Syntax and Parsing Last Time This Time the Compilation Process

Total Page:16

File Type:pdf, Size:1020Kb

Syntax and Parsing Last Time This Time the Compilation Process Last Time This Time Administrivia Interpreters and Compilers Syntax and Parsing Class Project Structure of a Compiler Types of Programming Languages: Lexical Analysis COMS W4115 Imperative, Object-Oriented, Functional, Logic, Dataflow Syntax Prof. Stephen A. Edwards Parsing Spring 2002 Columbia University Department of Computer Science Interpreters Compilers Source Program Source Program # # Input ! Interpreter ! Output Compiler The Compilation Process # Input ! Executable Program ! Output Structure of a Compiler Compiling a Simple Program What the Compiler Sees int gcd(int a, int b) # Program Text int gcd(int a, int b) { while (a != b) { Lexer { if (a > b) a -= b; # Token Stream else b -= a; while (a != b) { } Parser return a; if (a > b) a -= b; # Abstract Syntax Tree } else b -= a; Static semantics (type checking) i n t sp g c d ( i n t sp a , sp i # Annotated AST } n t sp b ) nl { nl sp sp w h i l e sp Translation to intermediate form return a; ( a sp ! = sp b ) sp { nl sp sp sp sp i # Three-address code } f sp ( a sp > sp b ) sp a sp - = sp b Code generation ; nl sp sp sp sp e l s e sp b sp - = sp # Assembly Code a ; nl sp sp } nl sp sp r e t u r n sp a ; nl } nl Text file is a sequence of characters After Lexical Analysis After Parsing After Semantic Analysis int gcd(int a, int b) func { func while (a != b) { int gcd args seq if (a > b) a -= b; else b -= a; int gcd args seq } arg arg while return return a; arg arg while return } int a int b != if a int a int b != if a int gcd ( int a , int b ) – while ( a Symbol a b > -= -= int gcd(int a, int b) a b > -= -= { Table: a b a b b a != b ) – if ( a > b ) a -= b ; while (a != b) { if (a > b) a -= b; a b a b b a int a else b -= a; else b -= a ; ˝ return a ; ˝ } int b return a; } A stream of tokens. Whitespace, comments removed. Types checked; references to symbols resolved Abstract syntax tree built from parsing rules. After Translation into 3-Address Code After Translation to 80386 Assembly L0: sne $1, a, b gcd: pushl %ebp % Save frame pointer seq $0, $1, 0 movl %esp,%ebp btrue $0, L1 % while (a != b) movl 8(%ebp),%eax % Load a from stack sl $3, b, a movl 12(%ebp),%edx % Load b from stack seq $2, $3, 0 .L8: cmpl %edx,%eax btrue $2, L4 % if (a < b) je .L3 % while (a != b) Lexical Analysis (Scanning) jle .L5 % if (a < b) sub a, a, b % a -= b int gcd(int a, int b) jmp L5 { subl %edx,%eax % a -= b while (a != b) { L4: sub b, b, a % b -= a if (a > b) a -= b; jmp .L8 else b -= a; L5: jmp L0 } .L5: subl %eax,%edx % b -= a return a; L1: ret a } jmp .L8 .L3: leave % Restore SP, BP Idealized assembly language w/ infinite registers ret Lexical Analysis (Scanning) Lexical Analysis The ANTLR Compiler Generator Goal is to translate a stream of characters Goal: simplify the job of the parser. Language and compiler for writing compilers i n t sp g c d ( i n t sp Scanners are usually much faster than parsers. Running ANTLR on an ANTLR file produces Java source files that can be compiled and run. a , sp i n t sp b Discard as many irrelevant details as possible (e.g., into a stream of tokens whitespace, comments). ANTLR can generate Parser does not care that the the identifer is • Scanners (lexical analyzers) ID ID LPAREN ID ID COMMA ID ID “supercalifragilisticexpialidocious.” int gcd ( int a , int b • Parsers Parser rules are only concerned with token types. • Each token consists of a token type and its text. Tree walkers Whitespace and comments are discarded. We will use all of these facilities in this class An ANTLR File for a Simple Scanner ANTLR Specifications for Scanners ANTLR Specifications class CalcLexer extends Lexer; Rules are names starting with a capital letter. Question mark makes a clause optional. A character in single quotes matches that character. PERSON : ("wo")? ’m’ (’a’|’e’) ’n’ ; LPAREN : ’(’ ; // Rules for puctuation RPAREN : ’)’ ; LPAREN : ’(’ ; (Matches man, men, woman, and women.) STAR : ’*’ ; A string in double quotes matches the string Double dots indicate a range of characters: PLUS : ’+’ ; SEMI : ’;’ ; IF : "if" ; DIGIT : ’0’..’9’; protected // Can only be used as a sub-rule A vertical bar indicates a choice: Asterisk and plus match “zero or more,” “one or more.” DIGIT : ’0’..’9’ ; // Any character between 0 and 9 INT : (DIGIT)+ ; // One or more digits OP : ’+’ | ’-’ | ’*’ | ’/’ ; ID : LETTER (LETTER | DIGIT)* ; NUMBER : (DIGIT)+ ; WS : (’ ’ | ’\t’ | ’\n’| ’\r’) // Whitespace { $setType(Token.SKIP); } ; // Action: ignore