Today Today • Grammar Principles of Programming Principles of Programming Languages XXII Languages XXII Wael Aboelsaadat Wael Aboelsaadat wael@cs.toronto.edu wael@cs.toronto.edu http://www.cs.toronto.edu/~wael http://www.cs.toronto.edu/~wael Acknowledgement: Some of the material in these lectures are base d on material by Prof. Diane Horton & Prof. Anthony Bonner Language Specification & Compilation Language Specification & Compilation Grammar: introduction Grammar: introduction • Grammar: – A Grammar is a formalism that describes which sequence of terminals are meaningful in a PL. Mathematically, it is defined as a quadruple ( N , T , P , S ) where: • N is the set of symbols called Nonterminals • T is the set of symbols called Terminals • P is the set of productions • S subsetof N is the nonterminal called the starting symbol – Example: G = (N,T,P,S) where N = {S} , T = {a,b}, P={S->aS, S->bS, S-> } • Production: A production is a rule of the form X � Y where X is a string of – symbols ( terminals or nonterminals ) containing at least one nonterminal, and Y is a string of symbols ( terminals or nonterminals ) 1
Grammar: context free Grammar: context free Grammar: Grammar: backus backus Naur Naur form form • Backus Naur Form (BNF) is a metalanguage for describing • A context free grammar (CFG) is a grammar in which |X| = 1, programming languages i.e. X is a single nonterminal – LHS: 1 nonterminal • A BNF grammar is a context free grammar – RHS: a sequence of terminals and nonterminals – E.g. • Notation: • S -> ab (CFG) • SA -> ab (non CFG) – Nonterminals are enclosed in angle brackets, i.e. “<“ and “>” “ instead of “ � ” in productions – Uses “::= • CFG is sufficient to describe most of the constructs in – Productions having the same left hand side can be grouped programming languages together using the alteration symbol “|” e.g <S> ::= a <S> | b <s> | – Lists are described using recursive rules Programming languages describable by CFG are recognizable • • A rule is recursive if its left-hand side appears on the right-hand side, by push down automata ( analogues to FSA with a stack ) e.g. <ident.list> ::= identifier | identifier, <ident.list> Grammar: BNF recursive rules Grammar: BNF recursive rules Grammar: extended BNF Grammar: extended BNF • Notation: • Left Recursive BNF Grammar: – (…|…|…) Any one of the alterations – A BNF grammar rule is left recursive if its LHS appears at the left – […] Optional part end of the RHS – (…)* or {…} or […]* repeat zero or more times e.g. <ident.list> ::= <ident.list> , identifier | identifier – (…) - or {…} - or […] - e.g. A � A x | y , yxx repeat one or more times – "x"or 'x' terminal symbol – Unquoted words non-terminal symbol • Right Recursive BNF Grammar: – A BNF grammar rule is right recursive if its LHS appears at the right end of the RHS • Example: e.g. <ident.list> ::= identifier | identifier, <ident.list> – Using the above notation e.g. A � x A | y , xxy < expression > : : = < expression > + < term > | < expression > - < term > | < term > could be written in the form of an iteration, as follows: The order of recursion has implications on the order of The order of recursion has implications on the order of < expression > : : = < term > [ ( + | -) < term > ]* evaluation and associativity. evaluation and associativity. 2
Grammar: definitions Grammar: definitions… Grammar: derivation Grammar: derivation Grammar: parsing Grammar: parsing Grammar: building parse trees Grammar: building parse trees • A parse tree describes the hierarchical syntactic structure of the sentence based on a given language 3
Grammar: grammars are not unique Grammar: grammars are not unique Grammar: ambiguity Grammar: ambiguity Grammar: sources of ambiguity Grammar: sources of ambiguity Grammar: inherently ambiguous Grammar: inherently ambiguous • Associativity and precedence of operators – Solution: • Change the grammar to reflect operator precedence X*Y-Z means ((X*Y) – Z) • Extent of a substructure – E.g. • Dangling else – Solution… • Obscure recursion – E.g. • exp � exp exp • A � A B – Solution: ?? 4
Grammar: is this ambiguous? Grammar: is this ambiguous? Grammar: is this ambiguous? Grammar: is this ambiguous? < assign > : : = < identifier > = < expression > < assign > : : = < identifier > = < expression > < identifier > : : = A|B|C < identifier > : : = A|B|C < expression > : : = < expression > + < expression > < expression > : : = < expression > + < expression > | < expression > - < expression > | < expression > - < expression > | ( < expression > ) | ( < expression > ) | < identifier > | < identifier > Yes, because the sentence A = B - C - A has two different parse trees The grammar does not force "normal" left-to-right evaluation of addition and subtraction. Grammar: is it really a problem? Grammar: is it really a problem? Grammar: an unambiguous version Grammar: an unambiguous version • The operation of addition is associative in mathematics. Hence < assign > : : = < identifier > = < expression > A + B + C < identifier > : : = A|B|C < expression > : : = < expression > + < term > can be performed as either | < expression > - < term > ( A + B ) + C or A + ( B + C ). | < term > < term > : : = < term >*< factor > | < factor > The multiply operation is also associative. < factor > : : = ( < expression > ) | < identifier > Therefore one might say the previous ambiguous grammar would be satisfactory for addition and multiplication. Tree for A = B + C * A But would it? Computer arithmetic is not exact, and one might want be able to control the order… 5
Evaluation Evaluation • CSC324H1F - 0101 – Wael Aboelsaadat • Tutorials – Anya Tafliovich (LM157) [Assignments: 1a,2a] – Hojjat Ghaderi (UC328) [Assignments: 1b,3a] – Hyonho Lee (LM123) [Assignments: 2b] 6
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