Context-Free Grammars: Understanding Syntactically Correct Programs, Study notes of Computer Science

Download Context-Free Grammars: Understanding Syntactically Correct Programs and more Study notes Computer Science in PDF only on Docsity! CS414-2008-02 Context-Free Grammars 1 02-0: Parsing • Once we have broken an input file into a sequence of tokens, the next step is to determine if that sequence of tokens forms a syntactically correct program – parsing • We will use a tool to create a parser – just like we used lex to create a parser • We need a way to describe syntactically correct programs • Context-Free Grammars 02-1: Context-Free Grammars • Set of Terminals (tokens) • Set of Non-Terminals • Set of Rules, each of the form: <Non-Terminal> → <Terminals & Non-Terminals> • Special Non-Terminal – Initial Symbol 02-2: Generating Strings with CFGs • Start with the initial symbol • Repeat: • Pick any non-terminal in the string • Replace that non-terminal with the right-hand side of some rule that has that non-terminal as a left-hand side Until all elements in the string are terminals 02-3: CFG Example E → E + E E → E − E E → E ∗ E E → E/E E → num 02-4: CFG Example E → E + E E → E − E E → E ∗ E E → E/E E → num E 02-5: CFG Example E → E + E E → E − E E → E ∗ E E → E/E E → num E ⇒ E + E CS414-2008-02 Context-Free Grammars 2 02-6: CFG Example E → E + E E → E − E E → E ∗ E E → E/E E → num E ⇒ E + E ⇒ E ∗ E + E 02-7: CFG Example E → E + E E → E − E E → E ∗ E E → E/E E → num E ⇒ E + E ⇒ E ∗ E + E ⇒ num ∗E + E 02-8: CFG Example E → E + E E → E − E E → E ∗ E E → E/E E → num E ⇒ E + E ⇒ E ∗ E + E ⇒ num ∗E + E ⇒ num ∗ num +E 02-9: CFG Example E → E + E E → E − E E → E ∗ E E → E/E E → num E ⇒ E + E ⇒ E ∗ E + E ⇒ num ∗E + E ⇒ num ∗ num +E ⇒ num ∗ num + num 02-10: CFG Example S → NP V NP NP →the N N → boy N → ball N → window V → threw V → broke CS414-2008-02 Context-Free Grammars 5 E → E + T E → E − T E → T T → T ∗ F T → T/F T → F F → num F → (E) 02-21: CFG for Statements • Expressions: id, num • Function calls: id(<input params>) • <input params> are expressions separated by commas • Block Statements { < list of statements > } • While statements (C syntax) All statements are terminated by a semi-colon ; 02-22: CFG for Statements S → id(P ); S → {L} S → while (E) S E → id | num P → ǫ P → EP ′ P ′ → ǫ P ′ → , EP ′ L → ǫ L → SL 02-23: Bakus Naur Form • Another term for Context-Free grammars is Bakus Naur Form, or BNF • We will use CFG and BNF interchangeably for this class 02-24: Extended Bakus Naur Form • Use regular expression notation (*, +, |, ?) in BNF (CFG) rules (1) S → { B } (2) S → print (id) (3) B → S ; C (4) C → S ; C (5) C → ǫ • Rules (3) - (5) describe 1 or more statements, terminated by ; 02-25: Extended Bakus Naur Form • Use regular expression notation (*, +, |, ?) in BNF (CFG) rules (1) S → { B } (2) S → print ”(” id ”)” (3) B → (S;)+ CS414-2008-02 Context-Free Grammars 6 • Rules (3) describes 1 or more statements, terminated by ; 02-26: Extended Bakus Naur Form • Pascal for statements: (1) S → for id := E to E do S (2) S → for id := E downto E do S 02-27: Extended Bakus Naur Form • Pascal for statements: (1) S → for id := E (to | downto) E do S • Why this is useful (other than just reducing typing) will be seen when we generate parsers