programming languages need to be precise a regular expression is one of the following: tokens are the building blocks of programs


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1 Chapter 2 :: Programming Language Syntax Programming Language Pragmatics Michael L. Scott Introduction programming languages need to be precise natural languages less so both form (syntax) and meaning (semantics) must be unambiguous example: digits digit we need good notation (or a metalanguage) to describe precise languages by recognizing tokens regular expressions contextfree grammars Tokens Regular Expressions tokens are the building blocks of programs shortest strings with individual meaning examples keywords (type names, control structures) identifiers (variable names) symbols (mathematical operators) constants (literals) considerations case sensitivity international characters maximum lengths a regular expression is one of the following: A character The empty string, denoted by Two regular expressions concatenated Two regular expressions separated by (i.e., or) A regular expression followed by the Kleene star (concatenation of zero or more strings) these simple rules help us find tokens in the programming language useful in unix/linux environments Regular Expressions numerical literals in Pascal may be generated by the following: arrow can be read as can be replaced by goes to the notation for contextfree grammars (CFG) is sometimes called BackusNaur Form (BNF) necessary since regular expressions cannot specify nested constructs used to define the syntax of a language with Kleene star and other facilitating symbols, the notation is termed Extended BNF (EBNF) 1
2 a CFG consists of a set of terminals T a set of nonterminals N appear on the left hand side of a production a start symbol S (a nonterminal) if not explicitly stated, it is the lefthand nonterminal of the first production a set of productions a production has the form A ω where A N and ω N T Derivations example grammar binarydigit 0 binarydigit 1 or equivalently binarydigit 0 1 Derivations consider the grammar Integer Digit Integer Digit Digit we can derive any unsigned integer, like 352, from this grammar: Integer Integer Digit Integer 2 Integer Digit 2 Integer 5 2 Digit Derivations a different derivation of 352 Integer Integer Digit Integer Digit Digit Digit Digit Digit 3 Digit Digit 3 5 Digit this is called a leftmost derivation since at each step, the leftmost nonterminal is replaced the previous derivation was a rightmost derivation Derivations notation for derivations Integer * 352 meaning that 352 can be derived in a finite number of steps using the grammar for Integer 352 ϵ L(G) meaning that 352 is a member of the language defined by grammar G L(G) { ω ϵ T* Integer * ω } meaning that the language defined by grammar G is the set of all symbol strings ω that can be derived as an Integer Grammars It is conventional in general discussions of grammars to use lower case letters near the beginning of the alphabet for terminals lower case letters near the end of the alphabet for strings of terminals upper case letters near the beginning of the alphabet for nonterminals upper case letters near the end of the alphabet for arbitrary symbols greek letters for arbitrary strings of symbols 2
3 Parse Trees a parse tree is a graphical representation of a derivation each internal node of the tree corresponds to a step in the derivation the children of a node represent a righthand side of a production each leaf node represents a symbol of the derived string reading from left to right Parse Trees the step, Integer Integer Digit appears in the parse tree as Parse Trees parse tree for 352 as in Integer expression grammar with precedence and associativity parse tree for expression grammar (with precedence) for * 5 parse tree for expression grammar (with left associativity) for
4 another grammar with precedence and associativity + and are leftassociative operators in mathematics * and / have higher precedence than + and parse tree for 4**2**3 + 5 * Grammar G 1 Ambiguous Grammars associativity and precedence shown in the structure of the parse tree highest precedence at the bottom leftassociativity on the left at each level a grammar is ambiguous if one of its strings has two or more different parse trees grammar G 1 above is unambiguous ambiguous expression grammar G 2 equivalent to G 1 fewer productions and nonterminals, but ambiguous Ambiguous Grammars Abstract Syntax Tree ambiguous parse of using G 2 the shape of a parse tree reveals the meaning of the program we want a tree that removes its inefficiency, but keeps its shape remove separator/punctuation terminal symbols remove all trivial root nonterminals replace remaining nonterminals with leaf terminals removes syntactic sugar and keeps essential elements of a language 4
