- 微博 QQ QQ空间 贴吧
Lisp 2 rules and natural language
2 . LISP – (LISt Processing) 1. Parenthesized prefix notation: (+ 2 4) 2. Expressions can be nested: (- (+ 2 3 4 5) (* 2 5)) 3. Evaluation rule: apply function to value of arguments. 4. Symbolic computation: other types Quote Primitive: numbers, characters, strings, symbols. Compound: lists. (append '(a b) '(c d)) --> (a b c d) append Quote: block the evaluation of the following expression. '(a b) --> (a b) (a b) --> error: a undefined function. 5. Self-evaluating types: numbers, characters, strings. 6. Symbols as variables - not case sensitive.
3 .VARIABLES 1. Define new objects in terms of others + name them. 2. (setf p '(a b)) --> (a b) p --> (a b) Quote 3. Symbols also used to name functions.
4 .SPECIAL FORMS: 1. Forms not evaluated according to the evaluation rule. 2. Special forms: defun, defparameter, setf, let, case, if, function, quote.
5 .LISTS 1. Primitive aggregating type. 2. Primitive functions: first, second, ..., length, last. append, cons, list.
6 .DEFINING NEW FUNCTIONS: 1. (defun <name> (<parameters>) "doc" <body>) defun (defun last-name (name) "Select last name from a name represented as a list." (first (last name))) (last-name '(john r vandamme)) --> vandamme (last-name '(john quirk MD)) --> MD 2. Importance of abstraction. (defun first-name (name) (first name))
7 .USING FUNCTIONS: 1. (setf names '((john x ford) (peter p rabbit) (fabianna f wayne))) (mapcar #'last-name names) --> (ford rabbit wayne) #' from name of function to function object. mapcar primitive. defparameter 2. (defparameter *titles* '(Mr Mrs Miss Madam Ms Sir Dr Admiral Major General)) (defun first-name (name) "Select first name from a list representing a name." (if (member (first name) *titles*) (first-name (rest name)) (first name))) (if <test> <then-part> <else-part>) ;; explanation of if ;; example of first-name (first-name '(Madam Major General Paula Jones)) --> Paula 3. Trace functions Omits all titles from the name list, returns the first name.
8 . HIGHER ORDER FUNCTIONS 1. Functions as first-class objects: can be manipulated, created, modified by running code. 2.Apply: (apply #'+ '(1 2 3 4)) --> 10 apply 3. Funcall: (funcall #'+ 1 2) --> 3 (funcall #'+ '(1 2)) --> funcall error (1 2) is not a number. 4. Function constructor: lambda. (lambda (parameter ...) body...): lambda non atomic name of a function. ((lambda (x) (+ x 2)) 4) --> 6 (funcall #'(lambda (x) (* x 2)) 4) --> 8 ***Can create functions at run time.***
9 .OTHER DATA TYPES 1. Strings: (length "abc") --> 3 2. Many number types. length
10 . Basic terminology • Atoms: word-like indivisible objects which can be numbers or symbols. • Lists: sentence-like objects formed from atoms or other lists, and enclosed in parentheses. • S-expressions: compositions of atoms and lists. • Procedures: step by step specifications how to do something. • Primitives: procedures supplied by the LISP itself Example: (+ 5 6) • User-defined procedures: procedures introduced by the programmer. Example: (students 'anna) • Program: a collection of procedures working together.
11 .S-expressions • An s-expression can have other s-expressions nested in it. Examples: (+ (* 5 7) ( / 2 4)) (This (is a dog) (or a cat)) • Expressions can be interpreted both, procedurally and declaratively. • If interpreted procedurally, an expression provides a direction for doing something. Such an expression is called a form, form and its first element is the name of a procedure to be used to produce the value. • The process of computing the value of an expression is called evaluation. • If interpreted declaratively, expressions represent data. Data and procedures have the same syntax.
12 .Evaluation of atoms • The value of a number is the number itself. Example: 5 ==> 5 • The value of a string is the string itself. Example: “Nice day” ==> “Nice day” • The value of the symbol T is T (true). • The value of the symbol NIL is NIL (false). • The symbol NIL and the empty list ( ) are the same thing. • Variables are names of memory locations. The contents stored in a given memory cell is the value of the variable serving as a name of this location. Example: Let x be a variable, and 5 be the contents of the memory cell called x. Then, the value of x is 5.
13 .Numbers • Integers: 179, 45 • Ratio: 5/7, 7/9 • Floating point: 5.2, 7.9 • Examples: * (/ 25 5) 5 * (/ 46 9) 46/9 ; do not divide evenly * (float (/ 46 9)) 5.111111 * (round (/ 46 9)) 5 ; the nearest integer 1/9 ; the remainder
14 .More numeric primitives * (- 6) * (+ 2 2.5) -6 4.5 * (- -6) * (expt 3 6) 6 729 * (max 5 7 2) * (sqrt 81) 7 9.0 * (min 5 7 2) * (sqrt 82) 2 9.055386 * (sqrt (* (+ 1 3) (* 2 2))) * (abs 6) 4.0 6 * (+ (round (/ 22 7)) (round (/ 7 3))) * (abs -6) 5 6
15 . LISP EVALUATION RULE 1. Every expression is either a list or an atom. 2. Every list to be evaluated is either a special form or a function application. 3. A special form expression is a list whose first element is a special form operator and is evaluated according to the special rule of that operator. 4. A function application is evaluated by first evaluating the arguments (the rest of the list) and then finding the function named by the first element of the list and applying it to the list of evaluated arguments. 5. Every atom is either a symbol or a non-symbol. 6. A symbol evaluates to the most recent value assigned to the variable. 7. A non-symbol atom evaluates to itself.
