UNIT -1
1.1 OVERVIEW OF LANGUAGE PROCESSING SYSTEM
1.2 Preprocessor
A preprocessor produce input to compilers. They may perform the following functions. 1. Macro processing: A preprocessor may allow a user to define macros that are short hands for longer constructs. 2. File inclusion: A preprocessor may include header files into the program text. 3. Rational preprocessor: these preprocessors augment older languages with more modern flow-of-control and data structuring facilities. 4. Language Extensions: These preprocessor attempts to add capabilities to the language by certain amounts to build-in macro 1.3 COMPILER Compiler is a translator program that translates a program written in (HLL) the source program and translate it into an equivalent program in (MLL) the target program. As an important part of a compiler is error showing to the programmer. Source pgm Compiler Error msg
target pgm
Department of CSE -2-
Executing a program written n HLL programming language is basically of two parts. the source program must first be compiled translated into a object program. Then the results object program is loaded into a memory executed. Source pgm Compiler obj pgm
Obj pgm input
Obj pgm
opj pgm output
1.4 ASSEMBLER: programmers found it difficult to write or read programs in machine language. They begin to use a mnemonic (symbols) for each machine instruction, which they would subsequently translate into machine language. Such a mnemonic machine language is now called an assembly language. Programs known as assembler were written to automate the translation of assembly language in to machine language. The input to an assembler program is called source program, the output is a machine language translation (object program). 1.5 INTERPRETER: An interpreter is a program that appears to execute a source program as if it were machine language.
Languages such as BASIC, SNOBOL, LISP can be translated using interpreters. JAVA also uses interpreter. The process of interpretation can be carried out in following phases. 1. Lexical analysis 2. Synatx analysis 3. Semantic analysis 4. Direct Execution Advantages: Modification of user program can be easily made and implemented as execution proceeds. Type of object that denotes a various may change dynamically. Debugging a program and finding errors is simplified task for a program used for interpretation. The interpreter for the language makes it machine independent.
Department of CSE -3-
JRE Group of Institutions Disadvantages: The execution of the program is slower. Memory consumption is more. 2 Loader and Link-editor: Once the assembler procedures an object program, that program must be placed into memory and executed. The assembler could place the object program directly in memory and transfer control to it, thereby causing the machine language program to be execute. This would waste core by leaving the assembler in memory while the user‟s program was being executed. Also the programmer would have to retranslate his program with each execution, thus wasting translation time. To over come this problems of wasted translation time and memory. System programmers developed another component called loader
“A loader is a program that places programs into memory and prepares them for execution.” It would be more efficient if subroutines could be translated into object form the loader could”relocate” directly behind the user‟s program. The task of adjusting programs o they may be placed in arbitrary core locations is called relocation. Relocation loaders perform four functions.
1.6 TRANSLATOR A translator is a program that takes as input a program written in one language and produces as output a program in another language. Beside program translation, the translator performs another very important role, the error-detection. Any violation of d HLL specification would be detected and reported to the programmers. Important role of translator are: 1 Translating the hll program input into an equivalent ml program. 2 Providing diagnostic messages wherever the programmer violates specification of the hll. 1.7 TYPE OF TRANSLATORS:INTERPRETOR COMPILER PREPROSSESSOR
Department of CSE -4-
JRE Group of Institutions 1.8 LIST OF COMPILERS 1. Ada compilers 2 .ALGOL compilers 3 .BASIC compilers 4 .C# compilers 5 .C compilers 6 .C++ compilers 7 .COBOL compilers 8 .D compilers 9 .Common Lisp compilers 10. ECMAScript interpreters 11. Eiffel compilers 12. Felix compilers 13. Fortran compilers 14. Haskell compilers 15 .Java compilers 16. Pascal compilers 17. PL/I compilers 18. Python compilers 19. Scheme compilers 20. Smalltalk compilers 21. CIL compilers 1.9 STRUCTURE OF THE COMPILER DESIGN Phases of a compiler: A compiler operates in phases. A phase is a logically interrelated operation that takes source program in one representation and produces output in another representation. The phases of a compiler are shown in below There are two phases of compilation. a. Analysis (Machine Independent/Language Dependent) b. Synthesis(Machine Dependent/Language independent) Compilation process is partitioned into no-of-sub processes called ‘phases’.
Department of CSE -5-
JRE Group of Institutions
Lexical Analysis:LA or Scanners reads the source program one character at a time, carving the source program into a sequence of automic units called tokens. Syntax Analysis:The second stage of translation is called Syntax analysis or parsing. In this phase expressions, statements, declarations etc… are identified by using the results of lexical analysis. Syntax analysis is aided by using techniques based on formal grammar of the programming language. Intermediate Code Generations:An intermediate representation of the final machine language code is produced. This phase bridges the analysis and synthesis phases of translation. Code Optimization :This is optional phase described to improve the intermediate code so that the output runs faster and takes less space. Code Generation:The last phase of translation is code generation. A number of optimizations to reduce the length of machine language program are carried out during this phase. The output of the code generator is the machine language program of the specified computer. Table Management (or) Book-keeping:-
Department of CSE -6-
JRE Group of Institutions This is the portion to keep the names used by the program and records essential information about each. The data structure used to record this information called a „Symbol Table‟. Error Handlers:It is invoked when a flaw error in the source program is detected.
The output of LA is a stream of tokens, which is passed to the next phase, the syntax analyzer or parser. The SA groups the tokens together into syntactic structure called as expression. Expression may further be combined to form statements. The syntactic structure can be regarded as a tree whose leaves are the token called as parse trees. The parser has two functions. It checks if the tokens from lexical analyzer, occur in pattern that are permitted by the specification for the source language. It also imposes on tokens a tree-like structure that is used by the sub-sequent phases of the compiler. Example, if a program contains the expression A+/B after lexical analysis this expression might appear to the syntax analyzer as the token sequence id+/id. On seeing the /, the syntax analyzer should detect an error situation, because the presence of these two adjacent binary operators violates the formulations rule of an expression. Syntax analysis is to make explicit the hierarchical structure of the incoming token stream by identifying which parts of the token stream should be grouped. Example, (A/B*C has two possible interpretations.) 1, divide A by B and then multiply by C or 2, multiply B by C and then use the result to divide A. each of these two interpretations can be represented in terms of a parse tree. Intermediate Code Generation:The intermediate code generation uses the structure produced by the syntax analyzer to create a stream of simple instructions. Many styles of intermediate code are possible. One common style uses instruction with one operator and a small number of operands. The output of the syntax analyzer is some representation of a parse tree. the intermediate code generation phase transforms this parse tree into an intermediate language representation of the source program. Code Optimization This is optional phase described to improve the intermediate code so that the output runs faster and takes less space. Its output is another intermediate code program that does the some job as the original, but in a way that saves time and / or spaces. 1, Local Optimization:There are local transformations that can be applied to a program to make an improvement. For example, If A > B goto L2 Department of CSE -7-
JRE Group of Institutions Goto L3 L2 : This can be replaced by a single statement If A < B goto L3 Another important local optimization is the elimination of common sub-expressions A := B + C + D E := B + C + F Might be evaluated as T1 := B + C A := T1 + D E := T1 + F Take this advantage of the common sub-expressions B + C. 2, Loop Optimization:Another important source of optimization concerns about increasing the speed of loops. A typical loop improvement is to move a computation that produces the same result each time around the loop to a point, in the program just before the loop is entered. Code generator :Cg produces the object code by deciding on the memory locations for data, selecting code to access each datum and selecting the registers in which each computation is to be done. Many computers have only a few high speed registers in which computations can be performed quickly. A good code generator would attempt to utilize registers as efficiently as possible. Table Management OR Book-keeping :A compiler needs to collect information about all the data objects that appear in the source program. The information about data objects is collected by the early phases of the compiler-lexical and syntactic analyzers. The data structure used to record this information is called as Symbol Table. Error Handing :One of the most important functions of a compiler is the detection and reporting of errors in the source program. The error message should allow the programmer to determine exactly where the errors have occurred. Errors may occur in all or the phases of a compiler. Whenever a phase of the compiler discovers an error, it must report the error to the error handler, which issues an appropriate diagnostic msg. Both of the table-management and error-Handling routines interact with all phases of the compiler.
Department of CSE -8-
JRE Group of Institutions Example: Position:= initial + rate *60
Semantic Analyzer = id1 id2 id3 + * 60 int to real Intermediate Code Generator temp1:= int to real (60) temp2:= id3 * temp1 temp3:= id2 + temp2 id1:= temp3.