Kleene Closure Scanner Behavior Implementing Scanners Automatically The asterisk operator (*) is called the Kleene Closure All rules (tokens) are considered simultaneously. The Regular Expressions (Rules) operator after the inventor of regular expressions, Stephen longest one that matches wins: # Cole Kleene, who pronounced his last name “CLAY-nee.” 1. Look at the next character in the file. Nondeterministic Finite Automata His son Ken writes “As far as I am aware this 2. Can the next character be added to any of the tokens # Subset Construction pronunciation is incorrect in all known languages. I believe under construction? that this novel pronunciation was invented by my father.” Deterministic Finite Automata 3. If so, add the character to the token being constructed # and go to step 1. Tables 4. Otherwise, return the token. How to keep track of multiple rules matching simultaneously? Build an automata. Regular Expressions and NFAs Deterministic Finite Automata Deterministic Finite Automata We are describing tokens with regular expressions: A state machine with an initial state ELSE: "else" ; ELSEIF: "elseif" ; • The symbol always matches Arcs indicate “consumed” input symbols. e l s e • A symbol from an alphabet, e.g., a, matches itself States with double lines are accepting. • If the next token has an arc, follow the arc. A sequence of two regular expressions e.g., e1e2 i Matches e1 followed by e2 If the next token has no arc and the state is accepting, return the token. • An “OR” of two regular expressions e.g., e1je2 If the next token has no arc and the state is not accepting, f Matches e1 or e2 syntax error. • The Kleene closure of a regular expression, e.g., (e)∗ Matches zero or more instances of e1 in sequence. Deterministic Finite Automata Nondeterminstic Finite Automata Translating REs into NFAs a IF: "if" ; DFAs with arcs. a ID: ’a’..’z’ (’a’..’z’ | ’0’..’9’)* ; Conceptually, arcs denote state equivalence. NUM: (’0’..’9’)+ ; e1e2 e1 e2 arcs add the ability to make nondeterministic f (schizophrenic) choices. e1 ID a-eg-z0-9 IF i When an NFA reaches a state with an arc, it moves into a-z0-9 e1je2 e2 every destination. a-hj-z a-z0-9 ID ID a-z90-9 NFAs can be in multiple states at once. 0-9 ∗ (e) e 0-9 NUM NUM 0-9 RE to NFAs Subset Construction Subset Construction Building an NFA for the regular expression How to compute a DFA from an NFA. An DFA can be exponentially larger than the corresponding NFA. (woj)m(aje)n Basic idea: each state of the DFA is a marking of the NFA a n produces n states versus 2 m Tools often try to strike a balance between the two w o representations. a m n e ANTLR uses a different technique. w m n e after simplification. Most arcs disappear. o Free-Format Languages Free-Format Languages FORTRAN 77 Typical style arising from scanner/parser division Java C C++ Algol Pascal FORTRAN 77 is not free-format. 72-character lines: Program text is a series of tokens possibly separated by Some deviate a little (e.g., C and C++ have a separate 100 IF(IN .EQ. ’Y’ .OR. IN .EQ. ’y’ .OR. whitespace and comments, which are both ignored. preprocessor) $ IN .EQ. ’T’ .OR. IN .EQ. ’t’) THEN • keywords (if while) But not all languages are free-format. 1 · · · 5 6 7 · · · 72 | {z } |{z} | {z } • punctuation (, ( +) Statement label Continuation Normal • identifiers (foo bar) When column 6 is not a space, line is considered part of • numbers (10 -3.14159e+32) the previous. • strings ("A String") Fixed-length line makes it easy to allocate a one-line buffer. Makes sense on punch cards. Python Syntax and Langauge Design Syntax and Language Design The Python scripting language groups with indentation Does syntax matter? Yes and no Some syntax is error-prone. Classic FORTRAN example: i = 0 More important is a language’s semantics—its meaning. DO 5 I = 1,25 ! Loop header (for i = 1 to 25) while i < 10: The syntax is aesthetic, but can be a religious issue. DO 5 I = 1.25 ! Assignment to variable DO5I i = i + 1 print i # Prints 1, 2, ..., 10 But aesthetics matter to people, and can be critical. Trying too hard to reuse existing syntax in C++: Verbosity does matter: smaller is usually better. vector< vector<int> > foo; i = 0 vector<vector<int>> foo; // Syntax error while i < 10: Too small can be a problem: APL is a compact, cryptic i = i + 1 language with its own character set (!) C distinguishes > and >> as different operators. print i # Just prints 10 E A TEST B;L This is succinct, but can be error-prone. L 0.5 E ((A A)+B B)*L How do you wrap a conditional around instructions? × × Keywords Parsing Keywords look like identifiers in most languages.
