Syntax

Syntax – Intro and Overview

CS331

Syntax
• Syntax defines what is grammatically valid in a programming
language
– Set of grammatical rules
– E.g. in English, a sentence cannot begin with a period
– Must be formal and exact or there will be ambiguity in a
programming language
• We will study three levels of syntax
– Lexical
• Defines the rules for tokens: literals, identifiers, etc.
– Concrete
• Actual representation scheme down to every semicolon, i.e. every lexical
token
– Abstract
• Description of a program’s information without worrying about specific
details such as where the parentheses or semicolons go

BNF Grammar
• BNF = Backus-Naur Form to specify a grammar
– Equivalent to a context free grammar
• Set of rewriting rules (a rule that can be applied multiple
times) defined on a set of nonterminal symbols, a set of
terminal symbols, and a start symbol
– Terminals, ∑ : Basic alphabet from which programs are
constructed. E.g., letters, digits, or keywords such as “int”,
“main”, “{“, “}”
– Nonterminals, N : Identify grammatical categories
– Start Symbol: One of the nonterminals which identifies the
principal category. E.g., “Sentence” for english, “Program” for a
programming language

Rewriting Rules
• Rewriting Rules, ρ
– Written using the symbols  and |
| is a separator for alternative definitions, i.e. “OR”
 is used to define a rule, i.e. “IS”

– Format
• LHS  RHS1 | RHS2 | RHS3 | …
• LHS is a single nonterminal
• RHS is any sequence of terminals and nonterminals

Sample Grammars
• Grammar for subset of English
Sentence  Noun Verb
Noun  Jack | Jill
Verb  eats | bites
• Grammar for a digit
Digit  0 | 1 | 2 | 3 | 4 | 5 | 6 |7 |8 |9
• Grammar for signed integers
SignedInteger  Sign Integer
Sign  + | -
Integer  Digit | Digit Integer
• Grammar for subset of Java
Assignment  Variable = Expression
Expression  Variable | Variable + Variable | Variable – Variable
Variable  X | Y

Derivation
• Process of parsing data using a grammar
– Apply rewrite rules to non-terminals on the RHS of an existing
rule
– To match, the derivation must terminate and be composed of
terminals only
• Example
Digit  0 | 1 | 2 | 3 | 4 | 5 | 6 |7 |8 |9
Integer  Digit | Digit Integer
– Is 352 an Integer?
Integer → Digit Integer → 3 Integer →
3 Digit Integer → 3 5 Integer →
3 5 Digit → 3 5 2

Intermediate formats are called sentential forms
This was called a Leftmost Derivation since we replaced the
leftmost nonterminal symbol each time (could also do Rightmost)

Derivation and Parse Trees
• The derivation can be
visualized as a parse
tree
Integer

Digit Integer

Digit Integer
3

5 Digit

2

Parse Tree Sketch for Programs

BNF and Languages
• The language defined by a BNF grammar is the set of all
strings that can be derived
– Language can be infinite, e.g. case of integers
• A language is ambiguous if it permits a string to be parsed
into two separate parse trees
– Generally want to avoid ambiguous grammars
– Example:
• Expr  Integer | Expr + Expr | Expr * Expr | Expr - Expr
• Parse: 3*4+1
– Expr * Expr → Integer * Expr →
3 * Expr → 3 * Expr+Expr → … 3 * 4 + 1
– Expr + Expr → Expr + Integer → Expr + 1
Expr * Expr +1 → … 3 * 4 + 1

Ambiguity
• Example for
AmbExp  Integer | AmbExp – AmbExp
2-3-4

Ambiguous IF Statement
Dangling ELSE:

if (x<0)
if (y<0) { y=y-1 }
else { y=0 };

Does the else go with the first or second if?

How to fix ambiguity?
• Use explicit grammar without ambiguity
– E.g., add an “ENDIF” for every “IF”
– Java makes a separate category for if-else vs. if:
IfThenStatement  If (Expr) Statement
IfThenElseStatement  If (Expr) StatementNoShortIf else
Statement
StatementNoShortIf contains everything except
IfThenStatement, so the else always goes with the
IfThenElse statement not the IfThenStatement
• Use precedence on symbols

Alternative to BNF
• The use of regular expressions is an alternate
way to express a language

Regex to EBNF
• The book uses some deviations from “standard”
regular expressions in Extended Backus Naur
Format (defined in a few slides)
{ M } means zero or more occurrences of M
( M | N) means one of M or N must be chosen
[M] means M is optional