16 .WHAT MAKES LISP DIFFERENT 1. Built-in support for Lists. 2. Automatic memory management. 3. Dynamic typing. 4. First-class functions. 5. Uniform syntax. 6. Extensibility
17 .Why LISP? • Especially designed for symbol manipulation. • Provides built-in support for lists (“everything is a list..”) • Automatic storage management (no need to keep track of memory allocation). • Interactive environment, which allows programs to be developed step by step. That is, if a change is to be introduced, only changed functions need to be recompiled.
18 .Everything's a List! • Data (a b c) • Functions (defun plus (x y) (+ x y)) • Simple syntax: (function-name arg1 arg2 …)
19 . LISP is Interpreted and interactive • Interpreted • Interactive USER(1): 12 12 USER(2): (+ 12 3) 15 USER(3): (setf Almost-age 31) 31 USER(4): Almost-age 31 USER(5): 'Almost-age ALMOST-AGE USER(6):
20 .Lisp is Symbolic • Why do we care about symbols? • Understand human cognition with a language like symbolic processing
21 . Physical Symbol System Hypothesis "A physical symbol system has the necessary and sufficient means for general intelligent action." (Newell & Simon 1976) • Physical symbol system • Set of entities called symbols - physical patterns that can occur as components • Expressions (or symbol structures) built of symbols
22 . Lisp is Dynamic • Functions are first-class objects • Pass functions as arguments to other functions USER(1): (+ 1 2 3) 6 USER(2): (apply #'+ '(1 2 3)) 6
23 .Funcall and Lambda – dynamic • Create functions on the fly USER(1): (funcall #'(lambda (x y) (+ x y)) 17 14) 31 • Lisp contains itself: eval
24 . Name Calling • Lisp remembers function names separately from variable names USER(22): (defun add (x y) (+ x y)) ADD USER(23): (setf add 9) 9 USER(24): add 9 USER(25): #'add #<Interpreted Function ADD>
25 . Problems with solutions: 1.Write a function (power 3 2) = 3^2 = 9 2. Write a function that counts the number of atoms in an expression. (count-atoms '(a (b) c)) --> 3 3. (count-anywhere 'a '(a ((a) b) a)) --> 3 4. (dot-product '(10 20) '(3 4)) --> 10x3 + 20x4 = 110 5. Write a function (flatten '(a (b) () ((c)))) --> (a b c) which removes all levels of parenthesis and returns a flat list of atoms. 6. Write a function (remove-dups '(a 1 1 a b 2 b)) --> (a 1 b 2) which removes all duplicate atoms from a flat list. (Note: there is a built-in remove-duplicates in Common Lisp, do not use it).
26 . Solutions 1-3 Write a function (power 3 2) = 3^2 = 9 (defun power (a b) "compute a^b - (power 3 2) ==> 9" (if (= b 0) 1 (* a (power a (- b 1))))) Write a function that counts the number of atoms in an expression. (count-atoms '(a (b) c)) --> 3 (defun count-atoms (exp) "count atoms in expresion - (count-atoms '(a (b) c)) ==> 3" (cond ((null exp) 0) ((atom exp) 1) (t (+ (count-atoms (first exp)) (count-atoms (rest exp)))))) (defun count-anywhere (a exp) (count-anywhere 'a '(a ((a) b) a)) --> 3 "count performances of a in expresion - (count-anywhere 'a '(a ((a) b) (a))) ==> 3" (cond ((null exp) 0) ((atom exp) (if (eq a exp) 1 0)) (t (+ (count-anywhere a (first exp)) (count-anywhere a (rest exp))))))
27 .Solutions Write a function (flatten '(a (b) () ((c)))) --> (a b c) which removes all levels of parenthesis and returns a flat list of atoms. (defun flatten (exp) "removes all levels of paranthesis and returns flat list of atoms (flatten '(a (b) () ((c)))) ==> (a b c)" (cond ((null exp) nil) ((atom exp) (list exp)) (t (append (flatten (first exp)) (flatten (rest exp))))))
28 . EXAMPLE A tree structure of nodes for data base 28
29 .Example of interaction with the program that will be shown: You type How it works? (questions) Is it a ANIMAL? (yes) Program responds You have some item in Is it a MAMMAL? (yes) mind, program asks, I give up - what is it? (whale) you respond. #S( NODE :NAME WHALE :YES NIL :NO NIL ) (questions) Program learned this. Is it a ANIMAL? (no) Now it knows Is it a VEGETABLE? (no) that whale is a mammal. Is it a MINERAL? (no) I give up - what is it? (fruit) #S( NODE :NAME FRUIT :YES NIL :NO NIL ) (questions) Is it a ANIMAL? (no) Is it a VEGETABLE? (no) You confirm that the program guessed correctly Is it a MINERAL? (no) (n Is it a FRUIT? (it) Program learned this. Now it knows that AHA! it is a fruit 29