok Mehta; 4.ppt
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Print, Read Print Read - reads a single expression Example
> (print '(A B)) Evaluates a single argument Can be a constant (ex. 100), a variable (x), or any single expression Prints its value on a new line Returns the value printed Read - reads a single expression Example: > (read)20 23 (A B) C 20 ;; Note: Only the 20 is read; rest is ignored > (progn (print 'Enter-temperature) (read)) Enter-temperature 20 20 CSCI Programming in Lisp; Instructor: Alok Mehta; 4.ppt
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Format Format Allows more elegant printing
> (progn (print "Enter temperature: ") (read)) "Enter temperature: " 32 32 > (progn (format t "~%Enter temperature: ") (read)) Enter temperature: 32 The second parameter (t) is the output buffer (T=stdout) The character “~” signifies that a control character follows The character “%” signifies a newline (Lisp: “~%” C: “\n”) The characters “~a” tells Lisp to substitute the next value printf ("The value is ( %d, %d )", x, y); /* A C stmt */ > (format t "The value is ( ~a, ~a )" x y) ;; Lisp way > (format t "The value is ( ~10a, ~a )" x y) ; Can get fancy CSCI Programming in Lisp; Instructor: Alok Mehta; 4.ppt
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Streams Write output to a file (e.g. knowledge base)
Prototype of with-open-file (with-open-file (<stream name> <file specification> :direction <:input or :output>) …) Example > (setf fact-database '((It is raining) (It is pouring) (The old man is snoring))) > (with-open-file (my-file ”myfile.lsp” :direction :output) (print fact-database my-file)) CSCI Programming in Lisp; Instructor: Alok Mehta; 4.ppt
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My-Trace-Load Redefine the built-in Lisp “Load” function
Example of Built In function > (load "a.lsp") Additional requirements Want to print each expression that is read in. Want to print the value returned by the expression Definition (defun my-trace-load (filename &aux next-expr next-result) (with-open-file (f filename :direction :input) (do ((next-expr (read f nil) (read f nil))) ((not next-expr)) (format t "~%~%Evaluating '~a'" next-expr) (setf next-result (eval next-expr)) (format t "~% Returned: '~a'" next-result)))) CSCI Programming in Lisp; Instructor: Alok Mehta; 4.ppt
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Read-Line, Read-Char Read-Line Read-Char
Reads an individual line (terminated by a carriage return) Returns it as a character string > (read-line)Hello World “Hello World” Read-Char Reads an individual character Returns it as a character > (read-char)x #\x ;; This is Lisp notation for the character ‘x’ CSCI Programming in Lisp; Instructor: Alok Mehta; 4.ppt
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Symbols We've used symbols as names for things
A symbol is much more than just a name Includes: name, package, value, function, plist (Property List) A symbol is a "substantial object" Some functions for manipulating symbols symbol-name, symbol-plist, intern,… Details are in Chapter 8 of textbook CSCI Programming in Lisp; Instructor: Alok Mehta; 4.ppt
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Symbol Names By default Lisp symbol names are upper case
> (symbol-name 'abc) "ABC" Can use "|" to delimit symbol names > (list '|abc|) ; no conversion "abc" > (list '|Lisp 1.5| '|| '|abc| '|ABC|) (|Lisp 1.5| || |abc| ABC) ; Note that only ABC doesn't have delimiter (default) Intern creates new symbols > (set (intern '|5.1/5)|) 999) 999 > |5.1/5)| CSCI Programming in Lisp; Instructor: Alok Mehta; 4.ppt
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Packages Package Large programs use multiple packages
A name space for symbols Large programs use multiple packages > (defpackage "MY-APPLICATION" ;; Creates new package (:use "COMMON-LISP" "MY-UTILITIES") ;; Other packages (:nicknames "APP") (:export "WIN" "LOSE" "DRAW")) ;; Symbols exported #<The MY-APPLICATION package> > (in-package my-application) ;; Sets this to be default New symbols are (by default) created in default package The default package, when Lisp is started is COMMON-LISP-USER The COMMON-LISP packages is automatically used CSCI Programming in Lisp; Instructor: Alok Mehta; 4.ppt