Code Optimizer Temp1:= id3 * 60.0 Department of CSE -9-
JRE Group of Institutions Id1:= id2 +temp1
Code Generator
MOVF MULF MOVF ADDF MOVF
id3, r2 *60.0, r2 id2, r2 r2, r1 r1, id1
1.10 TOKEN LA reads the source program one character at a time, carving the source program into a sequence of automatic units called „Tokens‟. 1, Type of the token. 2, Value of the token. Type : variable, operator, keyword, constant Value : N1ame of variable, current variable (or) pointer to symbol table. If the symbols given in the standard format the LA accepts and produces token as output. Each token is a sub-string of the program that is to be treated as a single unit. Token are two types. 1, Specific strings such as IF (or) semicolon. 2, Classes of string such as identifiers, label, constants.
Department of CSE - 10 -
UNIT -2 LEXICAL ANALYSIS
2.1 OVER VIEW OF LEXICAL ANALYSIS o To identify the tokens we need some method of describing the possible tokens that can appear in the input stream. For this purpose we introduce regular expression, a notation that can be used to describe essentially all the tokens of programming language. o Secondly , having decided what the tokens are, we need some mechanism to recognize these in the input stream. This is done by the token recognizers, which are designed using transition diagrams and finite automata. 2.2 ROLE OF LEXICAL ANALYZER the LA is the first phase of a compiler. It main task is to read the input character and produce as output a sequence of tokens that the parser uses for syntax analysis.
Upon receiving a „get next token‟ command form the parser, the lexical analyzer reads the input character until it can identify the next token. The LA return to the parser representation for the token it has found. The representation will be an integer code, if the token is a simple construct such as parenthesis, comma or colon. LA may also perform certain secondary tasks as the user interface. One such task is striping out from the source program the commands and white spaces in the form of blank, tab and new line characters. Another is correlating error message from the compiler with the source program.
Department of CSE - 11 -
2.3 LEXICAL ANALYSIS VS PARSING:
Lexical analysis
A Scanner simply turns an input String (say a file) into a list of tokens. These tokens represent things like identifiers, parentheses, operators etc. The lexical analyzer (the "lexer") parses individual symbols from the source code file into tokens. From there, the "parser" proper turns those whole tokens into sentences of your grammar
Parsing
A parser converts this list of tokens into a Tree-like object to represent how the tokens fit together to form a cohesive whole (sometimes referred to as a sentence). A parser does not give the nodes any meaning beyond structural cohesion. The next thing to do is extract meaning from this structure (sometimes called contextual analysis).
2.4 TOKEN, LEXEME, PATTERN: Token: Token is a sequence of characters that can be treated as a single logical entity. Typical tokens are, 1) Identifiers 2) keywords 3) operators 4) special symbols 5)constants Pattern: A set of strings in the input for which the same token is produced as output. This set of strings is described by a rule called a pattern associated with the token. Lexeme: A lexeme is a sequence of characters in the source program that is matched by the pattern for a token. Example: Description of token Token const if relation i nun literal lexeme const if =,> pi 3.14 "core" pattern const If < or or >= or letter followed by letters & digit any numeric constant any character b/w “and “except" pattern
Department of CSE - 12 -
JRE Group of Institutions A patter is a rule describing the set of lexemes that can represent a particular token in source program. 2.5 LEXICAL ERRORS: Lexical errors are the errors thrown by your lexer when unable to continue. Which means that there's no way to recognise a lexeme as a valid token for you lexer. Syntax errors, on the other side, will be thrown by your scanner when a given set of already recognised valid tokens don't match any of the right sides of your grammar rules. simple panic-mode error handling system requires that we return to a high-level parsing function when a parsing or lexical error is detected. Error-recovery actions are: i. Delete one character from the remaining input. ii. Insert a missing character in to the remaining input. iii. Replace a character by another character. iv. Transpose two adjacent characters.
2.6 DIFFERENCE BETWEEN COMPILER AND INTERPRETER
A compiler converts the high level instruction into machine language while an interpreter converts the high level instruction into an intermediate form. Before execution, entire program is executed by the compiler whereas after translating the first line, an interpreter then executes it and so on. List of errors is created by the compiler after the compilation process while an interpreter stops translating after the first error. An independent executable file is created by the compiler whereas interpreter is required by an interpreted program each time. The compiler produce object code whereas interpreter does not produce object code. In the process of compilation the program is analyzed only once and then the code is generated whereas source program is interpreted every time it is to be executed and every time the source program is analyzed. hence interpreter is less efficient than compiler. Examples of interpreter: A UPS Debugger is basically a graphical source level debugger but it contains built in C interpreter which can handle multiple source files. example of compiler: Borland c compiler or Turbo C compiler compiles the programs written in C or C++.
Department of CSE - 13 -
JRE Group of Institutions 2.7 REGULAR EXPRESSIONS Regular expression is a formula that describes a possible set of string. Component of regular expression.. X the character x . any character, usually accept a new line [x y z] any of the characters x, y, z, ….. R? a R or nothing (=optionally as R) R* zero or more occurrences….. R+ one or more occurrences …… R1R2 an R1 followed by an R2 R2R1 either an R1 or an R2. A token is either a single string or one of a collection of strings of a certain type. If we view the set of strings in each token class as an language, we can use the regular-expression notation to describe tokens. Consider an identifier, which is defined to be a letter followed by zero or more letters or digits. In regular expression notation we would write. Identifier = letter (letter | digit)* Here are the rules that define the regular expression over alphabet . o is a regular expression denoting { € }, that is, the language containing only the empty string. o For each „a‟ in ∑, is a regular expression denoting { a }, the language with only one string consisting of the single symbol „a‟ . o If R and S are regular expressions, then (R) | (S) means LrULs R.S means Lr.Ls R* denotes Lr* 2.8 REGULAR DEFINITIONS For notational convenience, we may wish to give names to regular expressions and to define regular expressions using these names as if they were symbols. Identifiers are the set or string of letters and digits beginning with a letter. The following regular definition provides a precise specification for this class of string. Example-1, Ab*|cd? Is equivalent to (a(b*)) | (c(d?)) Pascal identifier Letter - A | B | ……| Z | a | b |……| z| Digits - 0 | 1 | 2 | …. | 9 letter (letter / digit)* I d -
Department of CSE - 14 -
JRE Group of Institutions Recognition of tokens: We learn how to express pattern using regular expressions. Now, we must study how to take the patterns for all the needed tokens and build a piece of code that examins the input string and finds a prefix that is a lexeme matching one of the patterns. Stmt
Expr Term
if expr then stmt | If expr then else stmt |є
term relop term | term id |number
For relop ,we use the comparison operations of languages like Pascal or SQL where = is “equals” and < > is “not equals” because it presents an interesting structure of lexemes. The terminal of grammar, which are if, then , else, relop ,id and numbers are the names of tokens as far as the lexical analyzer is concerned, the patterns for the tokens are described using regular definitions. digit digits number letter id if then else relop -->[0,9] -->digit+ -->digit(.digit)?(e.[+-]?digits)? -->[A-Z,a-z] -->letter(letter/digit)* --> if -->then -->else -->/=/==/< >
In addition, we assign the lexical analyzer the job stripping out white space, by recognizing the “token” we defined by: ws
(blank/tab/newline)
+
Here, blank, tab and newline are abstract symbols that we use to express the ASCII characters of the same names. Token ws is different from the other tokens in that ,when we recognize it, we do not return it to parser ,but rather restart the lexical analysis from the character that follows the white space . It is the following token that gets returned to the parser. Lexeme Token Name Attribute Value Any ws _ _ if if _ then then _ else else _ Any id id pointer to table entry Any number number pointer to table entry < relop LT Department of CSE - 15 -
JRE Group of Institutions = letter (letter | digit) *| digit |
JRE Group of Institutions 2, each input symbol has at most one transition from any state. DFA formally defined by 5 tuple notation M = (Q, ∑, δ, qo, F), where Q is a finite „set of states‟, which is non empty. ∑ is „input alphabets‟, indicates input set. qo is an „initial state‟ and qo is in Q ie, qo, ∑, Q F is a set of „Final states‟, δ is a „transmission function‟ or mapping function, using this function the next state can be determined. The regular expression is converted into minimized DFA by the following procedure: Regular expression → NFA → DFA → Minimized DFA The Finite Automata is called DFA if there is only one path for a specific input from current state to next state. a So a S2
b
S1
From state S0 for input „a‟ there is only one path going to S2. similarly from S0 there is only one path for input going to S1.
2.13 NONDETERMINISTIC AUTOMATA A NFA is a mathematical model that consists of
A set of states S.
A set of input symbols ∑.
A transition for move from one state to an other.
A state so that is distinguished as the start (or initial) state. A set of states F distinguished as accepting (or final) state. A number of transition to a single symbol.
Department of CSE - 18 -
JRE Group of Institutions A NFA can be diagrammatically represented by a labeled directed graph, called a transition graph, In which the nodes are the states and the labeled edges represent the transition function. This graph looks like a transition diagram, but the same character can label two or more transitions out of one state and edges can be labeled by the special symbol € as well as by input symbols. The transition graph for an NFA that recognizes the language ( a | b ) * abb is shown
2.14 DEFINITION OF CFG It involves four quantities. CFG contain terminals, N-T, start symbol and production. Terminal are basic symbols form which string are formed. N-terminals are synthetic variables that denote sets of strings In a Grammar, one N-T are distinguished as the start symbol, and the set of string it denotes is the language defined by the grammar. The production of the grammar specify the manor in which the terminal and N-T can be combined to form strings. Each production consists of a N-T, followed by an arrow, followed by a string of one terminal and terminals.
