1. Testing Grammars For Top Down Parsers By Asma M Paracha, Frantisek F. Franek Dept. of Computing & Software McMaster University Hamilton, Ont

2. Presentation Outline Background Information Purdom’s Algorithm Implementation of Purdom’s Algorithm Test cases for MACS Conclusions & Future Work

3. Compiler Test Case Compiler is a computer program which accepts a source program as input and produces either an object code or error messages depending upon the source code. Test case for a compiler should have: 1. A test case description 2. A source program 3. An expected output Major Problem 1. Completeness of coverage 2. Unfeasible size of test data

4. Testing Grammar Grammar defines both a language and the basis of deriving elements for a language. Grammar is considered both as a program and a specification. Two important types of grammars: 1. Context free grammars 2. Regular grammars Grammar should be tested to verify: 1. It defines the same language for which it is written 2. For completeness (every terminal and every rule is used) 3. To remove ambiguity.

5. Context Free Grammars (CFG) CFG is a set of recursive rewriting rules used to generate strings in various patterns. Components of grammar: 1. N: Finite set of non-terminals 2. T: Finite set of terminals, does not intersect with N 3. S: Initial symbol from N (starting symbol) 4. P: Finite set of production rules of the form n  m No practical way to check the dynamic semantics of the language defined by CFG.

6. Testing Parser The process of checking a given program against the grammar rules to determine whether or not it is syntactically correct. Test data for parser is a program which use all the production rules of underlying grammar. Testing the parser

7. Purdom’s Algorithm Proposed by Purdom in 1972 for testing compilers for automatically generating sentences from the grammar by using every production rule at least once. Sentences generated are good to check most of compiler code and tables. Only checks the syntactic aspect, no guarantee for the proper execution. Generated sentences may be inconsistent with the contextual constraints for e.g. variable declarations, use of identifiers, type checking. Purdom’s algorithm verifies the compiler correctness, not interested in other aspects such as: Efficiency Performance

8. Testing MACS Compiler MACS is a simple object oriented language very much similar to C++ and Java. It is used in the forth coming book of Franek on compilers. MACS uses both LALR and LL(1) grammars and has a C++ bottom-up parser built using Bison/Flex and a Java top-down parser built using JavaCC. MACS LL(1) grammar has 77 terminlas,90 non-terminals and 301 production rules.

9. Implementation of Purdom’s algorithm Phase I (Shortest String Length) SLENShortest terminal string length for each symbol RLENThe length of shortest string derivable from each production rule SHORTFor every non-terminal, it contains the rule numbers which leads to shortest string derivation. Phase II (Shortest Derivation Length) DLENFor each non-terminal, the length of shortest terminal string which used it in its derivation PREVRule number which introduces a non-terminal in shortest string derivation

10. Implementation of Purdom’s algorithm (Contd..) Phase III (Generate Sentence) ONSTThe number of occurrences of each non-terminal on the stack. ONCEInformation about each non-terminal whether to use it or not and how to rewrite it. Contains anyone of the following values: 1. READY 2. UNSURE 3. FINISHED 4. INTEGER MARKInformation whether a rule has been used or not. Contains boolean values. STACKEvery symbol is pushed on the stack starting with the starting symbol “S”.A terminal is being popped every time it comes on the top and non-terminal is rewritten by an appropriate rule.

11. Results Purdom Generated SentencesMACS Test CasesSyntactically Correct Semantically Correct VOID CLASSNAME_DOT ID_LP CLASSNAME ID COMMA CONST CLASSNAME ID RP SEMICOL void A.a( A a1, const A b); XX VOID CLASSNAME_DOT ID_LP BOOL ID RP SEMICOL void A.a(bool b);XX PUBLIC VOID CLASSNAME_DOT COMMA CLASSNAME_DOT ID SEMICOL public void A.a,A.b; CLASS CLASSNAME SEMICOLclass A;XX CLASS ID LB RBclass a{}XX PUBLIC CONST VOID CLASSNAME_DOT ID SEMICOL public const void A.a;X PUBLIC SHARED VOID CLASSNAME_DOT ID SEMICOL public shared void A.a;X

12. Conclusions Parser testing is an area which needs more attention. Purdom’s algorithm is a complete method for testing small grammars. Test cases generated are incorporated with the semantic aspects of the language to perform the compiler validation. Future work includes testing the most advanced features of MACS compiler.