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Numbers Number crunching is one of Lisp's strengths
Many data types, automatically converted from one to another Many numeric functions Example: Factorial program was easier in Lisp (no overflow!) Four distinct types Types: Integer, Floating Point Number, Ratio, and Complex Number Examples: 100, , 3/2, #c(a b) ; #c(a b) = a+bi Predicates: integerp, floatp, ratiop, complexp Basic rules for automatic conversion If function receives floating point #'s, generally returns floating point #'s If a ratio divides evenly (for example, 4/2), it will be converted to integer If complex # has an imaginary part of zero, converted to a real CSCI Programming in Lisp; Instructor: Alok Mehta; 4.ppt
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Subset of Type Hierarchy
Lisp Expression Return Value (setf a 12); 12 (type a 'bit); NIL (type a 'fixnum); T (type a 'integer); T (integerp a); T (rationalp a); T (realp a); T (numberp a); T CSCI Programming in Lisp; Instructor: Alok Mehta; 4.ppt
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More on Numbers Conversion Comparison Other Misc. functions
(float) (truncate) (floor) (ceiling) (round) … > (mapcar #'float '(1 2/3 .5)) ( ) Comparison Use = to compare for equality (also, <,<=, >, >=, /=) > (= 4 4.0) T Other Misc. functions Max Min (expt x n) = X^n (exp x) = E^x (log x n) = logn X; N is optional (default = natural log) sqrt, sin, cos, tan CSCI Programming in Lisp; Instructor: Alok Mehta; 4.ppt
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Eval Eval - Evaluates an expression and returns its value
6 Top-level is also called the read-eval-print loop Reads expression, evaluates it, prints value, loops back > (defun our-toplevel () (loop (format t "%~> ") (print (eval (read)))) Eval Inefficient - slower than running compiled code Expression is evaluated without a lexical context CSCI Programming in Lisp; Instructor: Alok Mehta; 4.ppt
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Macros Macros A common way to write programs that write programs
Defmacro is used to define macros Example: A macro to set its argument to NIL > (defmacro nil! (x) (list 'setf x nil)) > (nil! A) ;; Expands to (setf A NIL), is then evaluated NIL macro-expand-1 Generates macro expansion (not eval'ed) > (macroexpand-1 '(nil! A)) (SETF A NIL) T CSCI Programming in Lisp; Instructor: Alok Mehta; 4.ppt
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Macros Typical procedure call (defun) Macro procedure (defmacro)
Evaluate arguments Call procedure Bind arguments to variables inside the procedure Macro procedure (defmacro) Macros do not evaluate their arguments When a macro is evaluated, an intermediate form is produced The intermediate form is evaluated, producing a value CSCI Programming in Lisp; Instructor: Alok Mehta; 4.ppt
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Example: Manually Define Pop
Review of the built in operation “Pop”: Implements Stack data structure “Pop” operation > (setf a '( )) > (pop a) 1 > a ( ) How would you emulate this using other functions? Attempt 1: Remove the element “1” from A > (setf a (rest a)) ( ) ;; A is set correctly to ( ), but we want “1” to be returned Attempt 2: Remove first element AND return it > (prog1 (first a) (setf a (rest a))) Attempt 3: Write a Lisp expression that generates above expression > (list 'prog1 (list 'first a) (list 'setf a (list 'rest a))) CSCI Programming in Lisp; Instructor: Alok Mehta; 4.ppt
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Our-Pop, using Macro Convert Lisp expression into a macro (Our-Pop)
> (defmacro our-pop (stack) (list 'prog1 (list 'first stack) (list 'setf stack (list 'rest stack)))) Note similarity to Defun Example Call > (OUR-POP a) Notes The parameter “A” is NOT evaluated “A” is substituted for stack wherever the variable stack appears (list 'first a) (list 'setf a (list 'rest a))) Intermediate form is generated (prog1 (first a) (setf a (rest a))) Intermediate form is evaluated A is set to (rest A); the first element is returned CSCI Programming in Lisp; Instructor: Alok Mehta; 4.ppt
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Our-Pop using Defun Why doesn’t this (defun) work the same way?