2.15 DEFINITION OF SYMBOL TABLE An extensible array of records. The identifier and the associated records contains collected information about the identifier. FUNCTION identify (Identifier name) RETURNING a pointer to identifier information contains The actual string A macro definition A keyword definition A list of type, variable & function definition A list of structure and union name definition A list of structure and union field selected definitions.
Department of CSE - 19 -
JRE Group of Institutions
2.16 Creating a lexical analyzer with Lex
2.17 Lex specifications:
A Lex program (the .l file ) consists of three parts: declarations %% translation rules %% auxiliary procedures 1. The declarations section includes declarations of variables,manifest constants(A manifest constant is an identifier that is declared to represent a constant e.g. # define PIE 3.14), and regular definitions. 2. The translation rules of a Lex program are statements of the form : p1 {action 1} p2 {action 2} p3 {action 3} … … … … where each p is a regular expression and each action is a program fragment describing what action the lexical analyzer should take when a pattern p matches a lexeme. In Lex the actions are written in C. 3. The third section holds whatever auxiliary procedures are needed by the actions.Alternatively these procedures can be compiled separately and loaded with the lexical analyzer. Department of CSE - 20 -
JRE Group of Institutions
Note: You can refer to a sample lex program given in page no. 109 of chapter 3 of the book: Compilers: Principles, Techniques, and Tools by Aho, Sethi & Ullman for more clarity.
2.18 INPUT BUFFERING The LA scans the characters of the source pgm one at a time to discover tokens. Because of large amount of time can be consumed scanning characters, specialized buffering techniques have been developed to reduce the amount of overhead required to process an input character. Buffering techniques: 1. Buffer pairs 2. Sentinels The lexical analyzer scans the characters of the source program one a t a time to discover tokens. Often, however, many characters beyond the next token many have to be examined before the next token itself can be determined. For this and other reasons, it is desirable for thelexical analyzer to read its input from an input buffer. Figure shows a buffer divided into two haves of, say 100 characters each. One pointer marks the beginning of the token being discovered. A look ahead pointer scans ahead of the beginning point, until the token is discovered .we view the position of each pointer as being between the character last read and thecharacter next to be read. In practice each buffering scheme adopts one convention either apointer is at the symbol last read or the symbol it is ready to read.
Token beginnings look ahead pointerThe distance which the lookahead pointer may have to travel past the actual token may belarge. For example, in a PL/I program we may see: DECALRE (ARG1, ARG2… ARG n) Without knowing whether DECLARE is a keyword or an array name until we see the character that follows the right parenthesis. In either case, the token itself ends at the second E. If the look ahead pointer travels beyond the buffer half in which it began, the other half must be loaded with the next characters from the source file. Since the buffer shown in above figure is of limited size there is an implied constraint on how much look ahead can be used before the next token is discovered. In the above example, ifthe look ahead traveled to the left half and all the way through the left half to the middle, we could not reload the right half, because we would lose characters that had not yet been groupedinto tokens. While we can make the buffer larger if we chose or use another buffering scheme,we cannot ignore the fact that overhead is limited.
Department of CSE - 21 -
JRE Group of Institutions
UNIT -3 SYNTAX ANALYSIS
3.1 ROLE OF THE PARSER Parser obtains a string of tokens from the lexical analyzer and verifies that it can be generated by the language for the source program. The parser should report any syntax errors in an intelligible fashion. The two types of parsers employed are: 1.Top down parser: which build parse trees from top(root) to bottom(leaves) 2.Bottom up parser: which build parse trees from leaves and work up the root. Therefore there are two types of parsing methods– top-down parsing and bottom-up parsing
3.2 TOP-DOWN PARSING A program that performs syntax analysis is called a parser. A syntax analyzer takes tokens as input and output error message if the program syntax is wrong. The parser uses symbol-lookahead and an approach called top-down parsing without backtracking. Top-downparsers check to see if a string can be generated by a grammar by creating a parse tree starting from the initial symbol and working down. Bottom-up parsers, however, check to see a string can be generated from a grammar by creating a parse tree from the leaves, and working up. Early parser generators such as YACC creates bottom-up parsers whereas many of Java parser generators such as JavaCC create top-down parsers.
3.3RECURSIVE DESCENT PARSING
Typically, top-down parsers are implemented as a set of recursive functions that descent through a parse tree for a string. This approach is known as recursive descent parsing, also known as LL(k) parsing where the first L stands for left-to-right, the second L stands for
Department of CSE - 22 -
JRE Group of Institutions leftmost-derivation, and k indicates k-symbol lookahead. Therefore, a parser using the single symbol look-ahead method and top-down parsing without backtracking is called LL(1) parser. In the following sections, we will also use an extended BNF notation in which some regulation expression operators are to be incorporated. A syntax expression defines sentences of the form , or . A syntax of the form defines sentences that consist of a sentence of the form followed by a sentence of the form followed by a sentence of the form . A syntax of the form defines zero or one occurrence of the form . A syntax of the form defines zero or more occurrences of the form . A usual implementation of an LL(1) parser is: o initialize its data structures, o get the lookahead token by calling scanner routines, and o call the routine that implements the start symbol.
Here is an example. proc syntaxAnalysis() begin initialize(); // initialize global data and structures nextToken(); // get the lookahead token
program(); // parser routine that implements the start symbol end;
3.4 FIRST AND FOLLOW To compute FIRST(X) for all grammar symbols X, apply the following rules until no more terminals or e can be added to any FIRST set. 1. If X is terminal, then FIRST(X) is {X}. 2. If X->e is a production, then add e to FIRST(X). 3. If X is nonterminal and X->Y1Y2...Yk is a production, then place a in FIRST(X) if for some i, a is in FIRST(Yi) and e is in all of FIRST(Y1),...,FIRST(Yi-1) that is, Y1.......Yi1=*>e. If e is in FIRST(Yj) for all j=1,2,...,k, then add e to FIRST(X). For example, everything in FIRST(Yj) is surely in FIRST(X). If y1 does not derive e, then we add nothing more to FIRST(X), but if Y1=*>e, then we add FIRST(Y2) and so on. Department of CSE - 23 -
JRE Group of Institutions To compute the FIRST(A) for all nonterminals A, apply the following rules until nothing can be added to any FOLLOW set. 1. Place $ in FOLLOW(S), where S is the start symbol and $ in the input right endmarker. 2. If there is a production A=>aBs where FIRST(s) except e is placed in FOLLOW(B). 3. If there is aproduction A->aB or a production A->aBs where FIRST(s) contains e, then everything in FOLLOW(A) is in FOLLOW(B). Consider the following example to understand the concept of First and Follow.Find the first and follow of all nonterminals in the GrammarE -> TE' E'-> +TE'|e T -> FT' T'-> *FT'|e F -> (E)|id Then:
For example, id and left parenthesis are added to FIRST(F) by rule 3 in definition of FIRST with i=1 in each case, since FIRST(id)=(id) and FIRST('(')= {(} by rule 1. Then by rule 3 with i=1, the production T -> FT' implies that id and left parenthesis belong to FIRST(T) also. To compute FOLLOW,we put $ in FOLLOW(E) by rule 1 for FOLLOW. By rule 2 applied toproduction F-> (E), right parenthesis is also in FOLLOW(E). By rule 3 applied to production E-> TE', $ and right parenthesis are in FOLLOW(E').
Department of CSE - 24 -
JRE Group of Institutions 3.5 CONSTRUCTION OF PREDICTIVE PARSING TABLES For any grammar G, the following algorithm can be used to construct the predictive parsing table. The algorithm is Input : Grammar G Output : Parsing table M Method 1. 1.For each production A-> a of the grammar, do steps 2 and 3. 2. For each terminal a in FIRST(a), add A->a, to M[A,a]. 3. If e is in First(a), add A->a to M[A,b] for each terminal b in FOLLOW(A). If e is in FIRST(a) and $ is in FOLLOW(A), add A->a to M[A,$]. 4. Make each undefined entry of M be error.
3.6.LL(1) GRAMMAR The above algorithm can be applied to any grammar G to produce a parsing table M. For some Grammars, for example if G is left recursive or ambiguous, then M will have at least one multiply-defined entry. A grammar whose parsing table has no multiply defined entries is said to be LL(1). It can be shown that the above algorithm can be used to produce for every LL(1) grammar G a parsing table M that parses all and only the sentences of G. LL(1) grammars have several distinctive properties. No ambiguous or left recursive grammar can be LL(1). There remains a question of what should be done in case of multiply defined entries. One easy solution is to eliminate all left recursion and left factoring, hoping to produce a grammar which will produce no multiply defined entries in the parse tables. Unfortunately there are some grammars which will give an LL(1) grammar after any kind of alteration. In general, there are no universal rules to convert multiply defined entries into single valued entries without affecting the language recognized by the parser.
