Understanding Variables, Instance Variables, and Semantic Errors in Programming, Exams of Computer Science

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Compilers CS414-2008-FRFinal Review

David Galles Department of Computer ScienceUniversity of San Francisco

FR-0:

Deterministic Finite Automata Set of states Initial State Final State(s) Transitions

DFA for else, end, identifiersCombine DFA

FR-2:

Automatic Creation of DFAs

We’d like a tool:

Describe the tokens in the language Automatically create DFA for tokens Then, automatically create C code that implementsthe DFA We need a method for describing tokens

FR-3:

Formal Languages Alphabet

Σ: Set of all possible symbols

(characters) in the input file

Think of

Σ^

as the set of symbols on the

keyboard String

w: Sequence of symbols from an alphabet String length

|w

|^ Number of characters in a

string:

|car

|^ = 3,

|abba

|^ = 4

Empty String

ǫ: String of length 0:

|ǫ|

Formal Language

: Set of strings over an

alphabet Formal Language

6 =^

Programming language – Formal

Language is only a set of strings.

FR-5:

Language Concatenation Language Concatenation

Given two formal

languages

L^1

and

L^2

, the concatenation of

L^1

and

L,^2

L^1

L^2

=^ {

xy|

x^ ∈

L^1

, y^

∈^ L

For example:{fire, truck, car} {car, dog} ={firecar, firedog, truckcar, truckdog, carcar, cardog}

FR-6:

Kleene Closure

Given a formal language

L:

0 L

=^

{ǫ} (^1) L =^

L

2 L

=^

LL

3 L

=^

LLL

4 L

=^

LLLL∗^ L=

0 L

1 L

⋃^

2 L

⋃^

...^

⋃^

n^ L

⋃^

FR-8:

r.e. Precedence

From highest to Lowest:Kleene Closure *ConcatenationAlternation

ab*c

|e = (a(b*)c)

|^ e

FR-9:

Regular Expression Examples

(a|b)*

all strings over {a,b}

binary integers (with leading zeroes)

a(a

|b)*a

all strings over {a,b} thatbegin and end with a

(a|b)*aa(a

|b)*

all strings over {a,b} thatcontain aa

b(abb)*(a

|ǫ)^

all strings over {a,b} thatdo not contain aa

FR-11:

r.e. Shorthand Examples Regular Expression

Language if^ {if}

["a"-"z"]["0"-"9","a"-"z"]*

Set of legal identifiers

["0"-"9"]+

Set of integers (with leading zero

(["0"-"9"]+"."["0"-"9"]*)

|^ Set of real numbers

(["0"-"9"]*"."["0"-"9"]+)

FR-12:

Parsing Once we have broken an input file into a sequenceof tokens, the next step is to determine if thatsequence of tokens forms a syntactically correctprogram – parsing We will use a tool to create a parser – just like weused lex to create a parser We need a way to describe syntactically correctprograms^ Context-Free Grammars

FR-14:

Generating Strings with CFGs Start with the initial symbol Repeat:^ Pick any non-terminal in the string^ Replace that non-terminal with the right-handside of some rule that has that non-terminal asa left-hand sideUntil all elements in the string are terminals

FR-15:

CFG Example

E^ →

E^

+^ E

E^ →

E^

−^ E

E^ →

E^

∗^ E

E^ →

E/E

E^ →

num

FR-17:

Ambiguous Grammars A Grammar is

ambiguous

if there is at least one

string with more than one parse tree The expression grammar we’ve seen so far isambiguous E^ →

E^

+^ E

E^ →

E^

−^ E

E^ →

E^

∗^ E

E^ →

E/E

E^ →

num

FR-18:

Expression Grammar

E^ →

E^

+^ T

E^ →

E^

−^ T

E^ →

T

T^ →

T^

∗^ F

T^ →

T /F

T^ →

F

F^ →

num F^ →

(E