Presentation on theme: "CS252: Systems Programming"— Presentation transcript:
1 CS252: Systems Programming Ninghui LiTopic 5: ParsingPrepared by Evan Hanau
2 An Introduction to Parsing with Yacc Context-Free GrammarsYacc ParsingAn example Infix Calculator Program
3 Context-Free Grammar Background: The Context-Free Grammar By CS252 you are already somewhat familiar with Regular Expressions.Regular expressions can be used to describe regular languages, which belong to a larger classification of language types.
4 Context-Free GrammarIn CS, we classify languages on the Chomsky Hierarchy.Type-0 Recursively EnumerableType-1 Context-SensitiveType-2 Context-FreeType-3 RegularType-(i) is a superset of Type-(i+1)
5 Context-Free GrammarLanguages generated by regular expressions belong to type 3.Note: Your specific regular expression engine (e.g. POSIX extended RE) is likely capable of more complex productions.In any case, we need more than regular expressions to parse computer programming languages and shell scripts.
6 Context-Free Grammar You can do a great deal with regular expressions. Exercise: Create a regular expression that matches on any English phrase that is a palindrome, for instance the string “some men interpret nine memos”.
7 Context-Free GrammarThis is in fact not possible with regex (by its strict CS definition!). You would be limited to palindromes of a finite length only.RE cannot express “anbn”, a string with some number of a’s followed by equal number of b’sThe expression a*b* does not require number of a’s equal that of b’sWe must use a context-free grammar to describe palindromes and other constructs.More powerful than a regular expression, and useful when some notion of “what came before” is required.
8 Backus-Naur formBNF or Backus-Naur form is used in CS to describe context-free grammars. It is often used to describe the syntax of programming languages.consists of one or more of the following:<nonterminal> ::= __expression__Where __expression__ consists of one or more terminals and nonterminals or nothing (epsilon).
10 Context-Free Grammar for Simple Expressions Let’s define a grammar for a primitive add or multiply expression:<expr> ::= <expr> * <expr>| <expr> + <expr>| numberIn this case, <expr> is a terminal and number, *, and + are the nonterminals.
11 Context-Free GrammarClearly, there is some ambiguity here, because operator precedence (sometimes referred to as binding) is not defined.The grammar does not distinguish between 2+2*2+2 = 16 (incorrect under normal rules) or 2+2*2+2 = 8 (correct).
12 Context-Free GrammarOne Solution: Define expressions of different levels:<expr> ::= <add_expr><add_expr> ::= <add_expr> + <mul_expr>| <mul_expr><mul_expr> ::= <mul_expr> * number| numberNow, multiplication will bind tighter than addition (this may require a few sample expressions to wrap your head around!)
13 Context-Free GrammarAssociativity follows from the above example (Hint: What side of the multiply and add operation did we have the “deeper” production on?)
14 CFG for palindrome <anbn> = // empty string <palindrome> ::= letter| // empty string<palindrome> ::= “a” <palindrome> “a”| “b” <palindrome> “b”….Or, <palindrome> ::= letter <palindrome> letterHowever, we need to check the two letters are the same.CFG for anbn:<anbn> = // empty string| “a” <anbn> “b”
15 Production rules (constraints) Chomsky Hierarchy (From Wikipedia Page)GrammarLanguagesAutomatonProduction rules (constraints)Type-0Recursively enumerableTuring machine (no restrictions)Type-1Context-sensitiveLinear-bounded non-deterministic Turing machine(equivalently, Right side no shorter than left)Type-2Context-freeNon-deterministic pushdown automatonType-3RegularFinite state automatonand
16 Chomsky Hierarchy Revisited. Type-0 Recursively EnumerableType-1 Context-SensitiveCannot encode all strings r1r2 such that r1 and r2 are two regular expressions that are equivalentType-2 Context-Free (Pushdown Automaton, i.e, Finite State Automaton with a Stack)Can encode anbn, but not anbncnType-3 Regular (Finite State Automaton)Can encode a*b*, but not anbn
17 Why is Context-Free Grammar Called Context Free? In a CFG, the left hand of each production is a single non-terminal, e.g.,<palindrome> ::= “a” <palindrome> “a”This means that “a”, followed by a <palindrome>, and by “a” will always be considered as <palindrome>, no matter what is the context, hence context free.In a Context-Sensitive Grammar, left hand of production rules can include other things
18 An Example Context-Sensitive Grammar for anbncn 1. S a B C 2. S a S B C 3. B C C B 4. a B a b 5. b B b b 6. b C b c 7. c C c cS→2 aSBC →1 aaBCBC→3 aaBBCC→4 aabBCC→5 aabbCC→6 aabbcC→7 aabbcc
19 Yacc & ParsingThere are many ways to parse BNF grammars, most of which are discussed in a compilers course.Recall: A finite state automaton (FSA) is used for regular expressions. (CS182).For a context-free grammar, we use a pushdown automaton, which combines features of a FSA with a stack.
