541 CS Lecture -*- Outline -*-
* Lexical (or micro-) syntax
** motivation is abstraction (working at the right level)
want to describe syntax of language at a higher level than characters
the higher level things are called tokens (words)
also may want to have different sets of tokens
(publication vs. working)
but to do that have to define the syntax of tokens
typically described as a regular language
because very simple
regularity guarantees not ambiguous
very fast to parse.
** Lexical conventions
*** blanks, whitespace
often used to separate tokens (words)
*** reserved words: if, then, etc. cannot be used as identifiers
*** keywords: (in Algol 60) are distinguished (by font, quotes etc)
*** keywords in context: keywords only recognized in certain contexts
/* PL/I example */
IF IF=THEN
THEN THEN=ELSE;
ELSE; IF=THEN=ELSE;
** Regular expressions (Watt, section 2.2.2)
go quickly...
---------------
Denotational semantics of
REGULAR EXPRESSIONS
Syntax:
re ::= char
| \epsilon
| re re
| re '|' re
| re *
| ( re )
| re +
Semantics: for all c in char,
r1, r2 in re
M[[c]] = {"c"}
M[[\epsilon]] = {""}
M[[r1 r2]] = {st | s in M[[r1]],
in t M[[r2]]}
M[[r1 | r2]] = M[[r1]] \union M[[r2]]
M[[r1*]] = {"", s,ss,...| s in M[[r1]]}
M[[(r1)]] = M[[r1]]
M[[r1+]] = M[[r1 (r1 *)]]
---------------
Examples:
ab denotes {"ab"}
a|b denotes {"a", "b"}
a* denotes {"", "a", "aa", ...} (all sequences of a's)
(ab)* denotes {"", "ab", "abab", "ababab", ...}
(a|b)* denotes {"", "a", "b", "ab", "ba", "aaa", ...}
(\epsilon|a)(a)*b denotes a*b --many equivalent forms
"(a|b|c|...|z|_|&...