The main difficulty in using predictive parsing is in writing a grammar for the source language such that a predictive parser can be constructed from the grammar. Although left recursion elimination and left factoring are easy to do, they make the resulting grammar hard to read and difficult to use the translation purposes. To alleviate some of this difficulty, a common organization for a parser in a compiler is to use a predictive parser for control Department of CSE - 25 -
JRE Group of Institutions constructs and to use operator precedence for expressions.however, if an lr parser generator is available, one can get all the benefits of predictive parsing and operator precedence automatically. 3.7.ERROR RECOVERY IN PREDICTIVE PARSING The stack of a nonrecursive predictive parser makes explicit the terminals and nonterminals that the parser hopes to match with the remainder of the input. We shall therefore refer to symbols on the parser stack in the following discussion. An error is detected during predictive parsing when the terminal on top of the stack does not match the next input symbol or when nonterminal A is on top of the stack, a is the next input symbol, and the parsing table entry M[A,a] is empty. Panic-mode error recovery is based on the idea of skipping symbols on the input until a token in a selected set of synchronizing tokens appears. Its effectiveness depends on the choice of synchronizing set. The sets should be chosen so that the parser recovers quickly from errors that are likely to occur in practice. Some heuristics are as follows
As a starting point, we can place all symbols in FOLLOW(A) into the synchronizing set for nonterminal A. If we skip tokens until an element of FOLLOW(A) is seen and pop A from the stack, it is likely that parsing can continue. It is not enough to use FOLLOW(A) as the synchronizingset for A. Fo example , if semicolons terminate statements, as in C, then keywords that begin statements may not appear in the FOLLOW set of the nonterminal generating expressions. A missing semicolon after an assignment may therefore result in the keyword beginning the next statement being skipped. Often, there is a hierarchica structure on constructs in a language; e.g., expressions appear within statement, which appear within bblocks,and so on. We can add to the synchronizing set of a lower construct the symbols that begin higher constructs. For example, we might add keywords that begin statements to the synchronizing sets for the nonterminals generaitn expressions. If we add symbols in FIRST(A) to the synchronizing set for nonterminal A, then it may be possible to resume parsing according to A if a symbol in FIRST(A) appears in the input.
Department of CSE - 26 -
JRE Group of Institutions If a nonterminal can generate the empty string, then the production deriving e can be used as a default. Doing so may postpone some error detection, but cannot cause an error to be missed. This approach reduces the number of nonterminals that have to be considered during error recovery. If a terminal on top of the stack cannot be matched, a simple idea is to pop the terminal, issue a message saying that the terminal was inserted, and continue parsing. In effect, this approach takes the synchronizing set of a token to consist of all other tokens.
Department of CSE - 27 -
JRE Group of Institutions
UNIT 4 LR PARSER
4.1 LR PARSING INTRODUCTION The "L" is for left-to-right scanning of the input and the "R" is for constructing a rightmost derivation in reverse.
4.2 WHY LR PARSING:
LR parsers can be constructed to recognize virtually all programming-language constructs for which context-free grammars can be written. The LR parsing method is the most general non-backtracking shift-reduce parsing method known, yet it can be implemented as efficiently as other shift-reduce methods.
The class of grammars that can be parsed using LR methods a proper subset of the is class of grammars that can be parsed with predictive parsers. An LR parser can detect a syntactic error as soon as it is possible to do so on a left-toright scan of the input.
The disadvantage is that it takes too much work to constuct an LR parser by hand for a typical programming-language grammar. But there are lots of LR parser generators available to make this task easy.
Department of CSE - 28 -
JRE Group of Institutions 4.3.MODELS OF LR PARSERS The schematic form of an LR parser is shown below.
The program uses a stack to store a string of the form s0X1s1X2...Xmsm where sm is on top. Each Xi is a grammar symbol and each si is a symbol representing a state. Each state symbol summarizes the information contained in the stack below it. The combination of the state symbol on top of the stack and the current input symbol are used to index the parsing table and determine the shiftreduce parsing decision. The parsing table consists of two parts: a parsing action function action and a goto function goto. The program driving the LR parser behaves as follows: It determines sm the state currently on top of the stack and ai the current input symbol. It then consults action[sm,ai], which can have one of four values:
shift s, where s is a state
reduce by a grammar production A -> b accept error
Department of CSE - 29 -
JRE Group of Institutions The function goto takes a state and grammar symbol as arguments and produces a state. For a parsing table constructed for a grammar G, the goto table is the transition function of a deterministic finite automaton that recognizes the viable prefixes of G. Recall that the viable prefixes of G are those prefixes of right-sentential forms that can appear on the stack of a shiftreduce parser because they do not extend past the rightmost handle. A configuration of an LR parser is a pair whose first component is the stack contents and whose second component is the unexpended input: (s0 X1 s1 X2 s2... Xm sm, ai ai+1... an$) This configuration represents the right-sentential form X1 X1 ... Xm ai ai+1 ...an in essentially the same way a shift-reduce parser would; only the presence of the states on the stack is new. Recall the sample parse we did (see Example 1: Sample bottom-up parse) in which we assembled the right-sentential form by concatenating the remainder of the input buffer to the top of the stack. The next move of the parser is determined by reading ai and sm, and consulting the parsing action table entry action[sm, ai]. Note that we are just looking at the state here and no symbol below it. We'll see how this actually works later. The configurations resulting after each of the four types of move are as follows: If action[sm, ai] = shift s, the parser executes a shift move entering the configuration (s0 X1 s1 X2 s2... Xm sm ai s, ai+1... an$) Here the parser has shifted both the current input symbol ai and the next symbol. If action[sm, ai] = reduce A -> b, then the parser executes a reduce move, entering the configuration, (s0 X1 s1 X2 s2... Xm-r sm-r A s, ai ai+1... an$) where s = goto[sm-r, A] and r is the length of b, the right side of the production. The parser first popped 2r symbols off the stack (r state symbols and r grammar symbols), exposing state sm-r. The parser then pushed both A, the left side of the production, and s, the entry for goto[sm-r, A], onto the stack. The current input symbol is not changed in a reduce move. The output of an LR parser is generated after a reduce move by executing the semantic action associated with the reducing production. For example, we might just print out the production reduced. If action[sm, ai] = accept, parsing is completed. Department of CSE - 30 -
JRE Group of Institutions 4.4.OPERATOR PRECEDENCE PARSING Precedence Relations Bottom-up parsers for a large class of context-free grammars can be easily developed using operator grammars.Operator grammars have the property that no production right side is empty or has two adjacent nonterminals. This property enables the implementation of efficient operator-precedence parsers. These parser rely on the following three precedence relations: Relation Meaning a b a takes precedence over b These operator precedence relations allow to delimit the handles in the right sentential forms: marks the right end.
Example: The input string: id1 + id2 * id3 after inserting precedence relations becomes $ + * $ Having precedence relations allows to identify handles as follows:
scan the string from left until seeing ·>
scan backwards the string from right to left until seeing .E + T] [E -> E. + T] [E -> E +. T] [E -> E + T.]