> (defun our-pop (stack) (prog1 (first stack) (setf stack (rest stack)))) > (setf a '( )) > (our-pop a) 1 > a ( ) Reason: Lisp passes parameters “by-value” The value of A is COPIED into the variable “stack” Any changes to the variable “stack” are done to the COPY, and NOT the original variable A When the function returns, the original value of A is unchanged CSCI Programming in Lisp; Instructor: Alok Mehta; 4.ppt
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Significance of Eval Steps
Macro evaluation has several steps (as noted) The parameter “A” is NOT evaluated “A” is substituted for stack wherever the variable stack appears Intermediate form is generated Intermediate form is evaluated Note that A is evaluated at step 4 above (not step 1) Why does this matter? Answer: For the same reason that it matters in C/C++ macros You may not want arguments evaluated at all Or, you may want them evaluated multiple times Macros give this flexibility CSCI Programming in Lisp; Instructor: Alok Mehta; 4.ppt
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Backquotes Significance of Evaluation Steps (cont) Backquote Mechanism
Consider > (defmacro our-if-macro (conditional then-part else-part) (list 'if conditional then-part else-part)) > (defun our-if-fun (conditional then-part else-part) (if conditional then-part else-part)) > (if (= 1 2) (print "Equal") (print "Not Equal")) Lisp evaluates all parameters of OUR-IF-FUN before function is called Backquote Mechanism Forward quotes: Entire next expression is not evaluated > (defun temp () (setf a '(a b c d e))) Backquote: Next expression is not evaluated (with exceptions) > (defun temp () (setf a `(a b c d e))) > (defun temp (x) (setf a `(a b c d e ,x)) The “,x” expression is evaluated; the value of X is used. CSCI Programming in Lisp; Instructor: Alok Mehta; 4.ppt
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Backquotes (cont.) Exceptions - Backquote evaluates the following
,variable - Evaluates the value of the variable > (setf x '(h i j)) > (setf a `(a b c ,x e f)) (A B C (H I J) E F) - Splices the elements of a list > (setf a `(a b c e f)) (A B C H I J E F) Backquotes simplify macro development > (defmacro our-if-macro (conditional then-part else-part) (list 'if conditional then-part else-part)) ;; old way `(if ,conditional ,then-part ,else-part)) CSCI Programming in Lisp; Instructor: Alok Mehta; 4.ppt
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Backquotes simplify macros
Original version of our-pop > (defmacro our-pop (stack) (list 'prog1 (list 'first stack) (list 'setf stack (list 'rest stack)))) Our-pop redefined using backquotes `(prog1 (first ,stack) (setf ,stack (rest ,stack)))) Syntax is much closer to the intermediate form Macros can be defined with following parameters Optional (&optional) Rest (&rest) Key (&key) CSCI Programming in Lisp; Instructor: Alok Mehta; 4.ppt
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Macro Design Macro: take a number n, evaluate its body n times
Example call > (ntimes 10 (princ ".")) ………. NIL First attempt (incorrect) > (defmacro ntimes (n &rest body) `(do ((x 0 (+ x 1))) ((>= x ,n)) For example call, within body of macro n bound to 10 body bound to ((princ ".")) (do ((x 0 (+ x 1))) ((>= x 10)) (princ ".")) Macro works for example. Why is it incorrect? CSCI Programming in Lisp; Instructor: Alok Mehta; 4.ppt
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Inadvertent Variable Capture
