Language translation Programming Language Design and Implementation (4th Edition) by T. Pratt and M. Zelkowitz Prentice Hall, 2001 Sections 3.1 - 3.3.1.

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Language translation Programming Language Design and Implementation (4th Edition) by T. Pratt and M. Zelkowitz Prentice Hall, 2001 Sections 3.1 - 3.3.1

Program structure Syntax What a program looks like BNF (John Bacus and Peter Naur) context free grammars) a useful notation for describing syntax FORTRAN은 문법이 formal하게 정의되지 않았다. Blank 무시 ::: Do10I=110  Do10I=1,10

Program structure Semantics Execution behavior Static semantics - Semantics determined at compile time: var A: integer; Type and storage for A int B[10]; Type and storage for array B float MyProcC(float x;float y){...}; Function attributes Dynamic semantics - Semantics determined during execution: X = ``ABC'' SNOBOL4 example: X a string X = 1 + 2; X an integer :(X) X an address; Go to label X

Aspects of a program Declarations - Information for compiler var A: integer; typedef struct { int A; float B } C; Control - Changes to state of the machine if (A<B) { ... } while (C>D) { ... } Structure often defined by a Backus Naur Form (BNF) grammar (First used in description of Algol in 1958. Peter Naur was chair of Algol committee, and John Backus was secretary of committee, who wrote report.) We will see later - BNF turns out to be same as context free grammars developed by Noam Chomsky, a linguist)

Stages in translating a program

Major stages Lexical analysis (Scanner): Breaking a program into primitive components, called tokens (identifiers, numbers, keywords, ...) We will see that regular grammars and finite state automata are formal models of this. Syntactic analysis (Parsing): Creating a syntax tree of the program. We will see that context free grammars and pushdown automata are formal models of this. Symbol table: Storing information about declared objects (identifiers, procedure names, ...) Semantic analysis: Understanding the relationship among the tokens in the program. Optimization: Rewriting the syntax tree to create a more efficient program. Code generation: Converting the parsed program into an executable form. We will briefly look at scanning and parsing. A full treatment of compiling is beyond scope of this course.

Translation environments

BNF grammars Nonterminal: A finite set of symbols: <sentence> <subject> <predicate> <verb> <article> <noun> Terminal: A finite set of symbols: the, boy, girl, ran, ate, cake Start symbol: One of the nonterminals: <sentence> Rules (productions): A finite set of replacement rules: <sentence> ::= <subject> <predicate> <subject> ::= <article> <noun> <predicate>::= <verb> <article> <noun> <verb> ::= ran | ate <article> ::= the <noun> ::= boy | girl | cake Replacement Operator: Replace any nonterminal by a right hand side value using any rule (written )

Example BNF sentences <sentence>  <subject> <predicate> First rule  <article> <noun> <predicate> Second rule  the <noun> <predicate> Fifth rule ...  the boy ate the cake Also from <sentence> you can derive  the cake ate the boy Syntax does not imply correct semantics Note: Rule <A> ::= <B><C> This BNF rule also written with equivalent syntax: A  BC

Languages Any string derived from the start symbol is a sentential form. Sentence: String of terminals derived from start symbol by repeated application of replacement operator A language generated by grammar G (written L(G)) is the set of all strings over the terminal alphabet (i.e., sentences) derived from start symbol. That is, a language is the set of sentential forms containing only terminal symbols.

Derivations A derivation is a sequence of sentential forms starting from start symbol. Derivation trees: Grammar: B  0B | 1B | 0 | 1 Derivation: B  0B  01B  010 From derivation get parse tree But derivations may not be unique S  SS | (S) | () S  SS (S)S (())S (())() S  SS  S() (S)() (())() Different derivations but get the same parse tree

Ambiguity But from some grammars you can get 2 different parse trees for the same string: ()()() Each corresponds to a unique derivation: S  SS  SSS ()SS ()()S ()()() A grammar is ambiguous if some sentence has 2 distinct parse trees. We desire unambiguous grammars to understand semantics.

Role of  How to characterize strings of length 0? – Semantically it makes sense to consider such strings. 1. In BNF, -productions: S  SS | (S) | () |  Can always delete them in grammar. For example: X  abYc Y   Delete -production and add production without : X  abc 2. In fsa -  moves means that in initial state, without input you can move to final state.

Syntax can be used to determine some semantics During Algol era, thought that BNF could be used for semantics of a program: What is the value of: 2 * 3 + 4 * 5? (a) 26 (b) 70 (c) 50 All are reasonable answers? Why?

Usual grammar for expressions E  E + T | T T  T * P | P P  i | ( E ) “Natural” value of expression is 26 Multiply 2 * 3 = 6 Multiply 4 * 5 = 20 Add 6 + 20 = 26

But the “precedence” of operations is only a convention Grammar for 70 E  E * T | T T  T + P | P P  i | ( E ) Grammar for 50 E  E + T | E * T | T T  i | ( E ) All 3 grammars generate exactly the same language, but each has a different semantics (i.e., expression value) for most expressions. Draw parse tree of expression 2*3+4*5 for each grammar

Classes of grammars BNF: Backus-Naur Form - Context free - Type 2 - Already described Regular grammars: subclass of BNF - Type 3: BNF rules are restricted: A  t N | t where: N = nonterminal, t = terminal Examples: Binary numbers: B  0 B | 1 B | 0 | 1 Identifiers: I  a L | b L | c L |...| z L | a |...| y | z L  1 L | 2 L |...| 9 L | 0 L | 1 |...| 9 | 0 | a L | b L | c L |...| z L | a |...| y | z ab7d

Other classes of grammars The context free and regular grammars are important for programming language design. We study these in detail. Other classes have theoretical importance, but not in this course: Context sensitive grammar: Type 1 - Rules:    where |  |  |  | [That is, length of   length of , i.e., all sentential forms are length non-decreasing] Unrestricted, recursively enumerable: Type 0 - Rules:   . No restrictions on  and .

The Big Picture Chomsky Hierarchy of Language Grammars (1956)