Department of CSE - 36 -
JRE Group of Institutions 4.11 CONSTRUCTING THE SLR PARSING TABLE To construct the parser table we must convert our NFA into a DFA. The states in the LR table will be the e-closures of the states corresponding to the items SO...the process of creating the LR state table parallels the process of constructing an equivalent DFA from a machine with e-transitions. Been there, done that - this is essentially the subset construction algorithm so we are in familiar territory here. We need two operations: closure() and goto(). closure() If I is a set of items for a grammar G, then closure(I) is the set of items constructed from I by the two rules: Initially every item in I is added to closure(I) If A -> a.Bb is in closure(I), and B -> g is a production, then add the initial item [B -> .g] to I, if it is not already there. Apply this rule until no more new items can be added to closure(I). From our grammar above, if I is the set of one item {[E'-> .E]}, then closure(I) contains: I0: E' -> .E E -> .E + T E -> .T T -> .T * F T -> .F F -> .(E) F -> .id goto() goto(I, X), where I is a set of items and X is a grammar symbol, is defined to be the closure of the set of all items [A -> aX.b] such that [A -> a.Xb] is in I. The idea here is fairly intuitive: if I is the set of items that are valid for some viable prefix g, then goto(I, X) is the set of items that are valid for the viable prefix gX. 4.12 SETS-OF-ITEMS-CONSTRUCTION To construct the canonical collection of sets of LR(0) items for augmented grammar G'. procedure items(G') begin Department of CSE - 37 -
JRE Group of Institutions C := {closure({[S' -> .S]})}; repeat for each set of items in C and each grammar symbol X such that goto(I, X) is not empty and not in C do add goto(I, X) to C; until no more sets of items can be added to C end; 4.13 ALGORITHM FOR CONSTRUCTING AN SLR PARSING TABLE Input: augmented grammar G' Output: SLR parsing table functions action and goto for G' Method: Construct C = {I0, I1 , ..., In} the collection of sets of LR(0) items for G'. State i is constructed from Ii: if [A -> a.ab] is in Ii and goto(Ii, a) = Ij, then set action[i, a] to "shift j". Here a must be a terminal. if [A -> a.] is in Ii, then set action[i, a] to "reduce A -> a" for all a in FOLLOW(A). Here A may not be S'. if [S' -> S.] is in Ii, then set action[i, $] to "accept" If any conflicting actions are generated by these rules, the grammar is not SLR(1) and the algorithm fails to produce a parser. The goto transitions for state i are constructed for all nonterminals A using the rule: If goto(Ii, A)= Ij, then goto[i, A] = j. All entries not defined by rules 2 and 3 are made "error". The inital state of the parser is the one constructed from the set of items containing [S' -> .S]. Let's work an example to get a feel for what is going on, An Example (1) E -> E * B (2) E -> E + B (3) E -> B (4) B -> 0 (5) B -> 1 Department of CSE - 38 -
JRE Group of Institutions The Action and Goto Table The two LR(0) parsing tables for this grammar look as follows:
Department of CSE - 39 -
JRE Group of Institutions
UNIT -5
5.1 CANONICAL LR PARSING By splitting states when necessary, we can arrange to have each state of an LR parser indicate exactly which input symbols can follow a handle a for which there is a possible reduction to A. As the text points out, sometimes the FOLLOW sets give too much informationand doesn't (can't) discriminate between different reductions. The general form of an LR(k) item becomes [A -> a.b, s] where A -> ab is a production and s is a string of terminals. The first part (A -> a.b) is called the core and the second part is the lookahead. In LR(1) |s| is 1, so s is a single terminal. A -> ab is the usual righthand side with a marker; any a in s is an incoming token in which we are interested. Completed items used to be reduced for every incoming token in FOLLOW(A), but now we will reduce only if the next input token is in the lookahead set s..if we get two productions A -> a and B -> a, we can tell them apart when a is a handle on the stack if the corresponding completed items have different lookahead parts. Furthermore, note that the lookahead has no effect for an item of the form [A -> a.b, a] if b is not e. Recall that our problem occurs for completed items, so what we have done now is to say that an item of the form [A -> a., a] calls for a reduction by A -> a only if the next input symbol is a. More formally, an LR(1) item [A -> a.b, a] is valid for a viable prefix g if there is a derivation S =>* s abw, where g = sa, and either a is the first symbol of w, or w is e and a is $. 5.2 ALGORITHM FOR CONSTRUCTION OF THE SETS OF LR(1) ITEMS Input: grammar G' Output: sets of LR(1) items that are the set of items valid for one or more viable prefixes of G' Method: closure(I) begin repeat
for each item [A -> a.Bb, a] in I, each production B -> g in G', and each terminal b in FIRST(ba) Department of CSE - 40 -
JRE Group of Institutions such that [B -> .g, b] is not in I do add [B -> .g, b] to I; until no more items can be added to I; end; 5.3 goto(I, X) begin let J be the set of items [A -> aX.b, a] such that [A -> a.Xb, a] is in I return closure(J); end; procedure items(G') begin C := {closure({S' -> .S, $})}; repeat for each set of items I in C and each grammar symbol X such that goto(I, X) is not empty and not in C do add goto(I, X) to C until no more sets of items can be added to C; end; An example, Consider the following grammer, S‟->S S->CC C->cC C->d Sets of LR(1) items I0: S‟->.S,$ S->.CC,$ C->.Cc,c/d C->.d,c/d I1:S‟->S.,$ I2:S->C.C,$ C->.Cc,$ C->.d,$
Department of CSE - 41 -
JRE Group of Institutions I3:C->c.C,c/d C->.Cc,c/d C->.d,c/d
I4: C->d.,c/d I5: S->CC.,$ I6: C->c.C,$ C->.cC,$ C->.d,$ I7:C->d.,$ I8:C->cC.,c/d I9:C->cC.,$ Here is what the corresponding DFA looks like
Department of CSE - 42 -
JRE Group of Institutions
5.4 ALGORITHM FOR PARSING TABLE
CONSTRUCTION
OF
THE
CANONICAL
LR
Input: grammar G' Output: canonical LR parsing table functions action and goto 1. Construct C = {I0, I1 , ..., In} the collection of sets of LR(1) items for G'.State i is constructed from Ii. 2. if [A -> a.ab, b>] is in Ii and goto(Ii, a) = Ij, then set action[i, a] to "shift j". Here a must be a terminal. 3. if [A -> a., a] is in Ii, then set action[i, a] to "reduce A -> a" for all a in FOLLOW(A). Here A may not be S'. 4. if [S' -> S.] is in Ii, then set action[i, $] to "accept" 5. If any conflicting actions are generated by these rules, the grammar is not LR(1) and the algorithm fails to produce a parser. 6. The goto transitions for state i are constructed for all nonterminals A using the rule: If goto(Ii, A)= Ij, then goto[i, A] = j. 7. All entries not defined by rules 2 and 3 are made "error". 8. The inital state of the parser is the one constructed from the set of items containing [S' -> .S, $].
Department of CSE - 43 -
JRE Group of Institutions
5.5.LALR PARSER: We begin with two observations. First, some of the states generated for LR(1) parsing have the same set of core (or first) components and differ only in their second component, the lookahead symbol. Our intuition is that we should be able to merge these states and reduce the number of states we have, getting close to the number of states that would be generated for LR(0) parsing. This observation suggests a hybrid approach: We can construct the canonical LR(1) sets of items and then look for sets of items having the same core. We merge these sets with common cores into one set of items. The merging of states with common cores can never produce a shift/reduce conflict that was not present in one of the original states because shift actions depend only on the core, not the lookahead. But it is possible for the merger to produce a reduce/reduce conflict. Our second observation is that we are really only interested in the lookahead symbol in places where there is a problem. So our next thought is to take the LR(0) set of items and add lookaheads only where they are needed. This leads to a more efficient, but much more complicated method. 5.6 ALGORITHM FOR EASY CONSTRUCTION OF AN LALR TABLE Input: G' Output: LALR parsing table functions with action and goto for G'. Method: 1. Construct C = {I0, I1 , ..., In} the collection of sets of LR(1) items for G'. 2. For each core present among the set of LR(1) items, find all sets having that core and replace these sets by the union. 3. Let C' = {J0, J1 , ..., Jm} be the resulting sets of LR(1) items. The parsing actions for state i are constructed from Ji in the same manner as in the construction of the canonical LR parsing table. 4. If there is a conflict, the grammar is not LALR(1) and the algorithm fails. 5. The goto table is constructed as follows: If J is the union of one or more sets of LR(1) items, that is, J = I0U I1 U ... U Ik, then the cores of goto(I0, X), goto(I1, X), ..., goto(Ik, X) are the same, since I0, I1 , ..., Ik all have the same core. Let K be the union of all sets of items having the same core asgoto(I1, X). Department of CSE - 44 -
JRE Group of Institutions 6. Then goto(J, X) = K. Consider the above example, I3 & I6 can be replaced by their union I36:C->c.C,c/d/$ C->.Cc,C/D/$ C->.d,c/d/$ I47:C->d.,c/d/$ I89:C->Cc.,c/d/$ Parsing Table
state 0 1 2 36 47 5 89
c S36
d S47
$
S 1
C 2
Accept S36 S36 R3 S47 S47 R3 R1 R2 R2 R2 5 89
5.7HANDLING ERRORS The LALR parser may continue to do reductions after the LR parser would have spotted an error, but the LALR parser will never do a shift after the point the LR parser would have discovered the error and will eventually find the error.
5.8 DANGLING ELSE The dangling else is a problem in computer programming in which an optional else clause in an If–then(–else) statement results in nested conditionals being ambiguous. Formally, the context-free grammar of the language is ambiguous, meaning there is more than one correct parse tree.