Recommended publications
  • Layout-Sensitive Generalized Parsing
    Layout-sensitive Generalized Parsing Sebastian Erdweg, Tillmann Rendel, Christian K¨astner,and Klaus Ostermann University of Marburg, Germany Abstract. The theory of context-free languages is well-understood and context-free parsers can be used as off-the-shelf tools in practice. In par- ticular, to use a context-free parser framework, a user does not need to understand its internals but can specify a language declaratively as a grammar. However, many languages in practice are not context-free. One particularly important class of such languages is layout-sensitive languages, in which the structure of code depends on indentation and whitespace. For example, Python, Haskell, F#, and Markdown use in- dentation instead of curly braces to determine the block structure of code. Their parsers (and lexers) are not declaratively specified but hand-tuned to account for layout-sensitivity. To support declarative specifications of layout-sensitive languages, we propose a parsing framework in which a user can annotate layout in a grammar. Annotations take the form of constraints on the relative posi- tioning of tokens in the parsed subtrees. For example, a user can declare that a block consists of statements that all start on the same column. We have integrated layout constraints into SDF and implemented a layout- sensitive generalized parser as an extension of generalized LR parsing. We evaluate the correctness and performance of our parser by parsing 33 290 open-source Haskell files. Layout-sensitive generalized parsing is easy to use, and its performance overhead compared to layout-insensitive parsing is small enough for practical application. 1 Introduction Most computer languages prescribe a textual syntax.
    [Show full text]
  • Parse Forest Diagnostics with Dr. Ambiguity
    View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by CWI's Institutional Repository Parse Forest Diagnostics with Dr. Ambiguity H. J. S. Basten and J. J. Vinju Centrum Wiskunde & Informatica (CWI) Science Park 123, 1098 XG Amsterdam, The Netherlands {Jurgen.Vinju,Bas.Basten}@cwi.nl Abstract In this paper we propose and evaluate a method for locating causes of ambiguity in context-free grammars by automatic analysis of parse forests. A parse forest is the set of parse trees of an ambiguous sentence. Deducing causes of ambiguity from observing parse forests is hard for grammar engineers because of (a) the size of the parse forests, (b) the complex shape of parse forests, and (c) the diversity of causes of ambiguity. We first analyze the diversity of ambiguities in grammars for programming lan- guages and the diversity of solutions to these ambiguities. Then we introduce DR.AMBIGUITY: a parse forest diagnostics tools that explains the causes of ambiguity by analyzing differences between parse trees and proposes solutions. We demonstrate its effectiveness using a small experiment with a grammar for Java 5. 1 Introduction This work is motivated by the use of parsers generated from general context-free gram- mars (CFGs). General parsing algorithms such as GLR and derivates [35,9,3,6,17], GLL [34,22], and Earley [16,32] support parser generation for highly non-deterministic context-free grammars. The advantages of constructing parsers using such technology are that grammars may be modular and that real programming languages (often requiring parser non-determinism) can be dealt with efficiently1.
