1. Specifying Languages CS 480/680 – Comparative Languages

2. Language Specification2 Specifying a Language  Informal methods Textbooks, tutorials, etc.  Formal definitions Needed for exactness  Compiler writers, etc. Like technical specifications for design  Syntax – what expressions are legal?  Semantics – what should they do?

3. Language Specification3 Context Free Grammars  Definition: A context-free grammar (CFG) is a 4-tuple, G = (V, , R, S) V = variables, non-terminal symbols  = terminal symbols (alphabet) R = production rules S = start symbol, S  V  V, , R, S are all finite

4. Language Specification4 A Context Free Grammar  V = A, B  = (a, b)  R =A  aAa A  B B  bBb B  A B    S = A A  aAaA  aAa  aaAaaA  aAa  aaBaaA  B  aabBbaaB  bBb  aabbBbbaaB  bBb  aabbbbaB  What language does this grammar specify?

5. Language Specification5 Another Example CFG  V = A  = (a, b)  R =A  aAa A  bAb A  a A  b A    S = A What language does this grammar specify?

6. Language Specification6 More examples  Write a CFG for the following languages: “All strings consisting of one or more a’s, followed by twice as many b’s.” “Strings with more a’s than b’s.”  There is an entire class devoted to formal specifications of languages: CS 466/666 – Introduction to Formal Languages

7. Language Specification7 A CFG for Integer Arithmetic Expressions  V =,,,  = [(, ), 0…9, , , ,  ]  R =    ( )  |  0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9   |  |  |   S =

8. Language Specification8 Derivation of an Expression    ( )  ( ) +  ( ) +  (  ) +  (  ) +  (  ) +  (  ) +  (7  ) +  (73  ) +  (73  ) +  (73  4) +  (73  4) +  (73  4) +  (73  4) + 9

9. Language Specification9 Parse Trees  The derivation of an expression can also be expressed as a tree  This parse tree can help to resolve the interpretation of an expression  A compiler reads in the source code, and produces a parse tree before generating code.

10. Language Specification10 Example Parse Tree  A simple CFG: E  E  E | 0 | 1  E  E  E  E  E  E  1  E  E  1  0  E  1  0  1 E E  E E  E 1 1 0 E E  E E  E 1 1 0 Since there are two parse trees for this expression, the grammar is ambiguous. (Note: the order of substitution is not the issue.) Since there are two parse trees for this expression, the grammar is ambiguous. (Note: the order of substitution is not the issue.) (1 – 0) – 11 – (0 – 1)

11. Language Specification11 Ambiguity  If there are two parse trees for any expression, the grammar is syntactically ambiguous  Programming languages should be specified by unambiguous grammars Otherwise it is difficult to determine the semantics of a syntactically correct statement a = b + c * d; Conventions (like operator precedence) can be used to clarify syntactically ambiguous grammars

12. Language Specification12 Disambiguating a grammar  We can disambiguate our simple grammar by adding explicit parentheses: E  (E  E) | 0 | 1  E  E  E  (E  E)  E  (1  E)  E  (1  0)  E  (1  0)  1  In general, you can remove ambiguity in a grammar by imposing state in the derivation.

13. Language Specification13 An ambiguous grammar  S  aSb | aSbb |  Language: L = {a n b m | 0  n  m  2n} The number of b’s is between the number of a’s and twice the number of a’s  aabbb can be generated two ways  Disambiguating: Step 1: Produce all a’s with matching b’s Step 2: Produce all extra b’s.  S  aSb | A | A  aAbb | abb

14. Language Specification14 BNF  Backus-Naur Form  A standard notation for CFG’s, often used in specifying languages Non-terminals (variables) are enclosed in <> ,  =  is the production symbol (  ) | is used for “or”

15. Language Specification15 BNF Example  .   |   Can we generate the number “.7” from this grammar?

16. Language Specification16 Extended BNF  Makes some constructs easier to specify  No more powerful than BNF  Rules: { } = “zero or more” [ ] = “optional” or, equivalently “zero or one” | = “or” ( ) are used for grouping

17. Language Specification17 Arithmetic Expressions  ::= + | – |  ::= * | / |  ::= number | name | | ( )  ::= { (+| – ) }  ::= { (*| / ) }  ::= ‘(’ ‘)’ | number | name