Wan Hussain Wan Ishak

Transcription

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2 September 1 st Session 2014/2015 (A141) Wan Hussain Wan Ishak School of Computing UUM College of Arts and Sciences Universiti Utara Malaysia (P) (E) hussain@uum.edu.my (U)

3 Lecture notes List, Operators and Arithmetic Arithmetic Constructing Expressions List Processing Character Strings and Structures

4 List List is one of the most important Prolog data structures. A list is an ordered sequence of zero or more terms written between square brackets and separated by commas. [a,b,c,d]

5 List

6 List [a,b,c,d] Elements The elements of a list can be any kind of Prolog terms, including other lists. [1,2,3,4] [a1,a2,a3] [sawi, kangkung] [kucing(comel), kucing(hitam)] [[satu,dua],[tiga,empat]]

7 List The empty list is written: [] Please note one element list [a] is not equivalent to the atom a.? [a] = a. no

8 List List can be constructed or decomposed through unification. Unify with [a,b,c] = X [X,b,Z] = [a,y,c] [[a,b],c] = [X,Y] [a(b),c(x)] = [Z,c(a)] Result X = [a,b,c] X = a, Y = b, Z = c X = [a,b], Y = c X = a, Z = a(b)

9 List More examples Unify with [X Y] = [a,b,c,d] Result X = a, Y = [b,c,d] [X Y] = [a] X = a, Y = [] [X,Y Z] = [a,b,c] X = a, Y = b, Z = [c] [X,Y,Z A] = [a,b,c] X = a, Y = b, Z = c, A = [] [X,Y Z] = [a W] X = a, W = [Y Z]

10 List The list can be divided into head and tail by the symbol. [H T] The first element is the head and the rest are the tail. Example: [a [b,c,d,e]]

11 List [a [b,c,d,e]] The tail of a list is always a list, the head of a list is an element. Every nonempty list has a head and a tail. [a,b,c,d] = [a [b,c,d]] [a] = [a []]

12 List Manipulation Built-in predicates Predicate append/3 length/2 member/2 member/3 remove/3 removeall/3 reverse/2 Function join or split lists get the length of a Prolog list get or check a member of a list get or check a member of a list and its position remove an element from a list remove all occurrences of an item from a list check or get the reverse of a list

13 List Manipulation append/3 Syntax: Example: append(first, Second, Whole) Join list Splitting list?- append([a,b], [c,d], Whole). Whole = [a,b,c,d]?- append([a,b], Second, [a,b,c,d]). Second = [c,d]?- append(first, [c,d], [a,b,c,d]). First = [a,b]

14 List Manipulation length/2 Syntax: Example: length(term, Length)?- length([a,b,c,d], Length). Length = 4

15 List Manipulation member/2 Syntax: Example:?- member(a, [a,b,c,d]). yes member(element, List)?- member(element, [a,b,c,d]). Element = a ; Element = b ; Element = c ; Element = d ;

16 List Manipulation member/3 Syntax: member(element, List, Position) Example: Element position?- member(c, [a,b,c,d], Position). Position = 3 ; Get Element at given position?- member(element, [a,b,c,d], 2). Element = b

17 List Manipulation member/3 (more example):?- member(element, [a,b,c,d], Position). Element = a, Position = 1 ; Get the element and its position Element = b, Position = 2 ; Element = c, Position = 3 ; Element = d, Position = 4 ;

18 List Manipulation remove/3 Syntax: remove(element, List, Remainder) Example: Takeout an element Element missing?????- remove(b, [a,b,c,d], Remainder). Remainder = [a,c,d] ;?- remove(element, [a,b,c,d], [a,b,d]). Element = c ;

19 List Manipulation remove/3 (more example):?- remove(element, [a,b,c,d], Remainder). Element = a, Remainder = [b,c,d] ; Element = b, Remainder = [a,c,d] ; Element = c, Remainder = [a,b,d] ; What element can be removed Element = d, Remainder = [a,b,c] ;

