LANGUAGE TRANSLATORS: WEEK 3

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LANGUAGE TRANSLATORS WEEK 3

• LECTURE
• Grammar Theory
• Introduction to Parsing
• Parser - Generators
• PRACTICAL/TUTORIAL
• JAVACUP Questions on grammar theory
• WEEKLY WORK Read Chapter 1 of Appels Book, read
  the JavaCup manual (both are online)

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GRAMMARS

• Theoretical properties and results about the
  nature of GRAMMARS have been used for 40 years to
  influence the design of PARSERS.
• A CONTEXT FREE (BNF) GRAMMAR contains a
  vocabulary terminals, non-terminals and
  productions of the form
• non-terminal v1 v2 .........vn
• where the vi are members of the vocabulary.
• One non-terminal is called the SPECIAL SYMBOL

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PROPERTIES OF GRAMMARS -1

• A syntax tree of a BNF Grammar G is a tree where
• - the root is the special symbol of G,
• - the leaves are terminals of G,
• - the nodes are non-terminals of G,
• - each node is the LHS of some production P of
  G in which the nodes children form the RHS of
  P

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PROPERTIES OF GRAMMARS -2

• A string is in the language generated by a BNF
  grammar G IFF it forms the leaves (in the correct
  order) of some syntax tree generated by G
• G is AMBIGUOUS IFF
• at least one of the strings in its language has
  more
• than one distinct syntax tree

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PROPERTIES OF GRAMMARS -3

• A BNF grammar G is LEFT-RECURSIVE if has at least
  one production of the form
• X X w
• where X is a non-terminal and w is a string of
  symbols in Gs vocabulary

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PROPERTIES OF GRAMMARS -4

• If w is a list of symbols in the vocabulary of
  BNF grammar G then
• First(w) set of TERMINAL symbols that may be at
  the front of ANY string derived from w using Gs
  productions

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PROPERTIES OF GRAMMARS -5

• If X is a non-terminal of BNF grammar G then
• Follow(X) set of TERMINAL symbols that can
  follow X in a derivation from Gs special symbol
  using Gs productions.
• Nullable(X) is true IFF the empty word can be
  derived from X

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PARSING

• A PARSER (or PARSING ALGORITHM) derives
  SYNTAX/PARSE TREES from a sequence of TOKENS
• Some well-known tools are little more than
  PARSERS e.g. Syntax Directed Editors - those that
  colour different syntax classes or point out
  syntax errors as you make them
• PARSING ALGORITHMS invariably are based on the
  CONTEXT FREE GRAMMAR that defines the language
  being parsed.

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Example

• Input String b 5 a 5 b
  PRINT(b a)
• Ouput PARSE TREE (as a Java data structure)
• new CompoundStm(
• new AssignStm("b",new NumExp(5)),
• new CompoundStm(
• new AssignStm("a", new OpExp(new
  NumExp(5),
• OpExp.Times,
  
• new
  IdExp("b"))),
• new PrintStm(new LastExpList(new
  OpExp(new IdExp("b"),
• OpExp.Times, new
  IdExp("a"))))
• )
• )

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PARSING ALGORITHMS

• Parsers that follow the languages grammar can be
  
• TOP DOWN - starting with the grammars special
  symbol, try to find a derivation of the string of
  tokens being parsed, consuming one token at a
  time
• BOTTOM UP - start with the string viewed as a
  stack. Match the top n tokens of the stack with
  the RHS of a grammar rule P and replace those
  tokens with the LHS of P

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PRACTICAL EXAMPLE OF THEORY

• A LL(1) PARSING TABLE (-like a program) can be
  automatically derived from a grammar G if and
  only if
• (i) G is NOT ambiguous
• (ii) G is NOT left recursive
• (iii) for EVERY two of Gs productions of the
  form
• X W1, X W2, it is the case that
  First(W1) and First(W2) have no common element

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Practical JavaCup

• JavaCup is a tool that inputs a GRAMMAR in BNF
  form ( other stuff..) and outputs a PARSE TREE
  (in the form of Java Constructors).
• Parsers created using JavaCup accept a sequence
  of TOKENS as input from a SCANNER such as last
  weeks.
• An easy way to show JavaCups use is to implement
  a simple interpreter with it
• (i) JavaCup inputs a grammar and creates a
  corresponding parser P in java.
• (ii) P accepts tokens from the scanned input and
  generates and passes the parse tree to some Java
  code which then EVALUATES it.

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SUMMARY

• Parsers check strings are legal according to
  grammatical definitions, and build up a structure
  representing legal strings (parse trees)
• Parsers can sometimes be auto-generated from the
  defining grammar
• Theory of grammars helps us in the
  auto-generation of parsers