Functional Programming 07 Symbols and Numbers Symbols Symbol

Functional Programming 07 Symbols and Numbers

Symbols - Symbol Names • A symbol can have any string as its name ▫ > (symbol-name ‘abc) “ABC” ▫ The name of the symbol is all uppercase letters ▫ Common Lisp is not case-sensitive ▫ > (eql ‘a. Bc ‘Abc) T ▫ > (Ca. R ‘(a b c) A

Symbols - Symbol Names • Use vertical bars to denote a symbol ▫ > (list ‘|Lisp 1. 5| ‘|abc| ‘|ABC|) (|Lisp 1. 5| || |abc| |ABC|) ▫ When the name of such a symbol is read, there is no case conversion ▫ > (symbol-name ‘|a b c|) “a b c”

Symbols - Property Lists • Every symbol has a property list (plist) • > (get ‘alizarin ‘color) NIL • > (setf (get ‘alizarin ‘color) ‘red) RED • > (get ‘alizarin ‘color) RED • > (setf (get ‘alizarin ‘transparency) ‘high) HIGH • > (symbol-plist ‘alizarin) (TRANSPARENCY HIGH COLOR RED)

Symbols - Symbols Are Big • Symbol is a substantial object

Symbols - Symbols Are Big • Symbols are real objects, not just names • When two variables are set to the same symbol, it’s the same as when two variables are set to the same list ▫ Both variables have pointers to the same object

Symbols - Creating Symbols • Packages are symbol-tables, mapping names to symbols • Every ordinary symbol belongs to a particular package • A symbol that belongs to a package is said to be interned in that package • The first time you type the name of a new symbol ▫ Lisp will create a new symbol object ▫ Lisp will intern it in the current package

Symbols - Multiple Packages • Larger programs are often divided up into multiple packages • If each part of a program is in its own package, then someone working on one part of the program will be able to use a symbol as the name of a function or variable without worrying that the name is already used elsewhere

Symbols - Multiple Packages • (defpackage : package-test (: use “COMMON-LISP” “MY-UTILITIES”) (: nicknames : test) (: export : a : b)) (in-package : test) ▫ ▫ Define a new package called my-application Uses two other packages: COMMON-LISP and MY-UTILITIES Nickname is app The my-application package itself exports three symbols: win, lose, and draw ▫ Code in other packages will be able to refer to them as e. g. test: a

Symbols - Multiple Packages • > (make-package : bob) #<Package BOB> • > (make-package : jane) #<Package JANE> • > (in-package : bob) #<Package BOB> • > (setf a 33) 33 • >a 33 • > (in-package : jane) #<Package JANE> • > (setf a 55) 55 • >a 55

Symbols - Multiple Packages • If Jane wants to use a function written by Bob ▫ > (in-package : jane) #<Package JANE> ▫ > bob: : a 33

Symbols - Keywords • Symbols in the keyword package (keywords) ▫ They always evaluate to themselves ▫ You can refer to them anywhere simply as : x, instead of keyword: x, e. g. (member ‘(a) ‘((a) (z)) : test #’equal) ▫ (defun noise (animal) (case animal (: dog : woof) (: cat : meow) (: pig : oink)))

Symbols - Example: Random Text • If you are going to write programs that operate on words, it’s often a good idea to use symbols instead of strings ▫ Symbols can be compared in one step with eql ▫ Strings have to be compared charater-by-character with string-equal or string= • > (read-text “. . \test. txt”) • > (hash-table-count *words*) • > (generate-text 100)

Symbols - Example: Random Text (defparameter *words* (make-hash-table : size 10000)) (defconstant maxword 100) (defun read-text (pathname) (with-open-file (s pathname : direction : input) (let ((buffer (make-string maxword)) (pos 0)) (do ((c (read-char s nil : eof))) ((eql c : eof)) (if (or (alpha-char-p c) (char= c #’)) (progn (setf (aref buffer pos) c) (incf pos)) (progn (unless (zerop pos) (see (intern (string-downcase (subseq buffer 0 pos)))) (setf pos 0)) (let ((p (punc c))) (if p (see p)))))