20 List Manipulation removeall/3 Syntax: removeall(item, List, Remainder)

21 List Manipulation removeall/3 (Example): Remove all repeated elements Remove all elements that match with the first element?- removeall(a, [a,b,a,b,a], Remainder). Remainder = [b,b]?- removeall(item, [a,b,a,b,a], Remainder). Item = a, Remainder = [b,b]?- removeall(item, [b,a,b,a], Remainder). Item = b, Remainder = [a,a]

22 List Manipulation Reverse/2 Syntax: Example: Reverse the list Causes error reverse(list, Revlist)?- reverse([a,b,c,d], Revlist). Revlist = [d,c,b,a]?- reverse(list, [d,c,b,a]). List = [a,b,c,d] ; Error 4, Heap Space Full, Trying ewrite/1

23 List Manipulation - Exercise What is the output??- append([ab],[b,c,d], X).?- reverse([b,c,d], R), append([ab], R, X).?- reverse([b,c,d], R), member(f, R, 1), remove(f, R, B), append([ab], B, X).

24 List Constructing Predicates append/3 length/2 member/2 member/3 remove/3 removeall/3 reverse/2 How to define or construct the predicates? How they are working/how they manipulate the list?

25 List Constructing Predicates append/3 addon/3 Syntax: addon(first, Second, Whole) Definition: addon ([],X,X). addon ([H T1],X,[H T2]):- addon (T1, X, T2). stop the recursion add element into the list

26 List Constructing Predicates append/3 addon/3 (1) addon ([],X,X). addon/3?- addon([a,b],[c],w). (2) addon ([H T1],X,[H T2]):- (2.1) addon (T1, X, T2). Ep. 1 Call (1) addon([],x,x). false [a,b]\=[] Call (2) addon([h T1],X,[H T2]). true [a,b]=[h T1] [c]=x Call (2.1) addon(t1,x,t2). W=[H T2] addon([b],[c],t2). go to Ep. 2 H=a T1=[b] X=[c] W=[a T2] T2=_

27 List Constructing Predicates append/3 addon/3 (1) addon ([],X,X). addon/3 From Ep.1, (2.1) addon([b],[c],t2). (2) addon ([H T1],X,[H T2]):- (2.1) addon (T1, X, T2). Ep. Call (1) addon([],x,x). false [b]\=[] 2 Call (2) addon([h T1],X,[H T2]). true [b]=[h T1] H=b [c]=x T1=[] W=[H T2] X=[c] Call (2.1) addon(t1,x,t2). W=[b T2] T2=_ addon([],[c],t2). go to Ep. 3

28 List Constructing Predicates append/3 addon/3 (1) addon ([],X,X). addon/3 From Ep.2, (2.1) addon([],[c],t2). (2) addon ([H T1],X,[H T2]):- (2.1) addon (T1, X, T2). Ep. 3 Call (1) addon([],x,x). true []=] Stop at Ep. 3 rule (1). Rule (2) will not execute. X=[c]

29 List Constructing Predicates?- addon([a,b],[c],w). W =[a,b,c] (1) addon ([],X,X). addon/3 (2) addon ([H T1],X,[H T2]):- (2.1) addon (T1, X, T2). Ep. 1 (2) addon([a [b]],[c],[a T2]):- (2.1) addon([b],[c],t2). [a [b,c]] T2 = [b,c] Ep. 2 (2) (2.1) addon([b []],[c],[b T2]):- addon([],[c],t2). [b [c]] T2 = [c] Ep. 3 (1) addon([],[c],[c]).