5 Abstract Syntax Tree Dangling Else with which if statement does the else associate? Dangling Else Ambiguity Dangling Else Solutions Algol 60, C, C++ associate each else with closest if use {}or begin/end to override Algol 68, Modula, Ada use explicit delimiter to end every conditional (e.g., if..fi) Java rewrite the grammar to limit what can appear in a conditional Extended BNF (EBNF) BNF recursion for iteration nonterminals for grouping EBNF additional metacharacters { } for a series of zero or more ( ) for a list; must pick one [ ] for an optional list; pick none or one EBNF Examples Expression is a list of Terms separated by operators + and  5
6 EBNF to BNF we can always rewrite an EBNF grammar as a BNF grammar can be rewritten as try rewriting EBNF rules with { } and ( ) while EBNF is no more powerful than BNF, its rules are often simpler and clearer recall that the scanner is responsible for tokenizing source removing comments may be difficult if nested (often) dealing with pragmas (i.e., significant comments) saving text of identifiers, numbers, strings saving source locations (file, line, column) for error messages suppose we are building an adhoc (handwritten) scanner for Pascal: we read the characters one at a time with lookahead if it is one of the onecharacter tokens { ( ) [ ] < >, ; = +  etc } we announce that token if it is a., we look at the next character if that is a dot, we announce. otherwise, we announce. and reuse the lookahead if it is a <, we look at the next character if that is a = we announce <= otherwise, we announce < and reuse the lookahead, etc if it is a letter, we keep reading letters and digits and maybe underscores until we can't anymore then we check to see if it is a reserve word if it is a digit, we keep reading until we find a nondigit if that is not a. we announce an integer otherwise, we keep looking for a real number if the character after the. is not a digit we announce an integer and reuse the. and the lookahead pictorial representation of a Pascal scanner as a finite automaton 6
7 a scanner can be represented by a deterministic finite automaton (DFA) lex, scangen, etc. build these things automatically from a set of regular expressions specifically, they construct a machine that accepts the language identifier int const real const comment symbol... we run the machine over and over to get one token after another nearly universal rule: always take the longest possible token from the input thus foobar is foobar and never f or foo or foob more to the point, is a real const and never 3,., and regular expressions "generate" a regular language; DFAs "recognize" it scanners tend to be built three ways adhoc semimechanical pure DFA (usually realized as nested case statements) tabledriven DFA adhoc generally yields the fastest, most compact code by doing lots of specialpurpose things, though good automaticallygenerated scanners come very close writing a pure DFA as a set of nested case statements is a surprisingly useful programming technique though it's often easier to use perl, awk, sed for details see Figure 2.11 tabledriven DFA is what lex and scangen produce lex (flex) in the form of C code scangen in the form of numeric tables and a separate driver (for details see Figure 2.12) note that the rule about longestpossible tokens means you return only when the next character can't be used to continue the current token the next character will generally need to be saved for the next token in some cases, you may need to peek at more than one character of lookahead in order to know whether to proceed in Pascal, for example, when you have a 3 and you a see a dot do you proceed (in hopes of getting 3.14)? or do you stop (in fear of getting 3..5)? in messier cases, you may not be able to get by with any fixed amount of lookahead; in Fortran, for example, we have DO 5 I = 1,25 loop DO 5 I = 1.25 assignment here, we need to remember we were in a potentially final state, and save enough information that we can back up to it, if we get stuck later 7
8 Parsing terminology: contextfree grammar (CFG) symbols terminals (tokens) nonterminals production derivations (leftmost and rightmost  canonical) parse trees sentential form Parsing by analogy to RE and DFAs, a contextfree grammar (CFG) is a generator for a contextfree language (CFL) a parser is a language recognizer there is an infinite number of grammars for every contextfree language not all grammars are created equal, however Parsing it turns out that for any CFG we can create a parser that runs in O(n^3) time there are two wellknown parsing algorithms that permit this Early's algorithm CookeYoungerKasami (CYK) algorithm O(n^3) time is clearly unacceptable for a parser in a compiler  too slow 8
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