Chapter 6 Fundamentals of the Logical Paradigm. Programming Languages and Paradigms J. Fenwick, B. Kurtz, C. Norris (to be published in 2012)

Transcription

1 Chapter 6 Fundamentals of the Logical Paradigm Programming Languages and Paradigms J. Fenwick, B. Kurtz, C. Norris (to be published in 2012)

2 Introduction In this second part of chapter 6 you will learn about Answering the Fundamental Questions for Prolog Name, binding, and scope Expressions and Horn Clauses Operators Flow control and unification Exception handling Concurrency A Case Study You will build a lexical analyzer (scanner) for Wren source code This is a somewhat tedious task of processing a source code file character by character, but Prolog is up to the task The scanner is essential to complete the parser and code generator in the next chapter

3 Name, Binding, and Scope - 1 Terms are either atoms, numbers, variables or compound terms An atom is a sequence of alphanumeric characters beginning with a lower case letter or a sequence of characters enclosed in single quotes jay Jay Fenwick Numeric literals are sequences of digits, e.g., 1234 Variables are represented by a sequence of letters, numbers and underscores, starting with either an upper case letter or an underscore Thefather _father

4 Name, Binding, and Scope - 2 Compound terms A list [1, a, [ hello ]]?- "abc" = [X, Y, Z]. X = 97 Y = 98 Z = 99 A functor is composed of an atom and a number of argument terms enclosed within parenthesis father('ethan', fatherof('baron')). sibling(x, Y) :- father(x, Z), father(y, Z), \+(X = Y). Prolog performs static scoping and the scope of a Prolog variable is the statement in which the variable appears

5 Expressions and Horn Clauses A Horn clause is one of the following two forms (P 1 ^ P 2 ^ ^ P n ) -> Q (R 1 ^ R 2 ^ ^ R n ) Written in Prolog this become Q :- P 1, P 2,, P n. % a rule R 1. R 2... R n. % a sequence of facts and (, ) has higher precedence than or ( ; ) Q :- P 1, P 2 ; P 3, P 4. is equivalent to: Q :- P 1, P 2. Q :- P 3, P 4.

6 Operators - 1 Operator Description Examples is Evaluates the expression on the right and determines whether it can be unified with the expression on the left. The expression on the left is not evaluated, thus the last example evaluates to no.?- X is 3. X = 3 yes?- 3 is 3. yes? is no =, \= Determines whether the left operand and the right operand can or can not be unified?- [X, Y] = [a, b]. X = a Y = b Yes?- X = 3. X = 3 yes?- X = Y. Y = X yes ==, \== Determines whether the left and right operands evaluate to the same values. In the first example, X is unbound and thus has no value.?- X == 3. no?- 3 * 4 == 3 * 4. yes?- X is 3, X == 3. X = 3 yes

7 Operators - 2 Operator Description Examples <, >, =<, >= Comparison operators. Notice the less than or equal to operator is =<?- 5 >= 4. yes?- X is 4, 3 =< X. X = 4 yes /, * Operators for division and multiplication?- X is 2 * 3, 10 > X. X = 6 yes?- X is 3, Y is 10/X. X = 3 Y = yes +, - Operators for addition and subtraction?- X is 3, Y is 4 - X + 7. X = 3 Y = 8 yes

8 Rules Flow Control Given a :- b, c, d. The interference engine tries to satisfy b first, then c, then d. If all 3 succeed, then a succeeds. Given a :- b, c. followed by a :- d, e. Rules of the same name are attempted from top to bottom; typically the base case is given first. A comparison of Haskell and Prolog mymember _ [] = False mymember x (y:z) = (x == y) mymember x z mymember(x, [X _]). mymember(x, [_ Y]) :- mymember(x, Y). How is the False case handled in Prolog?

9 Unification The constraints of the unification process are: Two predicates unify if they have the same name and arity and their arguments unify. For example, p(x, Y) does not unify with q(x, Y) because p and q are two different names. Two functor terms unify if they have the same name and arity and their terms unify. For example, f(a, b, X) unifies with f(a, Y, c) because the functors have the same name, arity and their terms unify. Two different constants do not unify. For example, fruit(apple) does not unify with fruit(banana). A constant unifies with a variable. For example, fruit(apple) unifies with fruit(x). Two variables unify. For example, fruit(x) unifies with fruit(y). Unification requires that all instances of the same variable in a rule must get the same value. For example, p(x, b, X) does not unify with p(y, Y, c) because Y must be b to make the second arguments equal and X must be c to make the third arguments equal. This makes the instantiation of the first predicate p(c, b, c) and the instantiation of the second predicate p(b, b, c).