    [Show full text]
  • Formal Languages - 3
    Formal Languages - 3 • Ambiguity in PLs – Problems with if-then-else constructs – Harder problems • Chomsky hierarchy for formal languages – Regular and context-free languages – Type 1: Context-sensitive languages – Type 0 languages and Turing machines Formal Languages-3, CS314 Fall 01© BGRyder 1 Dangling Else Ambiguity (Pascal) Start ::= Stmt Stmt ::= Ifstmt | Astmt Ifstmt ::= IF LogExp THEN Stmt | IF LogExp THEN Stmt ELSE Stmt Astmt ::= Id := Digit Digit ::= 0|1|2|3|4|5|6|7|8|9 LogExp::= Id = 0 Id ::= a|b|c|d|e|f|g|h|i|j|k|l|m|n|o|p|q|r|s|t|u|v|w|x|y|z How are compound if statements parsed using this grammar?? Formal Languages-3, CS314 Fall 01© BGRyder 2 1 IF x = 0 THEN IF y = 0 THEN z := 1 ELSE w := 2; Start Parse Tree 1 Stmt Ifstmt IF LogExp THEN Stmt Ifstmt Id = 0 IF LogExp THEN Stmt ELSE Stmt x Id = 0 Astmt Astmt Id := Digit y Id := Digit z 1 w 2 Formal Languages-3, CS314 Fall 01© BGRyder 3 IF x = 0 THEN IF y = 0 THEN z := 1 ELSE w := 2; Start Stmt Parse Tree 2 Ifstmt Q: which tree is correct? IF LogExp THEN Stmt ELSE Stmt Id = 0 Ifstmt Astmt IF LogExp THEN Stmt x Id := Digit Astmt Id = 0 w 2 Id := Digit y z 1 Formal Languages-3, CS314 Fall 01© BGRyder 4 2 How Solve the Dangling Else? • Algol60: use block structure if x = 0 then begin if y = 0 then z := 1 end else w := 2 • Algol68: use statement begin/end markers if x = 0 then if y = 0 then z := 1 fi else w := 2 fi • Pascal: change the if statement grammar to disallow parse tree 2; that is, always associate an else with the closest if Formal Languages-3, CS314 Fall 01© BGRyder 5 New Pascal Grammar Start ::= Stmt Stmt ::= Stmt1 | Stmt2 Stmt1 ::= IF LogExp THEN Stmt1 ELSE Stmt1 | Astmt Stmt2 ::= IF LogExp THEN Stmt | IF LogExp THEN Stmt1 ELSE Stmt2 Astmt ::= Id := Digit Digit ::= 0|1|2|3|4|5|6|7|8|9 LogExp::= Id = 0 Id ::= a|b|c|d|e|f|g|h|i|j|k|l|m|n|o|p|q|r|s|t|u|v|w|x|y|z Note: only if statements with IF..THEN..ELSE are allowed after the THEN clause of an IF-THEN-ELSE statement.
    [Show full text]
  • Ordered Sets in the Calculus of Data Structures
    Exercise 1: Balanced Parentheses Show that the following balanced parentheses grammar is ambiguous (by finding two parse trees for some input sequence) and find unambiguous grammar for the same language. B ::= | ( B ) | B B Remark • The same parse tree can be derived using two different derivations, e.g. B -> (B) -> (BB) -> ((B)B) -> ((B)) -> (()) B -> (B) -> (BB) -> ((B)B) -> (()B) -> (()) this correspond to different orders in which nodes in the tree are expanded • Ambiguity refers to the fact that there are actually multiple parse trees, not just multiple derivations. Towards Solution • (Note that we must preserve precisely the set of strings that can be derived) • This grammar: B ::= | A A ::= ( ) | A A | (A) solves the problem with multiple symbols generating different trees, but it is still ambiguous: string ( ) ( ) ( ) has two different parse trees Solution • Proposed solution: B ::= | B (B) • this is very smart! How to come up with it? • Clearly, rule B::= B B generates any sequence of B's. We can also encode it like this: B ::= C* C ::= (B) • Now we express sequence using recursive rule that does not create ambiguity: B ::= | C B C ::= (B) • but now, look, we "inline" C back into the rules for so we get exactly the rule B ::= | B (B) This grammar is not ambiguous and is the solution. We did not prove this fact (we only tried to find ambiguous trees but did not find any). Exercise 2: Dangling Else The dangling-else problem happens when the conditional statements are parsed using the following grammar. S ::= S ; S S ::= id := E S ::= if E then S S ::= if E then S else S Find an unambiguous grammar that accepts the same conditional statements and matches the else statement with the nearest unmatched if.
