Four Concepts in Programming Language Description

1. Syntax - The structure and composition of allowable phrases and sentences of the language.
2. Semantics - Meaning of the syntactic elements. We may think of providing syntactic elements as input to a semantic function which in turn provides some representation of the meaning of the elements as output.
   • The semanitic function of a language is in the logic of the compiler (or interpreter) which arranges arranges for program execution.
   • an equivalent semantic function, albeit using a different representation, should also be found in the mind of the programmer (we hope).
3. Pragmatics - referring to practical aspects of how constructs and features of a language may be used to achieve various objectives.
4. Metalanguage - A language in which a subject language is being described.
   • BNF (Backus-Naur Form) - to describe syntax.
   • Aximatic semantics - for describing semantics, but this is hard so in most cases we use English as a metalanguage to describe semantics.

BNF

• Introduced in the late 50's when Algol 60 was being developed.
• Context Free Grammars
• Chomsky's hiearchy
  • Phrase structure (Turing Machine)
    • d(S0, 0) = (1, S0, R)
      d(S0, 1) = (0, S0, R)
      d(S0, b) = (1, S1, L)
      d(S1, 0) = (0, S1, R)
      d(S1, 1) = (0, S1, R)
      
  • Context Sensitive Grammars(LBA)
  • Context Free Grammars(PDA) - BNF
  • Regular (FSA) - very strict
    

    	S -> 1S
    	S -> 0A
    	A -> 0S
    	A -> 1B
    	B -> 0B
    	B -> 1A
    	S -> emptyString
    

• English:

  <sentence> ::=  <noun phrase> <verb phrase>
  <noun phrase> ::= <article> <noun> <article> <adjective> <noun>
  <verb phrase> ::= <verb> | <verb><adverb>
  <article> ::= a | the
  <adjective> ::= large | hungry
  <noun> ::= rabbit | frog
  <verb> ::= writes | hops
  <adverb> ::= quickly | neatly
  
  

• a set of symbols including:
  • terminals
  • non terminals (can be replaced by other symbols)
  • a special symbol called the start symbol
• a set of rules for producing strings in the language.
• Postal Example:

  <postal-address> ::= <name-part> <street-address> <zip-part>
  
   <personal-part> ::= <name> | <initial> "."
  
   <name-part> ::= <personal-part> <last-name> [<jr-part>] <EOL>
  	       | <personal-part> <name-part>
  
   <street-address> ::= [<apt>] <house-num> <street-name> <EOL>
  
   <zip-part> ::= <town-name> "," <state-code> <ZIP-code> <EOL>
  

• Grammar for a simple assignment statements:

  <assign> -> <id> = <expr>
  <id> -> A | B | C
  <expr> -> <ID> + <expr>
            | <id> * <expr>
            | (<expr>)
            | <id>
  
  
  A = B * (A + C)
  

  • This grammar is Ambiguous, why?
  • A = B + C * A
  
  
• Fix the OP:

  <assign> -> <id> = <expr>
  <id> -> A | B | C
  <expr> -> <ID> + <term>
                | <term>
  <term> -> <term> * <factor>
                | <factor>
  <factor> -> (<expr>)
  	      |<id>
  

• BNF rules for Java