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


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1 Plan for Today Context Free s models for specifying programming languages syntax semantics example grammars derivations Parse trees yntaxdirected translation Used syntaxdirected translation to interpret expression language Topdown 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 Nonterminal! phrase phrase phrase phrase: string of terminals and nonterminals terminals: tokens of the language nonterminals 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: runtime 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 ContextFree Languages R { a n b n } { ww } Regular Languages a *b* (a b)* C453 Lecture Context Free Intro 5 ContextFree Languages Example ContextFree s Recursive definitions We will start here Pushdown utomata F + stack contextfree 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: ContextFree Languages n b n Can we derive a for: { a } R { ww } Regular Languages contextfree 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 contextfree grammar G : derivation: () () () () nother derivation: () () ()() ()() ContextFree 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 nonterminals by their RH x, until no nonterminals 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 nonterminal 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 nonterminal 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 depthfirst, postorder 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
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