10 Exception Handling The catch function takes three arguments. The first argument is the goal to be performed (comparable to the body of a try in Java). The second argument is the exception to be caught while solving the goal and may be a variable to allow any type of exception to be caught. The third argument is the function to be executed in the event of an exception. divide :- catch(causeerror, X, handleerror(x)). handleerror(x) :- write('caught Exception' : X), nl. causeerror :- result is 10 / 0.?- divide. Error:error(evaluation_error(zero_divisor),(is)/2) yes

11 Using threads fibonacci(1, 0). fibonacci(2, 1). Concurrency fibonacci(n, Result) :- N > 2, Nminus1 is N - 1, Nminus2 is N - 2, thread_create(callfibo(nminus1), Id1, []), thread_create(callfibo(nminus2), Id2, []), thread_join(id1, exited(n1)), thread_join(id2, exited(n2)), Result is N1 + N2. callfibo(n) :- fibonacci(n, Result), thread_exit(result).

12 Case Study: Building a Scanner for Wren Input to the scanner program gcd is var m,n : integer; begin read m; read n; while m <> n do if m < n then n := n - m else m := m - n end if end while; write m end Output from the scanner [program,ide(gcd),is,var,ide(m),comma,ide(n),colon,integer, semicolon,begin,read,ide(m),semicolon,read,ide(n),semicolon, while,ide(m),neq,ide(n),do,if,ide(m),less,ide(n),then,ide(n), assign,ide(n),minus,ide(m),else,ide(m),assign,ide(m),minus, ide(n),end,if,end,while,semicolon,write,ide(m),end,eop]

13 Opening the Source Code File The go rule go :- nl, write('>>> Lexical Analyzer for Wren <<<'), nl, write('enter name of source file: '), nl, getfilename(filename), nl, see(filename), scan(tokens), seen, write('scan successful'), nl,!, write(tokens), nl. Some new built-in Prolog rules write that displays the specified object on the console nl that forces a new line on the console see opens the file with the path specified by the user seen closes the file

14 The getfilename Rule The rule getfilename(f) :- get0(c),restfilename(c,cs),name(f,cs). restfilename(c,[c Cs]):-filechar(C),get0(D),restfilename(D,Cs). restfilename(c,[]). Some comments on this rule get0 fetches a single character from the file It is possible to write a single rule to fetch all the characters in the file name but it will be left recursive and always cause the Prolog interpreter to fail due to exhausting the stack space (see next slide) The restfilename rule is right recursive and will not blow up the Prolog interpreter Lab Activity: put these rules and the go rule into a scanner.pl file

15 Eliminating Left Recursion Left recursion occurs when the recursive call to the rule is the first item in the clauses to be satisfied iamrecursive(<params>) :- iamrecursive(<params>), This will cause Prolog to fail due to infinite recursion The general strategy to write right recursive Prolog code is to introduce a new rule The original rule only handles the first case, such as the first get0 in the getfilename rule The helper rule completes the operation using right recursion, as in the restfilename rule We will use this strategy several times in the scanner program

16 Reserved Words The reserved words in Wren are program,is,begin,end,var,integer,boolean,read,write, while,do,if,then,else,skip,or,and,true,false,not Here are the facts to recognize the first four reserved words reswd(program). reswd(is). reswd(begin). reswd(end). Lab Activity: Write the facts for the remaining reserved words and add to the scanner.pl file

17 Single Character Tokens Many single characters in Wren, such as (, will become full word tokens, such as lparen single(40,lparen). 40 is the ASCII code for a left parenthesis Lab Activity: Using a ASCII table write additional single facts for the following characters: rparen, times, plus, comma, minus, divides, semicolon, equal Some Prolog interpreters, such as gprolog, require rules or facts with the same name and arity (number of parameters) to be grouped into contiguous code; make sure you do this.

18 Single or Double Character Tokens Some single characters, such as <, may be part of a single character token, less, or a double character token, <= which is the token lteq double(58,colon). double(60,less). double(62,grtr). Here are a sample rule for a pair of characters pair(58,61,assign). Lab Activity: Add additional pair rules for <> (neq), <= (lteq), and >= (gteq).

