1. Definition A string is a sequence of symbols. Examples “Hi, Mom.” “YAK” “abbababba” “#@?_!L!!” Question In what ways do programmers use strings?

2. A string is also called a __________. An ____________ is the set of all possible symbols that can be included in a valid string. The pattern of symbols that make up a string or a set of strings is referred to as __________. The length of a string is the number of symbols in the sequence. The ______ string of a string of length zero (0). Some Special Notation denotes a blank (space) denotes a null string (alternative notations:  )

3. A language is set of strings. Examples Bit2Strings = { , 0, 1, 00, 01, 10, 11} Integers = { s | s is is a valid string representing an integer inn Arabic form} GoldiesComments = { the  porridge  is  too  hot., the  porridge  is  too  cold., the  porridge  is  just  right. } AdaIntegerOps = { +, - *, /, **, mod, rem,, >=, =, /= } SheepSpeak = { ba, baa, baaa, baaaa,... } AdaIdentifiers = { s | s is a valid identifier of the Ada programming language } Ada identifiers must begin with an alphabetic letter followed by zero or more alphabetic, numeric and/or underscore characters. FortranIdentifiers = { s | s is a valid identifier of the Fortran IV language } Fortran IV identifiers are like Ada’s, with two exceptions: (1) no underscores are permitted, (2) maximum length is 8 characters

4. (Using languages from the previous slide...) 1) Which languages are finite (and which are infinite)? Bit2Strings? GoldiesComments? AdaIntegerOps? SheepSpeak? AdaIdentifiers? FortranIdentifiers? 2) What is the “smallest” alphabet for each language? Bit2Strings GoldiesComments AdaIntegerOps SheepSpeak AdaIdentifiers FortranIdentifiers

5. A language that is used to define other languages is called a metalanguage. Metalanguages that are widely used by computer scientists: _____________ (especially context-free grammars) ___________ _________ ___________ _________ ____________ _________ ___________ __________

6. BNF is a tool used to define the syntax of programming languages by using a collection of rules. Each ________ (production) defines one part of the syntax. The syntax defined by a rule is named with a ___________ identifier. The form of a rule is as follows: nonterminal ::= syntaxOfNonterminal alternately written as shown below: nonterminal  syntaxOfNonterminal

7.  can be read “is defined to be” | separates alternative syntactic forms often used to enclose nonterminals ( ) can be used as grouping symbols Example   0 | 1

8. A second example  |  0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9

9. BNF language definitions make frequent use of recursive rules. Example  |  0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 Another Example   |  ; | while ( ) | if ( ) | ( )

10. BNF notation has been extended in many ways. Common EBNF Extensions Example Number  [ ‘+’ | ‘-’] Unsigned_Number Unsigned_Number  Integer | Integer ‘.‘ Integer eliminated from nonterminals (capitalized word phrases are used) [ ] encloses syntax that is optional { } encloses syntax that can be repeated consecutively 0 or more times Single-character symbols are generally quoted.

11. A second example Modula_If  IF Cond THEN Instruction_Sequence { Elseif_Part } [ Else_Part ] END Elseif_Part  ELSIF Cond THEN Instruction_Sequence Else_Part  ELSE Instruction_Sequence

12. A generator defines a metalanguage by stating rules that can be applied to generate each string of the language (and no other strings). The rules of a generator can be applied to provide a derivation of any string in the language. .    |   0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9  .  3.  3. 2  3. 2 1 Sample Derivation rule

13. A derivation tree captures a derivation by showing each applied rule from the nonterminal (parent node) to its derived string (ordered children). .    |   0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9  Frequently, a single derivation tree captures several different derivations.

14. A regular expression (RE) is a textual metalanguage. Operations concatenation RE 1 RE 2 a b denotes alternation RE 1 | RE 2 a | b denotes repetition RE 1 * or RE 1 + a* denotes a+ denotes any symbol.. denotes the alphabet range [  1 -  2 ] [a-e] denotes Note: There are many BNF languages that cannot be expressed as an RE.

15. A syntax diagram is a graphical metalanguage with the following characteristics: complete syntax diagram consists of one or more disconnected components of a directed graph. Every node in a syntax diagram contains a symbol(s) or the name of another component. There is one arc entering each component from the left and one leaving each component on the right Usage Each component represents one part of the syntax. A valid string is formed by following the arrows through the diagram, from left to right.

16. Example phoneNumber 785digit 1 2 3 4 5 6 7 8 9 0

17. Metalanguages fall into two categories: generators that can be applied to generate all possible strings. BNF is a ___________. recognizers that can be applied to any string to discover whether or not it is included in the language. Syntax diagrams can be applied _________________________________. REs are ________________.

18. Formatting Issues fixed format or free format? where are ends of lines/blanks permitted? are there line break requirements? Comments single line comments: -- or // Multi-line comments: /* … */ or { … } nested comments allowed? Limitations maximum line/identifier length? maximum number of components? Reserved words predefined identifiers (reserved words) that cannot be otherwise used? identifiers with default behavior that can be overridden (keywords)? Semantic Issues metalanguages generally ignore data typing restrictions metalanguages often ignore constant limitations