Consider Initialize x to 10, increment it 5 times > (let ((x 10)) (ntimes 5 (setf x (+ x 1))) x) 10 Expected value: 15 Why? Look at expansion (do ((x 0 (+ x 1))) ((>= x 5)) (setf x (+ x 1))) X is used in let and in the iteration setf increments iteration variable! CSCI Programming in Lisp; Instructor: Alok Mehta; 4.ppt
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Gensym Gives New Symbol
Generates a new (uninterned) symbol > (defmacro ntimes (n &rest body) ; Still incorrect though (let ((g (gensym))) `(do ((,g 0 (+ ,g 1))) ((>= ,g ,n)) The value of symbol G is a newly generated symbol How does this avoid the problem? What if the call has a variable G? Look at the expansion of (let ((x 10)) (ntimes 5 (setf x (+ x 1))) x) CSCI Programming in Lisp; Instructor: Alok Mehta; 4.ppt
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Expansion of ntimes (2) Substitute for N and BODY
> (let ((x 10)) (let ((g (gensym))) `(do ((,g 0 (+ ,g 1))) ((>= ,g ,5)) x (+ x 1))))) x) Generate intermediate form (do ((#:G34 0 (+ #:G34 1))) ((>= #:G34 5)) (setf x (+ x 1))) Evaluate 15 This works for our example … but ... CSCI Programming in Lisp; Instructor: Alok Mehta; 4.ppt
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Multiple Evaluation What happens when we want to debug…
> (let ((x 10) (niteration 3)) (ntimes niteration (setf x (+ x 1))) x) 13 To debug, insert a print expression (ntimes (print niteration) (setf x (+ x 1))) 3 The argument is evaluated multiple times Apparent when argument causes side-effects What if the argument was a (setf …) Non-intuitive: Expect argument to be evaluated only once. CSCI Programming in Lisp; Instructor: Alok Mehta; 4.ppt
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Avoiding Multiple Evaluation
Solution is to copy value when you get into macro Use copy when needed within macro > (defmacro ntimes (n &rest body) (let ((g (gensym)) (h (gensym))) `(let ((,h ,n)) (do ((,g 0 (+ ,g 1))) ((>= ,g ,h)) This is correct > (let ((x 10) (niteration 3)) (ntimes (print niteration) (setf x (+ x 1))) x) 3 13 CSCI Programming in Lisp; Instructor: Alok Mehta; 4.ppt
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Expansion of Ntimes (Final)
Pprint is a useful function for Pretty PRINTing expressions > (pprint (macroexpand-1 '(ntimes (print niteration) (setf x (+ x 1))))) (LET ((#:G93 (PRINT NITERATION))) (DO ((#:G92 0 (+ #:G92 1))) ((>= #:G92 #:G93)) (SETF X (+ X 1)))) Problems of Multiple Evaluation and Inadvertent Variable Capture Examples of errors that can occur when working with macros Errors are common in Lisp as well as languages like C/C++ CSCI Programming in Lisp; Instructor: Alok Mehta; 4.ppt
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Multiple Evaluation in Pop
Looking back at our Pop macro It suffers from multiple evaluation We can't use same technique, though Need to get the first AND do a setf to change the value > (defmacro our-pop (stack) `(prog1 (first ,stack) (setf ,stack (rest ,stack)))) Textbook solution avoids multiple evaluation Page 301 Uses a function get-setf-expansion to get to inner details of setf CSCI Programming in Lisp; Instructor: Alok Mehta; 4.ppt
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Case Study: Expert Systems
Overview of using Lisp for Symbolic Pattern Matching Rule Based Expert Systems and Forward Chaining Backward Chaining and PROLOG Motivational example Given: A set of Facts A set of Rules Desired result Answer complex questions and queries CSCI Programming in Lisp; Instructor: Alok Mehta; 4.ppt
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Smart Animal Guessing Facts about an animal named “Joey”