    [Show full text]
  • 14 a Simple Compiler - the Front End
    Compilers and Compiler Generators © P.D. Terry, 2000 14 A SIMPLE COMPILER - THE FRONT END At this point it may be of interest to consider the construction of a compiler for a simple programming language, specifically that of section 8.7. In a text of this nature it is impossible to discuss a full-blown compiler, and the value of our treatment may arguably be reduced by the fact that in dealing with toy languages and toy compilers we shall be evading some of the real issues that a compiler writer has to face. However, we hope the reader will find the ensuing discussion of interest, and that it will serve as a useful preparation for the study of much larger compilers. The technique we shall follow is one of slow refinement, supplementing the discussion with numerous asides on the issues that would be raised in compiling larger languages. Clearly, we could opt to develop a completely hand-crafted compiler, or simply to use a tool like Coco/R. We shall discuss both approaches. Even when a compiler is constructed by hand, having an attributed grammar to describe it is very worthwhile. On the source diskette can be found a great deal of code, illustrating different stages of development of our system. Although some of this code is listed in appendices, its volume precludes printing all of it. Some of it has deliberately been written in a way that allows for simple modification when attempting the exercises, and is thus not really of "production quality". For example, in order to allow components such as the symbol table handler and code generator to be used either with hand-crafted or with Coco/R generated systems, some compromises in design have been necessary.
    [Show full text]
  • Disambiguation Filters for Scannerless Generalized LR Parsers
    Disambiguation Filters for Scannerless Generalized LR Parsers Mark G. J. van den Brand1,4, Jeroen Scheerder2, Jurgen J. Vinju1, and Eelco Visser3 1 Centrum voor Wiskunde en Informatica (CWI) Kruislaan 413, 1098 SJ Amsterdam, The Netherlands {Mark.van.den.Brand,Jurgen.Vinju}@cwi.nl 2 Department of Philosophy, Utrecht University Heidelberglaan 8, 3584 CS Utrecht, The Netherlands [email protected] 3 Institute of Information and Computing Sciences, Utrecht University P.O. Box 80089, 3508TB Utrecht, The Netherlands [email protected] 4 LORIA-INRIA 615 rue du Jardin Botanique, BP 101, F-54602 Villers-l`es-Nancy Cedex, France Abstract. In this paper we present the fusion of generalized LR pars- ing and scannerless parsing. This combination supports syntax defini- tions in which all aspects (lexical and context-free) of the syntax of a language are defined explicitly in one formalism. Furthermore, there are no restrictions on the class of grammars, thus allowing a natural syntax tree structure. Ambiguities that arise through the use of unrestricted grammars are handled by explicit disambiguation constructs, instead of implicit defaults that are taken by traditional scanner and parser gener- ators. Hence, a syntax definition becomes a full declarative description of a language. Scannerless generalized LR parsing is a viable technique that has been applied in various industrial and academic projects. 1 Introduction Since the introduction of efficient deterministic parsing techniques, parsing is considered a closed topic for research, both by computer scientists and by practi- cioners in compiler construction. Tools based on deterministic parsing algorithms such as LEX & YACC [15,11] (LALR) and JavaCC (recursive descent), are con- sidered adequate for dealing with almost all modern (programming) languages.