Department of CSE - 45 -
JRE Group of Institutions In many programming languages one may write conditionally executed code in two forms: the if-then form, and the if-then-else form – the else clause is optional:
Consider the grammar: S ::= E $ E ::= E + E |E*E |(E) | id | num and four of its LALR(1) states: I0: S ::= . E $ ? I1: S ::= E . $ ?I2: E ::= E * . E E ::= . E + E E ::= . E * E E ::= . ( E ) I3: E ::= E * E . E ::= E . + E Department of CSE - 46 +*$ +*$ E ::= . id E ::= . num +*$ +*$ +*$ +*$ +*$ +*$
E ::= . E + E +*$ E ::= . E * E +*$ E ::= . ( E ) +*$ E ::= . id +*$ E ::= . num +*$
E ::= E . + E +*$ E ::= E . * E +*$
JRE Group of Institutions E ::= E . * E +*$ Here we have a shift-reduce error. Consider the first two items in I3. If we have a*b+c and we parsed a*b, do we reduce using E ::= E * E or do we shift more symbols? In the former case we get a parse tree (a*b)+c; in the latter case we get a*(b+c). To resolve this conflict, we can specify that * has higher precedence than +. The precedence of a grammar production is equal to the precedence of the rightmost token at the rhs of the production. For example, the precedence of the production E ::= E * E is equal to the precedence of the operator *, the precedence of the production E ::= ( E ) is equal to the precedence of the token ), and the precedence of the production E ::= if E then E else E is equal to the precedence of the token else. The idea is that if the look ahead has higher precedence than the production currently used, we shift. For example, if we are parsing E + E using the production rule E ::= E + E and the look ahead is *, we shift *. If the look ahead has the same precedence as that of the current production and is left associative, we reduce, otherwise we shift. The above grammar is valid if we define the precedence and associativity of all the operators. Thus, it is very important when you write a parser using CUP or any other LALR(1) parser generator to specify associativities and precedence‟s for most tokens (especially for those used as operators). Note: you can explicitly define the precedence of a rule in CUP using the %prec directive: E ::= MINUS E %prec UMINUS where UMINUS is a pseudo-token that has higher precedence than TIMES, MINUS etc, so that -1*2 is equal to (-1)*2, not to -(1*2). Another thing we can do when specifying an LALR(1) grammar for a parser generator is error recovery. All the entries in the ACTION and GOTO tables that have no content correspond to syntax errors. The simplest thing to do in case of error is to report it and stop the parsing. But we would like to continue parsing finding more errors. This is called error recovery. Consider the grammar: S ::= L = E ; | { SL } ; | error ;
SL ::= S ; | SL S ;
Department of CSE - 47 -
JRE Group of Institutions The special token error indicates to the parser what to do in case of invalid syntax for S (an invalid statement). In this case, it reads all the tokens from the input stream until it finds the first semicolon. The way the parser handles this is to first push an error state in the stack. In case of an error, the parser pops out elements from the stack until it finds an error state where it can proceed. Then it discards tokens from the input until a restart is possible. Inserting error handling productions in the proper places in a grammar to do good error recovery is considered very hard.
5.9LR ERROR RECOVERY
An LR parser will detect an error when it consults the parsing action table and find a blank or error entry. Errors are never detected by consulting the goto table. An LR parser will detect an error as soon as there is no valid continuation for the portion of the input thus far scanned. A canonical LR parser will not make even a single reduction before announcing the error. SLR and LALR parsers may make several reductions before detecting an error, but they will never shift an erroneous input symbol onto the stack. 5.10 PANIC-MODE ERROR RECOVERY We can implement panic-mode error recovery by scanning down the stack until a state s with a goto on a particular nonterminal A is found. Zero or more input symbols are then discarded until a symbol a is found that can legitimately follow A. The parser then stacks the state GOTO(s, A) and resumes normal parsing. The situation might exist where there is more than one choice for the nonterminal A. Normally these would be nonterminals representing major program pieces, e.g. an expression, a statement, or a block. For example, if A is the nonterminal stmt, a might be semicolon or }, which marks the end of a statement sequence. This method of error recovery attempts to eliminate the phrase containing the syntactic error. The parser determines that a string derivable from A contains an error. Part of that string has already been processed, and the result of this processing is a sequence of states on top of the stack. The remainder of the string is still in the input, and the parser attempts to skip over the remainder of this string by looking for a symbol on the input that can legitimately follow A. By removing states from the stack, skipping over the input, and pushing GOTO(s, A) on the stack, the parser pretends that if has found an instance of A and resumes normal parsing.
Department of CSE - 48 -
JRE Group of Institutions 5.11 PHRASE-LEVEL RECOVERY Phrase-level recovery is implemented by examining each error entry in the LR action table and deciding on the basis of language usage the most likely programmer error that would give rise to that error. An appropriate recovery procedure can then be constructed; presumably the top of the stack and/or first input symbol would be modified in a way deemed appropriate for each error entry. In designing specific error-handling routines for an LR parser, we can fill in each blank entry in the action field with a pointer to an error routine that will take the appropriate action selected by the compiler designer. The actions may include insertion or deletion of symbols from the stack or the input or both, or alteration and transposition of input symbols. We must make our choices so that the LR parser will not get into an infinite loop. A safe strategy will assure that at least one input symbol will be removed or shifted eventually, or that the stack will eventually shrink if the end of the input has been reached. Popping a stack state that covers a non terminal should be avoided, because this modification eliminates from the stack a construct that has already been successfully parsed.
Department of CSE - 49 -
JRE Group of Institutions
UNIT 6 SEMANTIC ANALYSIS
6.1 SEMANTIC ANALYSIS
Semantic Analysis computes additional information related to the meaning of the program once the syntactic structure is known. In typed languages as C, semantic analysis involves adding information to the symbol table and performing type checking. The information to be computed is beyond capabilities of standard parsing the techniques, therefore it is not regarded as syntax. As for Lexical and Syntax analysis, also for Semantic Analysis we need both a Representation Formalism and an Implementation Mechanism. As representation formalism this lecture illustrates what are called Syntax Directed Translations.
6.2 SYNTAX DIRECTED TRANSLATION
The Principle of Syntax Directed Translation states that the meaning of an input sentence is related to its syntactic structure, i.e., to its Parse-Tree. By Syntax Directed Translations we indicate those formalisms for specifying translations for programming language constructs guided by context-free grammars. o We associate Attributes to the grammar symbols representing the language constructs. o Values for attributes are computed by Semantic Rules associated with grammar productions. Evaluation of Semantic Rules may: o Generate Code; o Insert information into the Symbol Table; o Perform Semantic Check; o Issue error messages; o etc.
Department of CSE - 50 -
JRE Group of Institutions There are two notations for attaching semantic rules: 1. Syntax Directed Definitions. High-level specification hiding many implementation details (also called Attribute Grammars). 2. Translation Schemes. More implementation oriented: Indicate the order in which semantic rules are to be evaluated. Syntax Directed Definitions • Syntax Directed Definitions are a generalization of context-free grammars in which: 1. Grammar symbols have an associated set of Attributes; 2. Productions are associated with Semantic Rules for computing the values of attributes.
Such formalism generates Annotated Parse-Trees where each node of the tree is a record with a field for each attribute (e.g.,X.a indicates the attribute a of the grammar symbol X). The value of an attribute of a grammar symbol at a given parse-tree node is defined by a semantic rule associated with the production used at that node.
We distinguish between two kinds of attributes: 1. Synthesized Attributes. They are computed from the values of the attributes of the children nodes. 2. Inherited Attributes. They are computed from the values of the attributes of both the siblings and the parent nodes
Syntax Directed Definitions: An Example • Example. Let us consider the Grammar for arithmetic expressions. The Syntax Directed Definition associates to each non terminal a synthesized attribute called val.
