CSE443 Compilers Dr. Carl Alphonce alphonce@buffalo.edu 343 Davis - PowerPoint PPT Presentation

CSE443 Compilers Dr. Carl Alphonce alphonce@buffalo.edu 343 Davis Hall

Team formation Please sit with your teams starting next week. C vs SML?

Lexical Phases of structure a compiler Figure 1.6, page 5 of text

languages & grammars Formally, a grammar is defined by 4 items: 1. N, a set of non-terminals 2. ∑ , a set of terminals 3. P, a set of productions 4. S, a start symbol G = (N, ∑ , P, S)

languages & grammars N, a set of non-terminals ∑ , a set of terminals (alphabet) N ∩ ∑ = {} P, a set of productions of the form (right linear) X -> a X -> aY X -> ℇ X ∈ N, Y ∈ N, a ∈ ∑ , ℇ denotes the empty string S, a start symbol S ∈ N

Lexical Analysis Lexical structure described by regular grammar Deterministic finite state machine performs analysis

LANGUAGE operations If L and M are regular, so are: L ∪ M = { s | s ∈ L or s ∈ M } union LM = { st | s ∈ L and t ∈ M } concatenation L * = ∪ i=0, ∞ L i Kleene closure By definition, L 0 = { ℇ }

Given an alphabet ∑ REGular EXpression (regex) Inductive definition ℇ is a regex 𝓜 ( ℇ ) = { ℇ } For each a ∈ ∑ , a is a regex 𝓜 (a) = {a}

Regular expressions (regex) Inductive definition Assume r and s are regexes. r|s is a regex denoting 𝓜 (r) ∪ 𝓜 (s) rs is a regex denoting 𝓜 (r) 𝓜 (s) r * is a regex denoting ( 𝓜 (r)) * (r) is a regex denoting 𝓜 (r) Precedence: Kleene closure > concatenation > union Associativity: all left-associative (minimize use of parentheses: (r|s)|t = r|s|t )

Algebraic laws Assume r and s are regexes. Commutativity r|s = s|r Associativity r|(s|t) = (r|s)|t and r(st) = (rs)t Disributivity r(s|t) = rs|rt and (s|t)r = sr|tr Identity ℇ r = r ℇ = r Idempotency r ** = r *

We can describe a regular language using a regular expression

A regular expression can be recognized using a finite state machine. Machines: NFA non-deterministic finite automaton DFA deterministic finite automaton

Process of building lexical analyzer 1) spell out the language language

Process of building lexical analyzer 2) formulate a regular expression language regex

Process of building lexical analyzer 3) build an NFA language regex NFA

Process of building lexical analyzer 4) transform NFA to DFA language regex NFA DFA

Process of building lexical analyzer 5) transform DFA to a minimal DFA language regex NFA DFA DFA

Process of building lexical analyzer 5) The minimal DFA is character our lexical analyzer stream language regex NFA DFA DFA token stream lexical analyzer

Focus for today regex NFA

Nondeterministic Finite Automata (NFA) A finite set of states S An alphabet ∑ , ℇ ∉ ∑ 𝛆 ⊆ S X ( ∑ ∪ { ℇ }) X 𝒬 (S) (transition function) s 0 ∈ S (a single start state) F ⊆ S (a set of final or accepting states)

Deterministic Finite Automata (DFA) A finite set of states S An alphabet ∑ , ℇ ∉ ∑ 𝛆 ⊆ S X ∑ X S (transition function) s 0 ∈ S (a single start state) F ⊆ S (a set of final or accepting states)

Initial state: arrow from Regex -> NFA nowhere pointing in. Often labelled state 0. ℇ 1 0 N(s) ℇ ℇ 0 1 Final state: drawn with a ℇ double circle ℇ N(t) a 1 0 Arrows are labeled with ℇ or a ∈ ∑ . S | t for each a ∈ ∑

Regex -> NFA ℇ 1 0 N(s) ℇ ℇ 0 1 ℇ ℇ N(t) a 1 0 S | t for each a ∈ ∑

Regex -> NFA St 0 1 N(s) N(t) ℇ ℇ S * 0 1 N(s) ℇ ℇ

Simple example static

Simple example static c s t a t i 0 1 2 3 4 5 6

Simple example static struct c s a t i t ℇ 0 1 2 3 4 5 6 ℇ i F t s t r u c ℇ ℇ 7 8 9 10 11 12 13