20 Yacc & ParsingYacc generates what is known as a LALR parser, which is generated from the BNF grammar in your Yacc file. This parser is defined in the C source file that Yacc generates.We use Lex to make a lexer to generate our terminals, which are matched with regular expressions before being fed into the parser.
21 Yacc & ParsingYacc is capable of generating a powerful parser that will handle many different grammars.Input CharactersRule-Based BehaviorLEX LexerterminalsYACC Parser
22 Yacc & ParsingRecall that parsing combines a state machine with a stack. States go on a stack to keep track of where parsing is. Yacc uses a parse table which defines possible states.Yacc’s parser operates using two primary actions, shift and reduce.shift puts a state on the stack, reduce pops state(s) off the stack and reduces combinations of nonterminals and terminals to a single nonterminal. After a reduction to a rule, Yacc’s parser will optionally run some user-defined code.
23 Yacc & Parsing A very basic example: <rule> := “hello” “world” “\n”The parser would shift each word, successively pushing each state (.”hello”, .”world”, .”\n”) onto the stack. Then at the end of the rule, reduce everything to <rule> and pop the three states.
24 A Lex/Yacc Infix Calculator Yacc’s parser is powerful, but is not capable of parsing all grammars.Certain ambiguous grammars may produce what is known as a shift/reduce or reduce/reduce conflict. Yacc will, by default, shift instead of reduce.
25 Yacc & Parsing Consider the classic shift/reduce conflict example: <ifexp> ::= IF <expr> THEN <stmt> ELSE <stmt>| IF <expr> THEN <stmt>Yacc will have a shift/reduce conflict here, but will go with shift (the top option) by default. It’s greedy!
26 A Lex/Yacc Infix Calculator To demonstrate the utility of Lex and Yacc (or in our case, Flex and Bison) we provide an example infix calculator.Similar to several of the examples provided on the Lex and Yacc manpage at but with added features
27 A Lex/Yacc Infix Calculator Make sure to read ALL source code comments, particularly those that describe source file organization.Lex definition file: calculator.lYacc grammar file: calculator.yAST Classes: ast.ccSymbol table: symtab.cc
28 A Lex/Yacc Infix Calculator The example calculator application uses Lex and Yacc to parse mathematical expressions and produce an Abstract Syntax Tree, which is then used to evaluate those expressions.It allows the =, +, *, -, +, ^, () and unary minus operators, with appropriate levels of binding and precedence. Examine calculator.y, because it is heavily commented.
29 A Lex/Yacc Infix Calculator The symbol table (implemented here in simple O(n) access time) maps variables to values.Print the AST after every expression evaluation by running calculator with the –t flag, e.g. “calc –t”.
30 A Lex/Yacc Infix Calculator A calculator example. Type “2*2^3/3 and press enter:calc> 2*2^3/3=3.000/(/)\(^)2.000(*)
31 Review What are required: Able to write simple Context Free Grammars, similar to those used in implementing FIZAble to determine whether a string of tokens is accepted by a grammarAble to show how a string of tokens is parsed into some non-terminal (i.e., draw the parsing tree)