lesson_01.md 1.8 KB
Formal languages and compilers
Luca Oddone Breveglieri
Introduction
What is a formal language?
Contrary to natural language, it is meant to communicate with machines.
A language is formal if its syntax (structure) and semantic (interpretation) are defined in a precise algorithmic way.
There is an effective procedure to verify the grammatical correctness of a phrase and determine its meaning.
It is a mathematical object composed by:
- An alphabet and built over a
- grammar consisting in axiomatic rules
- or an automata
Hystorical notes
Years '50
- Chomsky proposes the mathematical model of a grammar (1956)
Years '60
- Connection between formal languages and automata
- Invention of formal grammars
- Development of automated compilation
Years '70-'80
- Formal language theory becomes a standard university discipline
- Introduction of SDKs like Flex or Bison
Lesson 1
Definition of a language
- Alphabet: finite set of elements
- String: Ordered set of atomic elements, possibly repeated
- Language: Finite or infinite set of strings
Strings can be both finite or infinite.
The cardinality of a language determines the number of elements contained,
It can be 0 for the empty language or infinite for infinite languages.
Operations on strings
Concatenation (product of strings)
- Is a basic operation,
- Is associative,
- Changes the length.
Empty string (or null string) Ɛ:
is the neutral element respective to concatenation
Substring:
Given a string x = u y v
- x is a prefix
- y is a substring
- v is a suffix
if u,v ≠ Ɛ, y is a proper substring