Use “{“ to mean the literal { not the regex {

RegEx Examples
• Booleans
– “true” | “false”
• Integers
– (0-9)+
• Identifiers
– (a-zA-Z){a-zA-Z0-9}
• Comments (letters/space only)
– “//”{a-zA-Z }(“r” | “n” | “rn”)
• Regular expressions seem pretty powerful
– Can you write one for the language anbn? (i.e. n a’s followed by n
b’s)

Extended BNF
• EBNF – variation of BNF that simplifies
specification of recursive rules using regular
expressions in the RHS of the rule
• Example:
– BNF rule
Expr  Term | Expr + Term | Expr – Term
Term  Factor | Term * Factor | Term / Factor
– EBNF equivalent
Expr  Term { [+|-] Term }
Term  Factor { [* | / ] Factor }
• EBNF tends to be shorter and easier to read

EBNF
• Consider:
Expr  Term{ (+|-) Term }
Term  Factor { (* | / ) Factor }
Factor  Identifier | Literal | (Expr)

Parse for X+2*Y

BNF and Lexical Analysis
• Lexicon of a programming language – set of all
nonterminals from which programs are written
• Nonterminals – referred to as tokens
– Each token is described by its type (e.g. identifier,
expression) and its value (the string it represents)
– Skipping whitespace or comments

or punctuation

Categories of Lexical Tokens
• Identifiers
• Literals
Includes Integers, true, false, floats, chars
• Keywords
bool char else false float if int main true while
• Operators
= || && == != < <= > >= + - * / % ! [ ]
• Punctuation
;.{}()

Issues to consider: Ignoring comments, role of whitespace,
distinguising the < operator from <=, distinguishing
identifiers from keywords like “if”

A Simple Lexical Syntax for a Small
Language, Clite
Primary → Identifier [ "["Expression"]" ] | Literal | "("Expression")"
| Type "("Expression")"

Identifier → Letter { Letter | Digit }
Letter → a | b | … | z | A | B | … Z
Digit → 0 | 1 | 2 | … | 9
Literal → Integer | Boolean | Float | Char
Integer → Digit { Digit }
Boolean → true | false
Float → Integer . Integer
Char → ‘ ASCIICHAR ‘

Major Stages in Compilation
• Lexical Analysis
– Translates source into a stream of Tokens, everything else
discarded
• Syntactic Analysis
– Parses tokens, detects syntax errors, develops abstract
representation
• Semantic Analysis
– Analyze the parse for semantic consistency, transform into a
format the architecture can efficiently run on
• Code Generation
– Use results of abstract representation as a basis for generating
executable machine code

Lexical Analysis & Compiling
Process

Difficulties: 1 to many mapping from HL source to machine code
Translation must be correct
Translation should be efficient

Lexical Analysis of Clite
• Lexical Analysis – transforms a program
into tokens (type, value). The rest is tossed.
• Example Clite program:
// Simple Program
int main() {
int x;
x = 3;
}

Result of Lexical Analysis:

Lexical Analysis (2)
Result of Lexical Analysis:
1 Type: Int Value: int
2 Type: Main Value: main
3 Type: LeftParen Value: ( // Simple Program
4 Type: RightParen Value: ) int main() {
5 Type: LeftBrace Value: { int x;
6 Type: Int Value: int x = 3;
7 Type: Identifier Value: x }
8 Type: Semicolon Value: ;
9 Type: Identifier Value: x
10 Type: Assign Value: =
11 Type: IntLiteral Value: 3
12 Type: Semicolon Value: ;
13 Type: RightBrace Value: }
14 Type: Eof Value: <<EOF>>

Lexical Analysis of Clite in Java
public class TokenTester {
public static void main (String[] args) {
Lexer lex = new Lexer (args[0]);
Token t;
int i = 1;

do
{
t = lex.next();
System.out.println(i+" Type: "+t.type()
+"tValue: "+t.value());
i++;
} while (t != Token.eofTok);
}
}

The source code for how the Lexer and Token classes are arranged
is the topic of chapter 3

Lexical to Concrete
• From the stream of tokens generated by our
lexical analyzer we can now parse them
using a concrete syntax

Concrete EBNF Syntax for Clite
Program → int main ( ) { Declarations Statements }
Declarations → { Declaration }
Declaration → Type Identifier [ "["Integer"]" ] { , Identifier ["["Integer"]"] };
Type → int | bool | float | char
Statements →{ Statement }
Statement → ; | Block | Assignment | IfStatement | WhileStatement
Block → { Statements }
Assignment → Identifier ["["Expression"]" ] = Expression ;
IfStatement → if "(" Expression ")" Statement [ else Statement ]
WhileStatement → while "("Expression")" Statement

Concrete Syntax;
Higher than lexical
syntax!