F1. (Joey’s mother has feathers) F2. (Joey does not fly) F3. (Joey swims) F4. (Joey is black and white) F5. (Joey lives in Antarctica) Rules about animals in general R1. If (animal X has feathers) THEN (animal X is a bird) R2. If (animal X is a bird) and (animal X swims) and (animal X does not fly) and (animal X is black and white) THEN (animal is a penguin) R3. If (animal X’s mother Z) THEN (animal X Z) Example: if (animal X’s mother has feathers) then (animal X has feathers) R4. If (animal X Z) THEN (animal’s mother Z) Notes By combining the facts and rules, we can deduce that Joey is a penguin, and that the Joey’s mother is a penguin. CSCI Programming in Lisp; Instructor: Alok Mehta; 4.ppt
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Symbolic Pattern Matching
Symbolic pattern matching example Match F1 with the IF part of R1 F1. (Joey’s mother has feathers) R1. If (animal X has feathers) THEN (animal X is a bird) The expression (Joey’s mother has feathers) matches the pattern (animal X has feathers). The association (animal X = Joey’s mother) is implied In general Symbolic pattern matching matching an ordinary expression (e.g. fact) to a pattern expression Unification: more advanced version of pattern matching match two pattern expressions to see if they can be made identical Find all substitutions that lead to this CSCI Programming in Lisp; Instructor: Alok Mehta; 4.ppt
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Rule Based Expert System
Rule Based Expert Systems Once the pattern matching step is done, then we know that Rule R1 can be combined with fact F1 F1. (Joey’s mother has feathers) R1. If (animal X has feathers) THEN (animal X is a bird) The association (animal X = Joey’s mother), along with the second part of the rule (animal X is a bird) leads to a derived fact: (Joey’s mother is a bird) CSCI Programming in Lisp; Instructor: Alok Mehta; 4.ppt
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Forward Chaining Basic philosophy:
Given a set of rules R and a set of facts F, what new facts (DF) can be derived? DF1: Joey has feathers (R3,F1) DF2: Joey’s mother is a bird (R1, F1) DF3: Joey is a bird (R1,DF1) [or, (R3,DF2)] DF4: Joey’s mother does not fly (R4, F2) DF5: Joey’s mother swims (R4, F3) DF6: Joey’s mother is black and white (R4, F4) DF7: Joey’s mother lives in Antarctica (R4, F5) DF8: Joey is a penguin (R2, DF3, F2, F3, F4) DF9: Joey’s mother is a penguin (R4, DF8) or (R2, DF2, DF5, DF4, DF6) CSCI Programming in Lisp; Instructor: Alok Mehta; 4.ppt
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Backward Chaining Basic philosophy
Can a statement (e.g. Joey is a penguin) be proven given the current set of facts and rules? Work backwards, to determine what facts, if true, can prove that Joey is a penguin (or prove that Joey is not a penguin). B1. R2: (Joey is a penguin) IF (a) Joey is a bird; (b) Joey swims; (c) Joey does not fly; and (d) Joey is black and white B2. R1: (Joey is a bird) IF (Joey has feathers) B4. R3: (Joey has feathers) IF (Joey’s mother has feathers) DF1. (Joey has feathers), since we know (Joey’s mother has feathers (F1) DF2. (Joey is a bird), since we know (Joey has feathers) (DF1) DF3. (Joey is a penguin), since (a), (b), (c), and (d) are known to be true (DF2, F3, F2, F4 respectively) The fact (Joey is a penguin) can be derived CSCI Programming in Lisp; Instructor: Alok Mehta; 4.ppt
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Does this apply in the real world?
