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Tutorial 7: Recursive Descent

2017-11-01

Language: set of words Word: string of letters/symbols Letter/Symbol: atomic "thing" Grammar: rules to define a language

Our language - simple arithmetic

Six operations: +, -, *, /, ^, ! Precendence:

  • +, - (lowest)
  • *, /
  • ^, =
  • !

Is a + b * c = (a + b) * c OR a + (b * c)

Arguments to operations are natural numbers.

I want to:

  • Read a string from standard in
  • Turn it into data structure
  • Evaluate
  • Pretty print in Reverse Polish Notation

Idea:

  • Parse the string into a "parse tree"
  • Parse tree - "proof" tthat a word is in a language

An arithmetic expression (AE) is any of:

  1. AE +/- AE such that +/- does not occur in () "top level"
  2. If there are no "top level" +/-, AE *// AE
  3. No top level *// => AE ^ AE (^ TL)
  4. AE! (! must be top)
  5. (AE)
  6. A number

Ex. (1 + 2) * 2 ^ 4

Parse tree:

    *
   / \
  ()  \
  |    \ 
  +     ^
 / \   / \
1   2 2   4

Abstract Syntax Tree: Parse tree minus the useless stuff

  • Ex: () is not very helpful in our parse tree

Ambiguity Problem: 1 - 2 - 3

  • Could be (1 - 2) - 3 = -4 or 1 - (2 - 3) = 2

So we decide that everything is left assosciative (arbitrary decision) and modify rule 1 to account for this.

  1. AE +/- (arithmetic expression WITHOUT -/+) such that +/- does not occur in () "top level"