Department of CSE - 51 -
JRE Group of Institutions
6.3 S-ATTRIBUTED DEFINITIONS Definition. An S-Attributed Definition is a Syntax Directed Definition that uses only synthesized attributes. • Evaluation Order. Semantic rules in a S-Attributed Definition can be evaluated by a bottom-up, or PostOrder, traversal of the parse-tree. • Example. The above arithmetic grammar is an example of an SAttributed Definition. The annotated parse-tree for the input 3*5+4n is:
Department of CSE - 52 -
JRE Group of Institutions
6.4 L-attributed definition
Definition: A SDD its L-attributed if each inherited attribute of Xi in the RHS of A ! X1 : :Xn depends only on 1. attributes of X1;X2; : : : ;Xi 1 (symbols to the left of Xi in the RHS) 2. inherited attributes of A. Restrictions for translation schemes: 1. Inherited attribute of Xi must be computed by an action before Xi. 2. An action must not refer to synthesized attribute of any symbol to the right of that action. 3. Synthesized attribute for A can only be computed after all attributes it references have been completed (usually at end of RHS). 6.5 SYMBOL TABLES A symbol table is a major data structure used in a compiler. Associates attributes with identifiers used in a program. For instance, a type attribute is usually associated with each identifier. A symbol table is a necessary component Definition (declaration) of identifiers appears once in a program .Use of identifiers may appear in many places of the program text Identifiers and attributes are entered by the analysis phases. When processing a definition (declaration) of an identifier. In simple languages with only global variables and implicit declarations. The scanner can enter an identifier into a symbol table if it is not already there In block-structured languages with scopes and explicit declarations: The parser and/or semantic analyzer enter identifiers and corresponding attributes Symbol table information is used by the analysis and synthesis phases To verify that used identifiers have been defined (declared) To verify that expressions and assignments are semantically correct – type checking To generate intermediate or target code
Symbol Table Interface The basic operations defined on a symbol table include:
allocate – to allocate a new empty symbol table
free – to remove all entries and free the storage of a symbol table
insert – to insert a name in a symbol table and return a pointer to its entry
Department of CSE - 53 -
JRE Group of Institutions
lookup – to search for a name and return a pointer to its entry set_attribute – to associate an attribute with a given entry
get_attribute – to get an attribute associated with a given entry
Other operations can be added depending on requirement For example, a delete operation removes a name previously inserted Some identifiers become invisible (out of scope) after exiting a block This interface provides an abstract view of a symbol table
Supports the simultaneous existence of multiple tables Implementation can vary without modifying the interface Basic Implementation Techniques First consideration is how to insert and lookup names Variety of implementation techniques Unordered List Simplest to implement Implemented as an array or a linked list Linked list can grow dynamically – alleviates problem of a fixed size array Insertion is fast O(1), but lookup is slow for large tables – O(n) on average Ordered List If an array is sorted, it can be searched using binary search – O(log2 n) Insertion into a sorted array is expensive – O(n) on average Useful when set of names is known in advance – table of reserved words Binary Search Tree Can grow dynamically Insertion and lookup are O(log2 n) on average
6.6 HASH TABLES AND HASH FUNCTIONS
A hash table is an array with index range: 0 to TableSize – 1
Most commonly used data structure to implement symbol tables Insertion and lookup can be made very fast – O(1)
A hash function maps an identifier name into a table index
Department of CSE - 54 -
JRE Group of Institutions
A hash function, h(name), should depend solely on name h(name) should be computed quickly
h should be uniform and randomizing in distributing names All table indices should be mapped with equal probability. Similar names should not cluster to the same table index
6.7 HASH FUNCTIONS _ Hash functions can be defined in many ways . . . _ A string can be treated as a sequence of integer words _ Several characters are fit into an integer word
_ Strings longer than one word are folded using exclusive-or or addition _ Hash value is obtained by taking integer word modulo TableSize
_ We can also compute a hash value character by character: _ h(name) = (c0 + c1 + … + cn–1) mod TableSize, where n is name length _ h(name) = (c0 * c1 * … * cn–1) mod TableSize _ h(name) = (cn–1 + ___ cn–2 + … + ___ c1 + __c0))) mod TableSize _ h(name) = (c0 * cn–1 * n) mod TableSize
6.8 RUNTIME ENVIRONMENT
Runtime organization of different storage locations
Representation of scopes and extents during program execution.
Components of executing program reside in blocks of memory (supplied by OS). Three kinds of entities that need to be managed at runtime:
o
Generated code for various procedures and programs.
forms text or code segment of your program: size known at compile time. o Data objects: Global variables/constants: size known at compile time Variables declared within procedures/blocks: size known Variables created dynamically: size unknown. o Stack to keep track of procedure activations. Subdivide memory conceptually into code and data areas:
Department of CSE - 55 -
JRE Group of Institutions
instructions Code: Program
Stack: Manage activation of procedures at runtime.
Heap: holds variables created dynamically
6.9 STORAGE ORGANIZATION 1Fixed-size objects can be placed in predefined locations.
2. Run-time stack and heap The STACK is used to store:
o
Procedure activations.
o The status of the machine just before calling a procedure, so that the status can be restored when the called procedure returns. o The HEAP stores data allocated under program control (e.g. by malloc() in C).
Department of CSE - 56 -
JRE Group of Institutions Activation records Any information needed for a single activation of a procedure is stored in the ACTIVATION RECORD (sometimes called the STACK FRAME). Today, we‟ll assume the stack grows DOWNWARD, as on, e.g., the Intel architecture. The activation record gets pushed for each procedure call and popped for each procedure return. 6.9 STATIC ALLOCATION Statically allocated names are bound to storage at compile time. Storage bindings of statically allocated names never change, so even if a name is local to a procedure, its name is always bound to the same storage. The compiler uses the type of a name (retrieved from the symbol table) to determine storage size required. The required number of bytes (possibly aligned) is set aside for the name.The address of the storage is fixed at compile time. Limitations: − The size required must be known at compile time. − Recursive procedures cannot be implemented as all locals are statically allocated. − No data structure can be created dynamically as all data is static.
Stack-dynamic allocation
Storage is organized as a stack. Activation records are pushed and popped.
Locals and parameters are contained in the activation records for the call. This means locals are bound to fresh storage on every call.
If we have a stack growing downwards, we just need a stack_top pointer. To allocate a new activation record, we just increase stack_top.
To deallocate an existing activation record, we just decrease stack_top.
Address generation in stack allocation
The position of the activation record on the stack cannot be determined statically.
Therefore the compiler must generate addresses RELATIVE to the activation record. If we have a downward-growing stack and a stack_top pointer, we generate addresses of the form stack_top + offset Department of CSE - 57 -
JRE Group of Institutions
6.10 HEAP ALLOCATION Some languages do not have tree-structured allocations. In these cases, activations have to be allocated on the heap. This allows strange situations, like callee activations that live longer than their callers‟ activations. This is not common Heap is used for allocating space for objects created at run timeFor example: nodes of dynamic data structures such as linked lists and trees Dynamic memory allocation and deallocation based on the requirements of the programmalloc() and free() in C programs new()and delete()in C++ programs new()and garbage collection in Java programs
Allocation and deallocation may be completely manual (C/C++), semi-automatic(Java), or fully automatic (Lisp) 6.11 PARAMETERS PASSING A language has first-class functionsif functions can bedeclared within any scope passed as arguments to other functions returned as results of functions. In a language with first-class functions and static scope, a function value is generally represented by a closure. a pair consisting of a pointer to function code a pointer to an activation record. Passing functions as arguments is very useful in structuring of systems using upcalls
An example: main()
{ int x = 4; int f (int y) { return x*y;
} int g (int →int h){ int x = 7; return h(3) + x; } Department of CSE - 58 -
JRE Group of Institutions g(f);//returns 12 } Passing Functions as Parameters – Implementation with Static Scope
Department of CSE - 59 -
JRE Group of Institutions
UNIT 7 INTERMEDIATE CODE
7.1. INTERMEDIATE CODE GENERATION In the analysis-synthesis model of a compiler, the front end analyzes a source program and creates an intermediate representation, from which the back end generates target code. This facilitates retargeting: enables attaching a back end for the new machine to an existing front end.
Logical Structure of a Compiler Front End
A compiler front end is organized as in figure above, where parsing, static checking, and intermediate-code generation are done sequentially; sometimes they can be combined and folded into parsing. All schemes can be implemented by creating a syntax tree and then walking the tree. Static Checking This includes type checking which ensures that operators are applied to compatible operands. It also includes any syntactic checks that remain after parsing like flow–of-control checks o Ex: Break statement within a loop construct Uniqueness checks o Labels in case statements Name-related checks Intermediate Representations We could translate the source program directly into the target language. However, there are benefits to having an intermediate, machine-independent representation.
Department of CSE - 60 -
JRE Group of Institutions
A clear distinction between the machine-independent and machine-dependent parts of the compiler Retargeting is facilitated the implementation of language processors for new machines will require replacing only the back-end. We could apply machine independent code optimization techniques
Intermediate representations span the gap between the source and target languages. • High Level Representations
closer to the source language easy to generate from an input program
code optimizations may not be straightforward
• Low Level Representations
closer to the target machine
Suitable for register allocation and instruction selection easier for optimizations, final code generation
There are several options for intermediate code. They can be either • Specific to the language being implemented P-code for Pascal Byte code for Java 7.2 LANGUAGE INDEPENDENT 3-ADDRESS CODE IR can be either an actual language or a group of internal data structures that are shared by the phases of the compiler. C used as intermediate language as it is flexible, compiles into efficient machine code and its compilers are widely available.In all cases, the intermediate code is a linearization of the syntax tree produced during syntax and semantic analysis. It is formed by breaking down the tree structure into sequential instructions, each of which is equivalent to a single, or small number of machine instructions. Machine code can then be generated (access might be required to symbol tables etc). TAC can range from high- to lowlevel, depending on the choice of operators. In general, it is a statement containing at most 3 addresses or operands. The general form is x := y op z, where “op” is an operator, x is the result, and y and z are operands. x, y, z are variables, constants, or “temporaries”. A three-address instruction Department of CSE - 61 -
JRE Group of Institutions consists of at most 3 addresses for each statement. It is a linear zed representation of a binary syntax tree. Explicit names correspond to interior nodes of the graph. E.g. for a looping statement , syntax tree represents components of the statement, whereas three-address code contains labels and jump instructions to represent the flow-of-control as in machine language. A TAC instruction has at most one operator on the RHS of an instruction; no built-up arithmetic expressions are permitted. e.g. x + y * z can be translated as t1 = y * z t2 = x + t1 Where t1 & t2 are compiler–generated temporary names. 5Since it unravels multi-operator arithmetic expressions and nested control-flow statements, it is useful for target code generation and optimization. Addresses and Instructions • TAC consists of a sequence of instructions, each instruction may have up to three addresses, prototypically t1 = t2 op t3 • Addresses may be one of: o A name. Each name is a symbol table index. For convenience, we writethe names as the identifier. o A constant.