Given a clinical specimen, need to know what tests to perform? Example facts about a specific patient specimen (to test whether a person has Syphilis): F1. Automated Reagin Test result is Reactive, Titer=8 F2. Microheme Agglutination Test is Non-Reactive F3. Specimen is from a pregnant woman F4. Prior history indicates a result of Reactive, Titer=2 F5. Prior test was performed 12 months ago Example rules R1. IF (Automated Reagin Test is Reactive, Titer >= 4) AND (Microheme Agglutination Test is Non-Reactive) THEN (Rapid Plasma Reagin test must be performed) R2. IF (Specimen is from a pregnant woman) THEN (Microheme Agglutination Test must be performed) R3. IF (Specimen is from a pregnant woman) THEN (Automated Reagin Test must be performed twice) Sample questions: What tests need to be performed? (Forward chaining) Should we do the RPR test? (Backward chaining) Is the specimen considered abnormal? (Backward chaining) CSCI Programming in Lisp; Instructor: Alok Mehta; 4.ppt
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Lisp Lisp is a good language for implementing expert systems.
Concise programs Flexible processing of lists Basic implementations are shown in chapters 24-27 Other applications of expert systems Mathematics: Calculus, geometry Computer configuration, electronic circuits Evaluate geological formations, planned investments Diagnosis of infections CSCI Programming in Lisp; Instructor: Alok Mehta; 4.ppt
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Building an Expert System
Knowledge representation how to represent facts, patterns, rules how to represent sets of these Build a pattern matcher Build the inference engine Forward Chaining and/or Backward Chaining CSCI Programming in Lisp; Instructor: Alok Mehta; 4.ppt
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Implementing Pattern Matching
Want a procedure to match patterns Input Animal X has feathers (pattern) ((? X) has feathers) ; Uses (? Var) for pattern variable Joey’s mother has feathers (regular expression or Fact) ((mother Joey) has feathers) Returns Mapping between pattern variables ( (X (mother Joey)) ) Example call > (match '((? X) has feathers) '((mother Joey) has feathers) ) ((X (mother Joey))) > (match '((? X) has (? Z)) '(Joey has feathers))) ((X Joey) (Z feathers)) CSCI Programming in Lisp; Instructor: Alok Mehta; 4.ppt
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Return values of Match Return value is a set of variable bindings
Example ((X Joey) (Z feathers)) General Form ( (var1 value1) (var2 value2) … (varN valueN) ) What if the two patterns don’t match? First attempt: On failure, return NIL > (match '((? X) has feathers)) '(Joey does not fly)) NIL But consider... > (match '(Joey has feathers) '(Joey has feathers))) This matches, but there is no need to bind any variables. So, need to return SUCCESS with a list of zero variable bindings: ( ) NIL <-- NIL = ( ) Need to differentiate between failed match and match with no variable bindings CSCI Programming in Lisp; Instructor: Alok Mehta; 4.ppt
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Return values of Match (cont.)
Approach taken by Winston/Horn Note: This is NOT the only way to do it NIL = Success, empty list of pattern variables FAIL = Symbol returned when the pattern and datum don’t match Examples > (match '((? X) has feathers) '((mother Joey) has feathers)) ((X (mother Joey))) > (match '((? X) has (? Z)) '(Joey has feathers))) ((X Joey) (Z feathers)) > (match '((? X) has feathers)) '(Joey does not fly)) FAIL > (match '(Joey has feathers) '(Joey has feathers))) NIL ; Treated as an empty list CSCI Programming in Lisp; Instructor: Alok Mehta; 4.ppt
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Match Function Definition