30 List Constructing Predicates length/2 noofterms/2 Syntax: noofterms(term, Length) Definition: noofterms([],0). noofterms([h Tail],K):- noofterms(tail,j), K is J + 1. stop the recursion calculate the length

31 List Constructing Predicates length/2 noofterms/2 noofterms/2 (1) noofterms([],0).?- noofterms([a,b,c],t). (2) noofterms([h Tail],K):- (2.1) noofterms(tail,j), (2.2) K is J + 1. Ep. 1 Call (1) noofterms([],0). false [a,b,c]\=[] Call (2) noofterms([h Tail],K). true [a,b,c]=[h Tail] Call (2.1) noofterms(tail,j). T=K noofterms([b,c],j). go to Ep. 2 Call (2.2) pending. (At the moment Sub goal 2.2 will not be called.) H=a Tail=[b,c] T=K=_

32 List Constructing Predicates length/2 noofterms/2 noofterms/2 (1) noofterms([],0). Ep. 2 From Ep.1, (2.1) noofterms([b,c],j). Call (1) noofterms([],0). false [b,c]\=[] (2) noofterms([h Tail],K):- (2.1) noofterms(tail,j), (2.2) K is J + 1. Call (2) noofterms([h Tail],K). true [b,c]=[h Tail] Call (2.1) noofterms(tail,j). J=K H=b Tail=[c] J=K=_ noofterms([c],j). go to Ep. 3 Call (2.2) pending. (At the moment Sub goal 2.2 will not be called.)

33 List Constructing Predicates length/2 noofterms/2 noofterms/2 (1) noofterms([],0). Ep. 3 From Ep.2, (2.1) noofterms([c],j). Call (1) noofterms([],0). false [c]\=[] (2) noofterms([h Tail],K):- (2.1) noofterms(tail,j), (2.2) K is J + 1. Call (2) noofterms([h Tail],K). true [c]=[h Tail] Call (2.1) noofterms(tail,j). J=K H=c Tail=[] J=K=_ noofterms([],j). go to Ep. 4 Call (2.2) pending. (At the moment Sub goal 2.2 will not be called.)

34 List Constructing Predicates length/2 noofterms/2 noofterms/2 (1) noofterms([],0). From Ep.3, (2.1) noofterms([],j). (2) noofterms([h Tail],K):- (2.1) noofterms(tail,j), (2.2) K is J + 1. Ep. 4 Call (1) noofterms([],0). true []=[] J=0 Prolog will now return to Ep. 3 to execute 2.2. Followed by Ep. 2 and Ep. 1.

35 List Constructing Predicates (1) noofterms([],0). noofterms/2? - noofterms([a,b,c],t). 1 (2) noofterms([a [b,c]],k):- K=3 (2.1) noofterms([b,c],j), J=2 (2.2) 2 K is J + 1. (2) noofterms([b [c]],k):- K=2 (2.1) noofterms([c],j), J=1 (2.2) 3 K is J + 1. (2) noofterms([c []],K):- (2.1) noofterms([],j), (2.2) K is J + 1. (2.2) 4 K (1) is J noofterms([],0) (2) noofterms([h Tail],K):- (2.1) noofterms(tail,j), (2.2) K is J + 1. K=1 J=0 In console T = 3 yes (2.2) (2.2) K is J + 1. K is J + 1. (2.2) K is J + 1. (2.2) K is J + 1. K is K is K is 0 + 1

36 List Constructing Predicates noofterms([a [b,c]],k). J = K = 2 K is noofterms([b [c]],k) J = K = 1 K is noofterms([c []],K). J = K = 0 K is noofterms([],0).

37 List Constructing Predicates member/2 is_in/2 Syntax: is_in (Element, List) Definition: is_in (X,[X T]). is_in (X,[H T]):- is_in(x, T). check if the Element is Head of the list if not, traverse the rest of the list (Tail)

38 List Constructing Predicates is_in(x,[a,b,c]). X = a Return X = a is_in(x,[b,c]). Return X = b X = b is_in(x,[c]). Return X = c X = c is_in(x,[]).

39 List Constructing Predicates is_in(c,[a,b,c]). c \= a is_in(c,[b,c]). C \= b is_in(c,[c]). c = c Return yes is_in(c,[]).