    [Show full text]
  • Introduction to Programming Languages and Syntax
    Programming Languages Session 1 – Main Theme Programming Languages Overview & Syntax Dr. Jean-Claude Franchitti New York University Computer Science Department Courant Institute of Mathematical Sciences Adapted from course textbook resources Programming Language Pragmatics (3rd Edition) Michael L. Scott, Copyright © 2009 Elsevier 1 Agenda 11 InstructorInstructor andand CourseCourse IntroductionIntroduction 22 IntroductionIntroduction toto ProgrammingProgramming LanguagesLanguages 33 ProgrammingProgramming LanguageLanguage SyntaxSyntax 44 ConclusionConclusion 2 Who am I? - Profile - ¾ 27 years of experience in the Information Technology Industry, including thirteen years of experience working for leading IT consulting firms such as Computer Sciences Corporation ¾ PhD in Computer Science from University of Colorado at Boulder ¾ Past CEO and CTO ¾ Held senior management and technical leadership roles in many large IT Strategy and Modernization projects for fortune 500 corporations in the insurance, banking, investment banking, pharmaceutical, retail, and information management industries ¾ Contributed to several high-profile ARPA and NSF research projects ¾ Played an active role as a member of the OMG, ODMG, and X3H2 standards committees and as a Professor of Computer Science at Columbia initially and New York University since 1997 ¾ Proven record of delivering business solutions on time and on budget ¾ Original designer and developer of jcrew.com and the suite of products now known as IBM InfoSphere DataStage ¾ Creator of the Enterprise
    [Show full text]
  • CS4200 | Compiler Construction | September 10, 2020 Disambiguation and Layout-Sensitive Syntax
    Disambiguation and Layout-Sensitive Syntax Eelco Visser CS4200 | Compiler Construction | September 10, 2020 Disambiguation and Layout-Sensitive Syntax Syntax Definition Summary Derivations - Generating sentences and trees from context-free grammars Ambiguity Declarative Disambiguation Rules - Associativity and priority Grammar Transformations - Eliminating ambiguity by transformation Layout-Sensitive Syntax - Disambiguation using layout constraints Structure Syntax = Structure module structure let inc = function(x) { x + 1 } imports Common in inc(3) context-free start-symbols Exp end context-free syntax Exp.Var = ID Exp.Int = INT Exp.Add = Exp "+" Exp Let( Exp.Fun = "function" "(" {ID ","}* ")" "{" Exp "}" [ Bnd( "inc" Exp.App = Exp "(" {Exp ","}* ")" , Fun(["x"], Add(Var("x"), Int("1"))) ) Exp.Let = "let" Bnd* "in" Exp "end" ] , App(Var("inc"), [Int("3")]) Bnd.Bnd = ID "=" Exp ) Token = Character module structure let inc = function(x) { x + 1 } imports Common in inc(3) context-free start-symbols Exp end context-free syntax Exp.Var = ID module Common Exp.Int = INT lexical syntax Exp.Add = Exp "+" Exp ID = [a-zA-Z] [a-zA-Z0-9]* Exp.Fun = "function" "(" {ID ","}* ")" "{" Exp "}" INT = [\-]? [0-9]+ Exp.App = Exp "(" {Exp ","}* ")" Exp.Let = "let" Bnd* "in" Exp "end" Lexical Syntax = Context-Free Syntax Bnd.Bnd = ID "=" Exp (But we don’t care about structure of lexical syntax) Literal = Non-Terminal module structure let inc = function(x) { x + 1 } imports Common in inc(3) context-free start-symbols Exp end context-free syntax syntax Exp.Var
    [Show full text]
  • Programming Languages
    Programming Languages CSCI-GA.2110-001 Summer 2011 Dr. Cory Plock What this course is ■ A study of programming language paradigms ◆ Imperitive ◆ Functional ◆ Logical ◆ Object-oriented ■ Tour of programming language history & roots. ■ Introduction to core language design & implementation concepts. ■ Exposure to new languages you may not have used before. ■ Ability to reason about language benefits/pitfalls. ■ A look at programming language implementation. ■ Offers an appreciation of language standards. ■ Provides the ability to more quickly learn new languages. 2 / 26 What this course isn’t ■ A comprehensive study of one or more languages. ■ An exercise in learning as many languages as possible. ■ A software engineering course. ■ A compiler course. 3 / 26 Introduction The main themes of programming language design and use: ■ Paradigm (Model of computation) ■ Expressiveness ◆ control structures ◆ abstraction mechanisms ◆ types and their operations ◆ tools for programming in the large ■ Ease of use: Writeability / Readability / Maintainability 4 / 26 Language as a tool for thought ■ Role of language as a communication vehicle among programmers can be just as important as ease of writing ■ All general-purpose languages are Turing complete (They can compute the same things) ■ But languages can make expression of certain algorithms difficult or easy. ◆ Try multiplying two Roman numerals ■ Idioms in language A may be useful inspiration when writing in language B. 5 / 26 Idioms ■ Copying a string q to p in C: while (*p++ = *q++) ; ■ Removing duplicates
    [Show full text]
  • A Practical Tutorial on Context Free Grammars
    A Practical Tutorial on Context Free Grammars Robert B. Heckendorn University of Idaho September 16, 2020 Contents 1 Some Definitions 3 2 Some Common Idioms and Hierarchical Development 5 2.1 A grammar for a language that allows a list of X's . .5 2.2 A Language that is a List of X's or Y's . .5 2.3 A Language that is a List of X's Terminated with a Semicolon . .5 2.4 Hierarchical Complexification . .6 2.5 A Language Where There are not Terminal Semicolons but Separating Commas . .6 2.6 A language where each X is followed by a terminating semicolon: . .6 2.7 An arg list of X's, Y's and Z's: . .6 2.8 A Simple Type Declaration: . .6 2.9 Augment the Type Grammar with the Keyword Static . .7 2.10 A Tree Structure as Nested Parentheses . .7 3 Associativity and Precedence 7 3.1 A Grammar for an Arithmetic Expression . .7 3.2 Grouping with Parentheses . .8 3.3 Unary operators . .9 3.4 An Example Problem . 10 4 How can Things go Wrong 10 4.1 Inescapable Productions . 10 4.2 Ambiguity . 11 4.2.1 Ambiguity by Ill-specified Associativity . 12 4.2.2 Ambiguity by Infinite Loop . 13 4.2.3 Ambiguity by Multiple Paths . 14 1 5 The Dangling Else 15 6 The Power of Context Free and incomplete grammars 16 7 Tips for Grammar Writing 18 8 Extended BNF 18 2 A grammar is used to specify the syntax of a language. It answers the question: What sentences are in the language and what are not? A sentence is a finite sequence of symbols from the alphabet of the language.
