COS 320 Compilers David Walker Outline Last Week Introduction to ML Today Lexical Analysis Reading Chapter 2 of Appel The Front End stream of characters stream of tokens Lexer abstract syntax Parser Type Checker Lexical Analysis Create sequence of tokens from characters Syntax Analysis Create abstract syntax tree from sequence of tokens Type Checking Check program for wellformedness constraints Lexical Analysis Lexical Analysis Breaks stream of ASCII characters source into tokens Token An atomic unit of program syntax i e a word as opposed to a sentence Tokens and their types Characters Recognized foo x listcount 10 45 3 14 2 1 50 100 if Type ID REAL SEMI LPAREN NUM IF Token ID foo ID x REAL 10 45 REAL 3 14 SEMI LPAREN NUM 50 NUM 100 IF Lexical Analysis Example x y 4 0 Lexical Analysis Example x y 4 0 Lexical Analysis ID x Lexical Analysis Example x y 4 0 Lexical Analysis ID x ASSIGN Lexical Analysis Example x y 4 0 Lexical Analysis ID x ASSIGN LPAREN ID y PLUS REAL 4 0 RPAREN SEMI Lexer Implementation Implementation Options 1 Write a Lexer from scratch Boring error prone and too much work Lexer Implementation Implementation Options 1 Write a Lexer from scratch Boring error prone and too much work 2 Use a Lexer Generator Quick and easy Good for lazy compiler writers Lexer Specification Lexer Implementation Implementation Options 1 Write a Lexer from scratch Boring error prone and too much work 2 Use a Lexer Generator Quick and easy Good for lazy compiler writers Lexer Specification Lexer lexer generator Lexer Implementation Implementation Options 1 Write a Lexer from scratch Boring error prone and too much work 2 Use a Lexer Generator Quick and easy Good for lazy compiler writers stream of characters Lexer Specification Lexer lexer generator stream of tokens How do we specify the lexer Develop another language We ll use a language involving regular expressions to specify tokens What is a lexer generator Another compiler Some Definitions We will want to define the language of legal tokens our lexer can recognize Alphabet a collection of symbols ASCII is an alphabet String a finite sequence of symbols taken from our alphabet Language of legal tokens a set of strings Language of ML keywords set of all strings which are ML keywords FINITE Language of ML tokens set of all strings which map to ML tokens INFINITE A language can also be a more general set of strings eg ML Language set of all strings representing correct ML programs INFINITE Regular Expressions Construction Base Cases For each symbol a in alphabet a is a RE denoting the set a Epsilon e denotes Inductive Cases M and N are REs Alternation M N denotes strings in M or N a b a b Concatenation M N denotes strings in M concatenated with strings in N a b a c aa ac ba bc Kleene closure M denotes strings formed by any number of repetitions of strings in M a b e a b aa ab ba bb Regular Expressions Integers begin with an optional minus sign continue with a sequence of digits Regular Expression e 0 1 2 3 4 5 6 7 8 9 Regular Expressions Integers begin with an optional minus sign continue with a sequence of digits Regular Expression e 0 1 2 3 4 5 6 7 8 9 So writing 0 1 2 3 4 5 6 7 8 9 and even worse a b c gets tedious Regular Expressions REs common abbreviations a c n a a a b c any character except n new line character one or more zero or one all abbreviations can be defined in terms of the standard REs Ambiguous Token Rule Sets A single RE is a completely unambiguous specification of a token call the association of an RE with a token a rule To lex an entire programming language we need many rules but ambiguities arise multiple REs or sequences of REs match the same string hence many token sequences possible Ambiguous Token Rule Sets Example Identifier tokens a z a z0 9 Sample keyword tokens if then How do we tokenize foobar if ID foobar or ID foo ID bar ID if or IF Ambiguous Token Rule Sets We resolve ambiguities using two conventions Longest match The regular expression that matches the longest string takes precedence Rule Priority The regular expressions identifying tokens are written down in sequence If two regular expressions match the same longest string the first regular expression in the sequence takes precedence Ambiguous Token Rule Sets Example Identifier tokens a z a z0 9 Sample keyword tokens if then How do we tokenize foobar ID foobar or ID foo ID bar use longest match to disambiguate if ID if or IF keyword rules have higher priority than identifier rule Lexer Implementation Implementation Options 1 Write Lexer from scratch Boring and error prone 2 Use Lexical Analyzer Generator Quick and easy ml lex is a lexical analyzer generator for ML lex and flex are lexical analyzer generators for C ML Lex Specification Lexical specification consists of 3 parts User Declarations plain ML types values functions ML LEX Definitions RE abbreviations special stuff Rules association of REs with tokens each token will be represented in plain ML User Declarations User Declarations User can define various values that are available to the action fragments Two values must be defined in this section type lexresult type of the value returned by each rule action fun eof called by lexer when end of input stream is reached ML LEX Definitions ML LEX Definitions User can define regular expression abbreviations DIGITS 0 9 LETTER a zA Z Define multiple lexers to work together Each is given a unique name s LEX1 LEX2 LEX3 Rules Rules lexer list regular expression action code A rule consists of a pattern and an action Pattern in a regular expression Action is a fragment of ordinary ML code Longest match rule priority used for disambiguation Rules may be prefixed with the list of lexers that are allowed to use this rule Rules Rule actions can use any value defined in the User Declarations section including type lexresult type of value returned by each rule action val eof unit lexresult called by lexer when end of input stream reached special variables yytext input substring matched by regular expression yypos file position of the beginning of matched string continue doesn t return token recursively calls lexer A Simple Lexer datatype token Num of int Id of string IF THEN ELSE EOF type lexresult token mandatory fun eof EOF mandatory fun itos s case Int fromString s of SOME x x NONE raise fail NUM 1 9 0 9 ID a zA Z a zA Z NUM if then else NUM ID IF THEN ELSE Num itos yytext Id yytext Using Multiple Lexers Rules prefixed with a lexer name are matched only