40 List Constructing Predicates remove/3 take_out/3 Syntax: take_out (Element, List, Remainder) Definition: take_out (X,[X R],R). element found take_out (X,[F R],[F S]):- take_out (X,R,S). traverse the list, at the same time create new list

41 List Constructing Predicates reverse/2 overturn/2 Syntax: overturn (List, Revlist) Definition: overturn (List,RevList):- overturn2(list,[],revlist). overturn2([h T],Z,W):- overturn2(t,[h Z],W). the element position overturn2([],x,x).

42 Character Strings Three ways to represent a string of characters in Prolog: As an atom atoms are compact but hard to take apart or manipulate. As a list of ASCII codes can use standard list processing techniques on them. As a list of one-character atoms - can use standard list processing techniques on them.

43 Character Strings Use write/1 with double quotes. Example:?- write( abc ). [97,98,99]

44 Character Strings Use put/1 or putb/1. Example: write_str([h T]):- put(h), write_str(t). write_str([]).

45 Character Strings Convert between an atom or number and a byte list - name/2. Syntax: name(atomic, List) Example:?- name(makan,list). List = [109,97,107,97,110]?- name(atomic, [109,97,107,97,110]). Atomic = makan

46 Character Strings Example (Prolog codes): splitnprint(ayat):- name(ayat,ayatlist), write_str(ayatlist). write_str([h T]):- put(h), write_str(t). write_str([]). Output:?- splitnprint(ahmad). ahmad

47 Character Strings (Exercise) Write a code/rule to print out as follows:?- print_splits("prolog"). p rolog pr olog pro log prol og prolo g prolog yes print_splits(word):- print_split(word,word). print_split([],word). print_split([_ T],Word):- append(h,t, Word), write_str(h), write(` `), write_str(t),nl, print_split(t, Word). write_str([]). write_str([h T]):- put(h), write_str(t).

48 Character Strings (Exercise) Write a code/rule to check whether the word end with s or not :?- end_with_s("flowers"). yes?- end_with_s("car"). no?- end_with_s("cars"). yes end_with_s(list):- length(list, L), member(115, List, L).

49 Operators Notation Data structure in Prolog: functor(arg1, arg2,, argn). Functor can become operator example: eat(ali,rice). Can be written as: Functor Linguistic Operator ali eat rice.

50 Operators Notation Types of operators Operator Example Infix Prefix +(3,4) Postfix 8 factorial

51 Linguistic Operator Operator can be defined using op/3. op/3 - Declares an operator with a given type and precedence. Syntax: Name of the operator op(precedence, Type, Name) Integer Atom or list of atoms

52 Linguistic Operator Precedence value for operator The value between The precedence value can influence the structure meaning: low precedence meaning high priority. Example: operator with 33 is given higher priority compare to 35. operator with 33 will be first executed.

53 Linguistic Operator Precedence Value The value between The precedence value can influence the structure meaning: low precedence meaning high priority. Example: operator with 33 is given higher priority compare to 35. operator with 33 will be first executed.

54 Linguistic Operator Precedence Value Example use display/1 To view the standard syntax Change the precedence value Error Wrongly use operator?- op(35,xfx,is_in). yes?- op(33,fx,room). yes?- display(apple is_in room kitchen). is_in(apple,room(kitchen))?- op(36,fx,room). yes Defining operator is_in and room?- display(apple is_in room kitchen).! ! Error 42 : Syntax Error! Goal : eread(_11848,_11850)?- display(room kitchen is_in house). room(is_in(kitchen,house))

55 Linguistic Operator Precedence Value Example?- op(35,xfx,is_in). yes?- op(33,fx,room). yes?- op(36,fx,room). yes?- display(apple is_in room kitchen). is_in(apple,room(kitchen))?- display(room kitchen is_in house). room(is_in(kitchen,house))