o A compiler-generated temporary. Each time a temporary address is needed, the compiler generates another name from the stream t1, t2, t3, etc. • Temporary names allow for code optimization to easily move Instructions • At target-code generation time, these names will be allocated to registers or to memory. • TAC Instructions o Symbolic labels will be used by instructions that alter the flow of control. The instruction addresses of labels will be filled in later. L: t1 = t2 op t3 o Assignment instructions: x = y op z • Includes binary arithmetic and logical operations o Unary assignments: x = op y
Department of CSE - 62 -
JRE Group of Institutions • Includes unary arithmetic op (-) and logical op (!) and type conversion o o Copy instructions: x = y Unconditional jump: goto L
• L is a symbolic label of an instruction o Conditional jumps: if x goto L If x is true, execute instruction L next ifFalse x goto L If x is false, execute instruction L next o Conditional jumps: if x relop y goto L – Procedure calls. For a procedure call p(x1, …, xn) param x1 … param xn call p, n
– Function calls : y= p(x1, …, xn) y = call p,n , return y – Indexed copy instructions: x = y[i] and x[i] = y
Left: sets x to the value in the location i memory units beyond y
Right: sets the contents of the location i memory units beyond x to y
– Address and pointer instructions: • x = &y sets the value of x to be the location (address) of y. • x = *y, presumably y is a pointer or temporary whose value is a location. The value of x is set to the contents of that location. • *x = y sets the value of the object pointed to by x to the value of y. Example: Given the statement do i = i+1; while (a[i] < v ); , the TAC can be written as below in two ways, using either symbolic labels or position number of instructions for labels.
Department of CSE - 63 -
JRE Group of Institutions
Types of three address code There are different types of statements in source program to which three address code has to be generated. Along with operands and operators, three address code also use labels to provide flow of control for statements like if-then-else, for and while. The different types of three address code statements are: Assignment statement a = b op c In the above case b and c are operands, while op is binary or logical operator. The result of applying op on b and c is stored in a. Unary operation a = op b This is used for unary minus or logical negation. Example: a = b * (- c) + d Three address code for the above example will be t1 = -c t2 = t1 * b t3 = t2 + d a = t3 Copy Statement a=b The value of b is stored in variable a.
Unconditional jump goto L Creates label L and generates three-address code „goto L‟ v. Creates label L, generate code for expression exp, If the exp returns value true then go to the statement labelled L. exp returns a value false go to the statement immediately following the if statement. Function call For a function fun with n arguments a1,a2,a3….an ie., fun(a1, a2, a3,…an), Department of CSE - 64 -
JRE Group of Institutions the three address code will be Param a1 Param a2 … Param an Call fun, n Where param defines the arguments to function. Array indexing In order to access the elements of array either single dimension or multidimension, three address code requires base address and offset value. Base address consists of the address of first element in an array. Other elements of the array can be accessed using the base address and offset value. Example: x = y[i] Memory location m = Base address of y + Displacement i x = contents of memory location m similarly x[i] = y Memory location m = Base address of x + Displacement i The value of y is stored in memory location m Pointer assignment
x = &y x stores the address of memory location y x = *y y is a pointer whose r-value is location *x = y sets r-value of the object pointed by x to the r-value of y Intermediate representation should have an operator set which is rich to implement most of the operations of source language. It should also help in mapping to restricted instruction set of target machine. Data Structure Three address code is represented as record structure with fields for operator and operands. These
Department of CSE - 65 -
JRE Group of Institutions records can be stored as array or linked list. Most common implementations of three address code areQuadruples, Triples and Indirect triples. 7.3 QUADRUPLESQuadruples consists of four fields in the record structure. One field to store operator op, two fields to store operands or arguments arg1and arg2 and one field to store result res. res = arg1 op arg2 Example: a = b + c b is represented as arg1, c is represented as arg2, + as op and a as res. Unary operators like „-„do not use agr2. Operators like param do not use agr2 nor result. For conditional and unconditional statements res is label. Arg1, arg2 and res are pointers to symbol table or literal table for the names. Example: a = -b * d + c + (-b) * d Three address code for the above statement is as follows t1 = - b t2 = t1 * d t3 = t2 + c t4 = - b t5 = t4 * d t6 = t3 + t5 a = t6 Quadruples for the above example is as follows
Department of CSE - 66 -
JRE Group of Institutions
7.4 TRIPLES
Triples uses only three fields in the record structure. One field for operator, two fields for operands named as arg1 and arg2. Value of temporary variable can be accessed by the position of the statement the computes it and not by location as in quadruples.
Example: a = -b * d + c + (-b) * d Triples for the above example is as follows
Department of CSE - 67 -
JRE Group of Institutions
Arg1 and arg2 may be pointers to symbol table for program variables or literal table for constant or pointers into triple structure for intermediate results. Example: Triples for statement x[i] = y which generates two records is as follows
Triples for statement x = y[i] which generates two records is as follows
Triples are alternative ways for representing syntax tree or Directed acyclic graph for program defined names. Indirect Triples Indirect triples are used to achieve indirection in listing of pointers. That is, it uses pointers to triples than listing of triples themselves. Example: a = -b * d + c + (-b) * d
Department of CSE - 68 -
JRE Group of Institutions
Conditional operator and operands. Representations include quadruples, triples and indirect triples.
7.5 SYNTAX TREES
Syntax trees are high level IR. They depict the natural hierarchical structure of the source program. Nodes represent constructs in source program and the children of a node represent meaningful components of the construct. Syntax trees are suited for static type checking.
Variants of Syntax Trees: DAG A directed acyclic graph (DAG) for an expression identifies the common sub expressions (sub expressions that occur more than once) of the expression. DAG's can be constructed by using the same techniques that construct syntax trees. A DAG has leaves corresponding to atomic operands and interior nodes corresponding to operators. A node N in a DAG has more than one parent if N represents a common sub expression, so a DAG represents expressions concisely. It gives clues to compiler about the generating efficient code to evaluate expressions. Example 1: Given the grammar below, for the input string id + id * id , the parse tree, Department of CSE - 69 -
JRE Group of Institutions syntax tree and the DAG are as shown.
Example : DAG for the expression a + a * (b - c) + ( b - c ) * d is shown below.
Department of CSE - 70 -
JRE Group of Institutions
Using the SDD to draw syntax tree or DAG for a given expression:• Draw the parse tree • Perform a post order traversal of the parse tree • Perform the semantic actions at every node during the traversal – Constructs a DAG if before creating a new node, these functions check whether an identical node already exists. If yes, the existing node is returned. SDD to produce Syntax trees or DAG is shown below.
For the expression a + a * ( b – c) + (b - c) * d, steps for constructing the DAG is as below.
Department of CSE - 71 -
JRE Group of Institutions 7.6 BASIC BLOCKS AND FLOW GRAPHS A graph representation of three-address statements, called a flow graph, is useful for understanding code-generation algorithms, even if the graph is not explicitly constructed by a code-generation algorithm. Nodes in the flow graph represent computations, and the edges represent the flow of control. Flow graph of a program can be used as a vehicle to collect information about the intermediate program. Some register-assignment algorithms use flow graphs to find the inner loops where a program is expected to spend most of its time.
BASIC BLOCKS A basic block is a sequence of consecutive statements in which flow of control enters at the beginning and leaves at the end without halt or possibility of branching except at the end. The following sequence of three-address statements forms a basic block: t1 := a*a t2 := a*b t3 := 2*t2 t4 := t1+t3 t5 := b*b t6 := t4+t5 A three-address statement x := y+z is said to define x and to use y or z. A name in a basic block is said to live at a given point if its value is used after that point in the program, perhaps in another basic block. The following algorithm can be used to partition a sequence of three-address statements into basic blocks. Algorithm 1: Partition into basic blocks. Input: A sequence of three-address statements. Output: A list of basic blocks with each three-address statement in exactly one block. Method: 1. We first determine the set of leaders, the first statements of basic blocks. The rules we use are the following: I) The first statement is a leader. II) Any statement that is the target of a conditional or unconditional goto is a leader. Department of CSE - 72 -
JRE Group of Institutions III) Any statement that immediately follows a goto or conditional goto statement is a leader. 2. For each leader, its basic block consists of the leader and all statements up to but not including the next leader or the end of the program. Example 3: Consider the fragment of source code shown in fig. 7; it computes the dot product of two vectors a and b of length 20. A list of three-address statements performing this computation on our target machine is shown in fig. 8. begin prod := 0; i := 1; do begin prod := prod + a[i] * b[i]; i := i+1; end while i