Concrete EBNF Syntax for Clite
Expression → Conjunction { || Conjunction }
Conjunction →Equality { && Equality }
Equality → Relation [ EquOp Relation ]
EquOp → == | !=
Relation → Addition [ RelOp Addition ]
RelOp → < | <= | > | >= References lexical
Addition → Term { AddOp Term } syntax
AddOp → + | -
Term → Factor { MulOp Factor }
MulOp → * | / | %
Factor → [ UnaryOp ] Primary
UnaryOp → - | !
Primary → Identifier [ "["Expression"]" ] | Literal | "("Expression")" |
Type "(" Expression ")"

Syntax Diagram
• Alternate way to specify a language
• Popularized with Pascal
• Not any more powerful than BNF, EBNF, or regular
expressions

Linking Syntax and Semantics
• What we’ve described so far has been
concrete syntax
– Defines all parts of the language above the
lexical level
• Assignments, loops, functions, definitions, etc.
• Uses BNF or variant to describe the language
• An abstract syntax links the concrete syntax
to the semantic level

Abstract Syntax
• Defines essential syntactic elements without
describing how they are concretely
constructed
• Consider the following Pascal and C loops
Pascal C
while i<n do begin while (i<n) {
i:=i+1 i=i+1;
end }

Small differences in concrete syntax; identical abstract construct

Abstract Syntax Format
• Defined using rules of the form
– LHS = RHS
• LHS is the name of an abstract syntactic class
• RHS is a list of essential components that define the
class
– Similar to defining a variable. Data type or abstract
syntactic class, and name
– Components are separated by ;
• Recursion naturally occurs among the
definitions as with BNF

Abstract Syntax Example
• Loop
Loop = Expression test ; Statement body
– The abstract class Loop has two components, a test which is a
member of the abstract class Expression, and a body which is a
member of an abstract class Statement

• Nice by-product: If parsing abstract syntax in Java, it
makes sense to actually define a class for each abstract
syntactic class, e.g.
class Loop extends Statement {
Expression test;
Statement body;
}

Abstract Syntax of Clite
Program = Declarations decpart; Statements body;
Declarations = Declaration*
Declaration = VariableDecl | ArrayDecl
VariableDecl = Variable v; Type t
ArrayDecl = Variable v; Type t; Integer size
Type = int | bool | float | char
Statements = Statement*
Statement = Skip | Block | Assignment |
Conditional | Loop
Skip =
Block = Statements
Conditional = Expression test;
Statement thenbranch, elsebranch
Loop = Expression test; Statement body
Assignment = VariableRef target; Expression source
Expression = VariableRef | Value | Binary | Unary

Abstract Syntax of Clite
VariableRef = Variable | ArrayRef
Binary = Operator op; Expression term1, term2
Unary = UnaryOp op; Expression term
Operator = BooleanOp | RelationalOp | ArithmeticOp
BooleanOp = && | ||
RelationalOp = = | ! | != | < | <= | > | >=
ArithmeticOp = + | - | * | /
UnaryOp = ! | -
Variable = String id
ArrayRef = String id; Expression index
Value = IntValue | BoolValue | FloatValue | CharValue
IntValue = Integer intValue
FloatValue = Float floatValue
BoolValue = Boolean boolValue
CharValue = Character charValue

Java AbstractSyntax for Clite
class Loop extends Statement {
Expression test;
Statement body;
}
Class Assignment extends Statement {
// Assignment = Variable target; Expression source
Variable target;
Expression source;
}

…
Much more… see the file (when available)

Abstract Syntax Tree
• Just as we can build a parse tree from a BNF grammar, we
can build an abstract syntax tree from an abstract syntax
• Example for: x+2*y
Expression = Variable | Value | Binary
Binary = Operator op ; Expression term1, term2

Binary node

Expr

Sample Clite Program
• Compute nth fib number

Abstract Syntax for Loop of Clite Program

Concrete and Abstract Syntax
• Aren’t the two redundant?
– A little bit
• The concrete syntax tells the programmer exactly
what to write to have a valid program
• The abstract syntax allows valid programs in two
different languages to share common abstract
representations
– It is closer to semantics
– We need both!

What’s coming up?
• Semantic analysis
– Do the types match? What does this mean?
char a=‘c’;
int sum=0;
sum = sum = a;
• Can associate machine code with the abstract
parse
– Code generation
– Code optimization

Syntax

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