56 Linguistic Operator Defining Type If the precedence value is the same Prolog will read either from left to right or right to left based on the type. Type for operator Types fx fy xf yf xfx xfy yfx Meaning non-associative prefix operator right associative prefix operator non-associative postfix operator left associative postfix operator non-associative infix operator right associative infix operator left associative infix operator prefix postfix infix

57 Using Linguistic Operator Example cth.pl % Linguistic operators :- op(800, fx, if), op(700, xfx, then), op(300, xfy, or), op(200, xfy, and). % Facts binatang(comel). binatang(tompok). makan(comel,ikan). Makan(tompok,ikan). mengiau(comel). mengiau(tompok). % Rules if binatang(x) and makan(x,ikan) then kucing(x).

58 Using Linguistic Operator Examine % Rules if binatang(x) and makan(x,ikan) then kucing(x). Standard Syntax if(then(and(binatang(_13214),makan(_13214,ikan)), kucing(_13214)))

59 Arithmetic 2 Operation + 1 =? Arithmetic how we do calculation in Prolog. Use predicate is/2 not =/2.

60 Arithmetic Operation is/2 takes an arithmetic expression on its right, evaluates it, and unifies the result with its argument on the left. Example: Format: X is X is 9. A = 1, X is A is <argument > is <arithmetic expression>.

61 Arithmetic Operation Wrong expression: is 3. Type error - not in the right format. 2 is 1 + X Instantiation error value of X is unknown.

62 Arithmetic Operation Different with is/2 and =/2 : is/2 evaluate its right argument and unifies it with its argument on the left do calculation. =/2 is to test if both arguments on the left and right are unify do unification.

63 Arithmetic Operators Common arithmetic operators (infix operators) Operator & Symbol Example & Output + Addition X is Subtraction X is * Multiplication X is 3 * 2. 6 / Floating-point division X is 3 / // Integer division X is 3 // 2. 1

64 Arithmetic Operation Other arithmetic functions supported in LPA Prolog

65 Arithmetic Operators The precedence of operators: Example: X is 1 2 * 5 ^ 2 / Equivalent to Where ^ is performed first, then * and /, and finally + and -. X is (1 (((2 * (5 ^ 2)) / 8) + 6))

66 Using Arithmetic Operators Example:?- papar(5) printout(n):- 2. printout(1, N) printout(n, N) printout(x, N):- 7. printout_num(x), 8. nl, 9. NewX is X + 1, 10. printout(newx, N) printout_num(0) printout_num(x):- 15. write(x), 16. NewX is X - 1, 17. printout_num(newx).

67 Constructing Expression Different between Prolog an other programming languages is: Other programming language evaluate arithmetic expression s whenever they occur Prolog evaluates them only in specific places.

68 Constructing Expression List of built-in Predicates that evaluate expressions. R is Ex Ex1 =:= Ex2 Ex1 =\= Ex2 Ex1 > Ex2 Ex1 < Ex2 Ex1 >= Ex2 Ex1 =< Ex2 Evaluates Ex and unifies result with R test if the results of two expressions are equal test if the results of two expressions are not equal test if the result of one expression is greater than another test if the result of one expression is less than another test if one expression is greater than or equal to another test if one expression is less than or equal to another

69 Exercise Explain which of the following succeed, fail, or raise error conditions, and why: 1.?- 5 is ?- 5 =:= ?- 5 = ?- 5 is 2 + What. 5.?- 4+1 = ?- 4+1 is ?- 4+1 =:= ?- What is ?- What =:= ?- What is ?- What = ?- What =\= 2+3.

70 Practical Calculation When using expressions in Prolog, we are mixing the styles of encoding knowledge. Normal syntax: Can be written as:? X is ?- sum(2, 3, X).

71 Practical Calculation Example: doublevalue(x, Z):- Z is X * X. areaofsquare(p, L, Area):- Area is P * L.