    [Show full text]
  • Context Free Languages
    Context Free Languages COMP2600 — Formal Methods for Software Engineering Katya Lebedeva Australian National University Semester 2, 2016 Slides by Katya Lebedeva and Ranald Clouston. COMP 2600 — Context Free Languages 1 Ambiguity The definition of CF grammars allow for the possibility of having more than one structure for a given sentence. This ambiguity may make the meaning of a sentence unclear. A context-free grammar G is unambiguous iff every string can be derived by at most one parse tree. G is ambiguous iff there exists any word w 2 L(G) derivable by more than one parse trees. COMP 2600 — Context Free Languages 2 Dangling else Take the code if e1 then if e2 then s1 else s2 where e1, e2 are boolean expressions and s1, s2 are subprograms. Does this mean if e1 then( if e2 then s1 else s2) or if e1 then( if e2 then s1) else s2 The dangling else is a problem in computer programming in which an optional else clause in an “ifthen(else)” statement results in nested conditionals being ambiguous. COMP 2600 — Context Free Languages 3 This is a problem that often comes up in compiler construction, especially parsing. COMP 2600 — Context Free Languages 4 Inherently Ambiguous Languages Not all context-free languages can be given unambiguous grammars – some are inherently ambiguous. Consider the language L = faib jck j i = j or j = kg How do we know that this is context-free? First, notice that L = faibickg [ faib jc jg We then combine CFGs for each side of this union (a standard trick): S ! T j W T ! UV W ! XY U ! aUb j e X ! aX j e V ! cV j e Y ! bYc j e COMP 2600 — Context Free Languages 5 The problem with L is that its sub-languages faibickg and faib jc jg have a non-empty intersection.
    [Show full text]
  • 165142A8ddd2a8637ad23690e
    CS 345 Lexical and Syntactic Analysis Vitaly Shmatikov slide 1 Reading Assignment Mitchell, Chapters 4.1 C Reference Manual, Chapters 2 and 7 slide 2 Syntax Syntax of a programming language is a precise description of all grammatically correct programs • Precise formal syntax was first used in ALGOL 60 Lexical syntax • Basic symbols (names, values, operators, etc.) Concrete syntax • Rules for writing expressions, statements, programs Abstract syntax • Internal representation of expressions and statements, capturing their “meaning” (i.e., semantics) slide 3 Grammars A meta-language is a language used to define other languages A grammar is a meta-language used to define the syntax of a language. It consists of: • Finite set of terminal symbols • Finite set of non-terminal symbols Backus-Naur • Finite set of production rules Form (BNF) • Start symbol • Language = (possibly infinite) set of all sequences of symbols that can be derived by applying production rules starting from the start symbol slide 4 Example: Decimal Numbers Grammar for unsigned decimal integers • Terminal symbols: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 • Non-terminal symbols: Digit, Integer Shorthand for • Production rules: Integer → Digit – Integer → Digit | Integer Digit Integer → Integer Digit – Digit → 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 • Start symbol: Integer Can derive any unsigned integer using this grammar • Language = set of all unsigned decimal integers slide 5 Derivation of 352 as an Integer Production rules: Integer → Digit | Integer Digit Integer ⇒ Integer Digit Digit
    [Show full text]