19 Recognizing Groups of Characters Character groups, such as digits, lower case characters, and upper case characters are contiguous within a range of ASCII values Here is a rule for lower case lower(c) :- 97=<C,C=<122. % a-z Lab Activity: Add two additional rules to test if a character is upper case, name it upper, or a digit, name it digit.

20 Other Utility Fact and Rules space(32). tabch(9). period(46). slash(47). endline(10). endfile(26). endfile(-1). whitespace(c) :- space(c) ; tabch(c) ; endline(c). idchar(c) :- lower(c) ; digit(c). filechar(c) :- lower(c); upper(c); digit(c); period(c); slash(c). Lab Activity: Add these to your scanner.pl file

21 Building the scan Rule The scan and getch rules scan([t Lt]) :- tab(4), getch(c), gettoken(c, T, D), restprog(t, D, Lt). getch(c):- get0(c),(endline(c),nl,tab(4); endfile(c),nl; put(c)). Most of the work is done by the gettoken rule Here is the restprog rule restprog(eop,c,[]). % end of file in previous character restprog(t,c,[u Lt]):- gettoken(c,u,d),restprog(u,d,lt).

22 The gettoken rules - 1 There is a long sequence of rules; we add them one by one; the general form of the rule is: gettoken(<current char>, token, <next char>) Here is the first example when end of file is encountered. gettoken(c, eop, 0) :- endfile(c). Lab Activity: Write the gettoken rule for the case when a single character unambiguously corresponds to a token, such as ( corresponding to lparen.

23 The gettoken rules - 2 The next rule is when the current character is one of the three characters that either corresponds to a single character token or a two character token gettoken(c, T, E) :- double(c,u),getch(d), (pair(c,d,t),getch(e); T=U,E=D). Lab Activity: Keep your scanner.pl file up to date by adding the gettoken rules as discussed

24 The gettoken rules - 3 A lower case letter indicates a start of an identifier or a reserved word; the following rule takes care of both cases gettoken(c, T, E) :- lower(c), getch(d), restid(d, Lc, E), name(i, [C Lc]), (reswd(i),t=i ; T=ide(I)). Lab Activity: Write the restid rules. The general form of these rules are: restid(<current char>, seq of ASCII values, <next char>) The first rule is the general recursive case where you keep fetching characters until the idchar goal fails. The second rule handles this case where the current character is not an idchar; it matches the first to third arguments and returns the empty list of characters as the second argument

25 The gettoken rules - 4 Lab Activity: Write the gettoken rule for integer literals. Suppose the literal is the sequence of digits 123 then the token returned is num(123). You will need a restnum rule that is very similar to the restid in the previous exercise. To complete this exercise you are writing a single gettoken rule and two restnum rules, the second handling the base case. The final two gettoken rules are gettoken(c, T, E) :- whitespace(c), getch(d), gettoken(d,t,e). gettoken(c, T, E) :- write('illegal character: '), put(c), nl, abort. The first rules removes white space and the second one (the final gettoken) reports an illegal character and aborts.

26 A Word about Singleton Variables Prolog will issue a warning if a rule contains a singleton variable; that is, a variable that appears only once in the rule and is not used elsewhere. gettoken(c, T, E) :- write('illegal character: '), put(c), nl, abort. How you can remove singletons You can remove any singleton variable by replacing it with the _ character This will remove the singleton warning The argument for keeping singletons From the compiler/interpreter perspective a singleton binds a name to a value unnecessarily From a documentation perspective, the singleton says what the term represents, it makes the rule more readable and consistent for a human programmer

27 Tools for Debugging The spy rules You can either spy on everything or on a particular predicate (the more common usage)?- spy(gettoken). Spy will show on the console the call to the specified predicate along with the result produced The rule nospy will turn off a spy point The trace rules Turn on with trace(gettoken) and turn off with notrace This causes the program to enter single step mode When you are in single-step mode there are a variety of options on how to proceed; pressing return will continue the single-step mode.

28 Completing the Scanner Enter all of your code in the scanner.pl file If there are any missing rules or facts, complete them Test your program with the gcd program stored in an external file as given at the start of section 6.4 Debugging may be tedious, but often that is the life of a computer scientist Now test your scanner with the product and divide programs from section 2.1; fix any remaining errors