Symbols - Example: Random Text (defun punc (c) (case c (#. ‘|. |) (#, ‘|, |) (#; ‘|; |) (#! ‘|!|) (#? ‘|? |) )) (let ((prev ‘|. |)) (defun see (symb) (let ((pair (assoc symb (gethash prev *words*)))) (if (null pair) (push (cons symb 1) (gethash prev *words*)) (incf (cdr pair)))) (setf prev symb)))

Symbols - Example: Random Text (defun generate-text (n &optional (prev ‘|. |)) (if (zerop n) (terpri) (let ((next (random-next prev))) (format t “~A “ next) (generate-text (1 - n) next)))) (defun random-next (prev) (let* ((choices (gethash prev *words*)) ( i (random (reduce #’+ choices : key #’cdr )))) (dolist (pair choices) (if (minusp (decf i (cdr pair))) (return (car pair))))))

Term Project • Due: June 27 • Write a program to analyze the input article and produce: ▫ The title of the article ▫ The abstract of the article • Explain your evaluation strategies to decide whether a title or an abstract is suitable for this article • Requirements ▫ Program demo ▫ Detailed report

Numbers - Types • Four types of numbers ▫ ▫ Integer 2001 Floating-point number 253. 72 or 2. 5372 e 2 Ratio 2/3 Complex number #c(a b) is a+bi • Predicates for numbers ▫ integerp ▫ floatp ▫ complexp

Numbers - Types • Rules for determining what kind of number a computation will return ▫ If a numeric function receives one or more floating-point numbers as arguments, the return value will be a floatingpoint number (or a complex number with floating-point components) �(+ 1. 0 2) evaluates to 3. 0 �(+ #c(0 1. 0) 2) evaluates to #c(2. 0 1. 0) ▫ Ratios that divide evenly will be converted into integers �(/ 10 2) returns 5 ▫ Complex numbers whose imaginary part would be zero will be converted into reals �(+ #c(1 -1) #c(2 1)) returns 3 • > (list (ratiop 2/2) (complexp #c(1 0))) ? ?

Numbers – Conversion and Extraction • > (mapcar #’float ‘(1 2/3. 5)) (1. 0 0. 6666667 0. 5) • > (truncate 1. 3) 1 0. 29999995 • floor • ceiling • (defun our-truncate (n) (if (> n 0) (floor n) (ceiling n)))

Numbers – Conversion and Extraction • round: retuns the nearest even digit ▫ > (mapcar #’round ‘(-2. 5 -1. 5 2. 5)) (-2 -2 2 2) • signum: returns either 1, 0, or -1, depending on whether its argument is positive, zero, or negative ▫ (* (abs x) (signum x)) = x

Numbers – Comparison • > (= 1 1. 0) T • > (eql 1 1. 0) NIL • > (equal 1 1. 0) ? ? • (<= w x y z) ≡ (and (<= w x) (<= x y) (<= y z)) • (/= w x y z) ≡ (and (/= w x) (/=w y) (/= w z) (/= x y) (/=x z) (/= y z)) • > (list (minusp -0. 0) (zerop -0. 0)) (NIL T) • > (list (max 1 2 3 4 5) (min 1 2 3 4 5)) (5 1)

Numbers – Arithmetic • (- x y z) ≡ (- (- x y) z) • (-1 x) returns x-1 • (incf x n) ≡ (setf x (+ x n)) (decf x n) ≡ (setf x (- x n)) • > (/ 365 12) 365/12 • > (float 365/12) 30. 416666 • > (/ 3) 1/3 • (/ x y z) ≡ (/ (/ x y) z)

Numbers – Exponentiation • (expt x n) → ▫ > (expt 2 5) 32 • (log x n) → ▫ (log 32 2) 5. 0 • > (exp 2) 7. 389056 • > (log 7. 389056) 2. 0 • > (expt 27 1/3) 3. 0 • > (sqrt 4) 2. 0

Homework • Modify the following program (defun mirror? (s) (let ((length s))) (and (evenp len) (let ((mid (/ len 2))) (equal (subseq s 0 mid) (reverse (subseq s mid))))))) to recognize all palindromes

Homework • (defun palindrome? (x) (let ((mid (/ (length x) 2))) (equal (subseq x 0 (floor mid)) (reverse (subseq x (ceiling mid))))))