Function definition for MATCH: 4 basic branches ;; Calculates and returns bindings (if successful) ;; Or, returns 'FAIL (defun match (p d &optional bindings) ;; 1. If P and D are both atoms, ;; If they’re equal, it’s a match, otherwise FAIL ;; e.g. (match 'FEATHERS 'FEATHERS) ;; 2. If P is a pattern variable ;; Assign the value of D to the pattern variable in P ;; e.g. (match '(? X) 'JOEY) ;; should assign the value JOEY to the variable X ;; 3. If P and D are both Lists ;; Recursively solve for matches ;; e.g. (match '(A B (? X) (D E)) '(A B C (D E))) ;; should recursively call match on (A vs. A) ;; (B vs. B) ((? X) vs. C) ((D E) vs. (D E)) ;; 4. Any other case (e.g. atom vs. list, etc.) ;; FAIL ) CSCI Programming in Lisp; Instructor: Alok Mehta; 4.ppt
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Match: Case 1, Case 4 Part 1: Build up Cond infrastructure
Implement case 1 (P and D are both atoms) Implement case 4 (Everything Else) (defun match (p d &optional bindings) (cond ((and (atom p) (atom d)) ;; Case 1: Both p and d are atoms ;; If P and D are equal: Match. Return bindings ;; Otherwise, return FAIL (if (eql p d) bindings 'FAIL)) (…Case 2…) (…Case 3…) (t ;; Case 4: Any other case. Return FAIL 'FAIL) ) CSCI Programming in Lisp; Instructor: Alok Mehta; 4.ppt
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Match: Case 3 Case 3 (P and D are lists and need to be solved recursively) Algorithm ;; A) Match the first pair, to get new bindings ;; B) If first pair failed, ;; C) return fail ;; D) Otherwise, using the bindings returned ;; by step (A), match remaining pairs Code (defun match (p d &optional bindings) (cond (…Case 1…) (…Case 2…) ((and (listp p) (listp d)) ; P and D are both Lists ;; Recursively solve for matches (let ((result (match (first p) (first d) bindings))) ;(A) (if (eq 'fail result) ;(B) 'FAIL ;(C) (match (rest p) (rest d) result)))) ;(D) (…Case 4…) )) CSCI Programming in Lisp; Instructor: Alok Mehta; 4.ppt
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Match, Case 2 Case 2: P is a variable, D is a piece of data
Example: P=(? X); D=Joey Make the binding (X Joey) Add it to the bindings already defined Old Bindings: ( (A apple) (B banana) ) After adding: ( (X Joey) (A apple) (B banana) ) Code for adding a new binding to a list of bindings (defun add-binding (p d bindings) (cons (list (second p) d) bindings)) CSCI Programming in Lisp; Instructor: Alok Mehta; 4.ppt
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Match, Case 2 (continued)
Note: Before adding a binding, need to check if the binding already exists If binding exists, it should match previous binding Example 1 > (match '((? X) (? Y) implies (? X) (? Z)) (Joey smokes implies Joey (will get cancer))) ( (X Joey) (Y smokes) (Z (will get cancer))) NOT ((X Joey) (Y smokes) (X Joey) (Z (will get cancer))) When the algorithm finds (X Joey), no new binding should be created Example 2 (Joey smokes implies Mary (will get cancer))) FAIL This should fail because X cannot be bound to both Joey and Mary When the algorithm finds (X Joey) while trying to bind (X Mary), the routine should return FAIL CSCI Programming in Lisp; Instructor: Alok Mehta; 4.ppt
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Match, Case 2 (continued)
Example 1 (match '(? X) 'Joey '((X Joey) (Y smokes) (Z (will get cancer))) Example 2 (match '(? X) 'Mary Example 3 '((Y smokes) (Z (will get cancer))) Algorithm ;; 1. Check if variable is already bound ;; 2. If bound, try to match the value of the variable ;; to the datum ;; If bound and the binding matches, return binding ;; (nothing new needs to be done). (Example 1) ;; If bound and the binding doesn’t match, return FAIL ;; (Example 2) ;; 5. If not bound, add a binding (Example 3) CSCI Programming in Lisp; Instructor: Alok Mehta; 4.ppt
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Match, Case 2 (continued)
Find-binding: Uses Assoc > (find-binding '(? X) '((X Joey) (Y smokes) (Z (will get…))) (X Joey) Match (defun match (p d &optional bindings) (cond (…Case 1…) ((and (listp p) (eq (second p) '?)) ; Is p=~ (? X) (let (binding (find-binding p bindings)) ; (1) (if binding ; (2) (match (second binding) d bindings) ; (3,4) (add-binding p d bindings) ; (5) ))) (…Case 3…) (…Case 4…) )) CSCI Programming in Lisp; Instructor: Alok Mehta; 4.ppt
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