Plan for Today. Regular Expressions: repetition and choice. Syntax and Semantics. Context Free Grammars

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Valentine Clark
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1 Plan for Today Context Free s models for specifying programming languages syntax semantics example grammars derivations Parse trees yntax-directed translation Used syntax-directed translation to interpret expression language Top-down Predictive Parsing Regular Expressions: repetition and choice let : a b c word : let + What regular expressions cannot express: nesting, e.g. matching parentheses: ( ) (( )) ((( ))) to any depth Why? DF has only a finite # states and thus cannot encode that it has seen N ( -s and thus now must see N ) -s for the parentheses to match (for any N). For that we need a recursive definition mechanism: : ( ) C453 Lecture Context Free Intro 1 C453 Lecture Context Free Intro 2 Context Free s CFG: set of productions of the form yntax and emantics Regular Expressions define what correct tokens are Non-terminal! phrase phrase phrase phrase: string of terminals and non-terminals terminals: tokens of the language non-terminals represent sets of strings of tokens of the language Context Free s define what correctly formed programs are ut are all correctly formed programs meaningful? Example: stmt! iftmt whiletmt iftmt! IF OPEN boolexpr CLOE tmt whiletmt! WHILE OPEN boolexpr CLOE tmt C453 Lecture Context Free Intro 3 C453 Lecture Context Free Intro 4

2 yntax and emantics Our Next Class of Languages Regular Expressions define what correct tokens are Context Free s define what correctly formed programs are ut are all correctly formed programs meaningful? NO: the program can have semantic errors some can be detected by the compiler: type errors, undefined errors some cannot: run-time errors, program does not compute what it is supposed to The semantics of a program defines its meaning. Here, we do syntax directed translation / interpretation Context-Free Languages R { a n b n } { ww } Regular Languages a *b* (a b)* C453 Lecture Context Free Intro 5 Context-Free Languages Example Context-Free s Recursive definitions We will start here Pushdown utomata F + stack context-free grammar G: ab derivation: ab aabb aabb nother derivation: ab aabb aaabbb aaabbb

3 n pplication of this Language Deriving another grammar L(G) = ab Describes parentheses: n n { a b : n 0} (((( )))) Gave a grammar for: Context-Free Languages n b n Can we derive a for: { a } R { ww } Regular Languages context-free grammar G : derivation: Example aa bb aa abba abba Representing ll Properly Nested Parentheses L(G) = ab n n { a b : n 0} nother derivation: aa abba abaaba abaaba Describes parentheses: (((( )))) Can we build a grammar to include any valid combination of ( )? For example ( ( ) ( ( ) ) )

4 Possible context-free grammar G : derivation: () () () () nother derivation: () () ()() ()() Context-Free s Nonterminals G = ( V, T,, P) Terminals tart symbol Productions of the form: Nonterminal x tring of symbols, Nonterminals and terminals Derivation, Language : G=(V,T,,P) Derivation: tart with start symbol Keep replacing non-terminals by their RH x, until no non-terminals are left The resulting string (sentence) is part of the language L(G) The Language L(G) defined by the CFG G: L(G) = the set of all strings of terminals that can be derived this way Derivation Order Given a grammar with rules: aa 4. b lways expand the leftmost non-terminal Leftmost derivation: 2 3 aa aa aab aab 4 5 C453 Lecture Context Free Intro 15

5 Derivation Order tring Given a grammar with rules: aa 3. lways expand the rightmost non-terminal 4. b 5. tm --> id := Exp Exp --> num Exp --> ( tm, Exp ) Leftmost derivation: a := ( b := ( c := 3, 2 ), 1 ) tm ==> a := Exp ==> a := ( tm, Exp ) ==> a := ( b := Exp, Exp ) ==> a := ( b := ( tm, Exp ), Exp ) ==> a := ( b := ( c := Exp, Exp ), Exp ) ==> a := ( b := ( c := 3, Exp ), Exp ) ==> a := ( b := ( c := 3, 2), Exp ) ==> a := ( b := ( c := 3, 2), 1) Rightmost derivation: b b aab aab 2 3 Rightmost derivation: tm ==> a := Exp ==> a := ( tm, Exp ) ==> a := ( tm, 1) ==> Parse Trees aa b Parse Trees aa b a a aa

6 Parse Trees aa b aa aab Parse Trees aa b aa aab aab a a b a a b Parse Trees aa b aa aab aab aab a a b yield aab = aab entential forms aa b Partial parse tree

7 aa Partial parse tree a a sentential form ometimes, derivation order doesn t matter Leftmost: aa aa aab aab Rightmost: ame parse tree b b aab aab a a b Does it matter here? Parse Tree How about here? tm --> id := Exp Exp --> num Exp --> ( tm, Exp ) tring a := ( b := ( c := 3, 2 ), 1 ) (1) exp --> exp * exp (2) exp --> exp + exp (3) exp --> NUM tring * 6 What does this question mean? C453 Lecture Context Free Intro 27 C453 Lecture Context Free Intro 28

8 yntax Directed Translation or Interpretation Use parse tree to Translate one language to another Create a data structure of the program Interpret, or evaluate, the program Works conceptually by Parser discovers the parse tree Parser executes certain actions while traversing the parse tree using a depth-first, post-order traversal Interpret this program tm --> id := Exp Exp --> num Exp --> ( tm, Exp ) tring a := ( b := ( c := 3, 2 ), 1 ) Parse Tree C453 Lecture Context Free Intro 29 C453 Lecture Context Free Intro 30 How about here? emantic Rules for Expression Example (1) exp --> exp * exp (2) exp --> exp + exp (3) exp --> NUM tring * 6 C453 Lecture Context Free Intro 31 C453 Lecture Context Free Intro 32

Lecture 8: Context Free Grammars

Lecture 8: Context Free Grammars Lecture 8: Context Free s Dr Kieran T. Herley Department of Computer Science University College Cork 2017-2018 KH (12/10/17) Lecture 8: Context Free s 2017-2018 1 / 1 Specifying Non-Regular Languages Recall