Eliminating left recursion (informally) ● Direct left rec. – For each A -> A α 1 | ... | A α n | β 1 | ... | β n – Rewrite: A -> β 1A' | ... | β n A' – Introduce: A' -> α 1A' | ... | α nA' | ε ● Indirect left rec. – A -> B and B -> Ax | Ay – Substitute B, cover all combinations: A -> Ax | Ay – Apply direct left rec. ● Most importantly: – Convince yourself that this does not change the language, only the sequence of productions applied in a derivation
Introducing Lex and Yacc ● Lex and Yacc are languages with many implementations – we'll use the 'flex' and 'bison' ones ● They are tied to each other, as well as having a somewhat hackish interface to C – both compile int C, and large sections of a Lex or Yacc specification will be written in C, directly included in the resulting scanner/parser ● Specifications (*.l and *.y files) are written in 3 sections, separated by a line containing only '%%' – Initialization – Rules – Function implementations
The initialization section ● The first section sets the context for the rules – make sure all functions used in the rule set have been prototyped, and declare any variables – Anything between '%{' and '%}' will be included verbatim (#include, global state vars, prototypes) ● There is a small host of specific commands for both Lex and Yacc, necessities will be covered here ● The rest are covered in this book: – The book is not fantastic, but it can be a useful reference
Lex: Rules Rules in a Lex specification are transformed to an automaton in a ● function called yylex(), which scans an input stream until it accepts, and returns a token value to indicate what it accepted A rule is a regular expression, optionally tied to a small block of C ● code – the typical task here is to return the appropriate token value for the matched reg.exp. Yacc specs can generate a header file full of named token values ● – this will be called “y.tab.h” by default, and can be #included by a Lex spec so you don't have to make up your own token values Character classes are made with [], e.g. ● – [A-Z]+ (one or more capital letters) – [0-9]* (zero or more digits) – [A-Za-z0-9] (one alphanumeric character) – Etc. etc.
Lex: Internal state ● Sometimes a token value is not enough information: – ...so you matched an INTEGER. What's it's value? – ...so you matched a STRING. What does it say? – ...etc ● The characters are shoved into a buffer (char *) called 'yytext' as they are matched – when a rule completes, this buffer will contain the matching text – Shortly thereafter, it will contain the next match instead. Copy what you need while you can. ● There is also a variable called 'yylval' which can be used for a spot of communication with the parser.
Lex: Initialization ● Typing up regular expressions can get messy. Common parts can be given names in the initialization section, such as – DIGIT [0-9] – WHITESPACE [\ \t\n] ● These can be referred to in the rules as {DIGIT} and {WHITESPACE} to make things a little more readable ● By default there is a prototyped function 'yywrap' which you are supposed to implement in order to handle transitions between multiple input streams (when one runs out of characters). ● We won't need that - '%option noyywrap' will stop flex from nagging you about defining it.
Yacc: Rules ● Yacc rules are grammar productions with slightly different typography: “A -> B | C” reads A : B { /* some code */ } | C { /* other code */ } – (Whitespace is immaterial, but I mostly write like this) ; ● Parser constructs rightmost derivation, (shift/reduce parsing = tracing the syntax tree) ● Code for a production is called when the production is matched ● If the right hand side of the production is just a token from the scanner, associated values can be taken from yylval
Yacc: Variables Consider the production ● – if_stmt : IF expr THEN stmt ELSE stmt ENDIF { /*code*/ } Since we want the /*code*/ to do something with the values which ● triggered the production, we need a mechanism to refer to them Yacc provides its own abstract variables: ● – $$ is the left hand side of the production (typically the target of an assignment) – $1 refers to IF (most likely a token, here) – $2 refers to expr (which is probably either a value or some kind of data structure – $3 refers to THEN (a token again) – $4 refers the first stmt, (...and so on and so forth...) What are the types of all these? ●
The types of grammar entities ● All terminals/nonterminals are by default made of type “YYSTYPE”, which can be #define-d by the programmer ● If more than one type is needed in a grammar, it can be defined as a union ● “%union { uint8_t ui; char *str; }” in the init. section will make it possible to refer to 'yylval.ui' and 'yylval.str' when passing values from the scanner ● Inside the parser, types are given to symbols with an own directive: in this context “%type <ui> expr” will make “expr” symbols in the grammar be treated as 8-bit unsigned ints (when they are referred to as $x)
Tokens ● The tokens which are sent to the header file (included by the scanner) can be defined in the init. Section – the following defines tokens for strings, numbers, and keywords if/else – %token STRING NUMBER IF ELSE ● Tokens can be %type-d just like other symbols
yyerror ● “int yyerror ( char * )” is called with an error string parameter whenever parsing fails because the text is grammatically incorrect ● Yacc needs an implementation of this ● There is an uninformative one in the provided code – it could easily be improved with more helpful messages, line # where the error occurred, etc., but we'll pass on that for the moment
What to put where? ● It's possible (but tricky) to make a compiler without separating lexical, syntactical and semantic properties ● Lexical analysis can be done with grammars, and both scanners and parsers can do work related to semantics ● The result very easily becomes a complicated mess ● Recognizing these as distinct things is a simplified model of languages, not a law of nature. It does not capture every truth about a language, but it helps designers to think about one thing at a time ● How to apply this model is a decision you make, but the theory is most helpful when you stick to isolating the three types of analysis from each other
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