Transcript No Slide Title

Some CFL Practicalities
CPSC 388
Ellen Walker
Hiram College
Grammar for Expressions
• Exp -> Exp Op Exp | ( Exp ) | number
• Op -> + | – | *
• Non-terminals: Exp, Op
• Terminals: number, +, –, *, (, )
• Terminals are tokens not necessarily
characters!
Simple Grammar for Statement
• Stmt -> If-Stmt | … other statements
• If-Stmt -> if ( Exp ) Stmt | if ( Exp ) Stmt
else Stmt
• Exp -> … on previous slide
More Concise If-Stmt using 
• If-Stmt -> if ( Exp ) Stmt ElsePart
• ElsePart -> else Stmt | 
Epsilon Placement is Significant
• How do these languages differ?
L1:
S -> x ; S | x
L2:
S-> x ; S | 
L3:
S-> x ; S | A
A -> x | 
L4:
S-> N | 
N -> x ; N | x
Recursion in Grammars
• When a rule refers to its own LHS in the
RHS, the rule is recursive
– Left-recursion (LHS is first)
– Right-recursion (LHS is last)
• “Exp -> Exp Op Exp” is both leftrecursive and right-recursive!
Why Recursion?
• Without recursion, languages must be
finite
– All possible derivations can be enumerated
in advance
– Example:
• S-> aB
• B -> b | Cc
• C -> c
Recursion in Multiple Rules
• Stmt -> If-Stmt | … other statements
• If-Stmt -> if ( Exp ) Stmt | if ( Exp ) Stmt
else Stmt
• Stmt => If-Stmt => if … Stmt …
• There is a recursion on Stmt, but it
takes 2 rules
Ambiguous Grammars
• If there is a string that has two different
derivations (with different parse trees),
the grammar is ambiguous.
• Only one string is needed to determine
ambiguity
Exp Grammar is Ambiguous
• Exp -> Exp Op Exp | ( Exp ) | number
• Op -> + | – | *
Exp
Exp
Exp Op
Exp
Exp
Exp Op
Exp
number + number * number
Exp Op
Op
Exp
Exp
number + number * number
Dangling Else
// w true when x!=0 and y=0
If (x!=0)
if (y!=0) z=true;
else w=true;
// w true when x=0
If (x!=0)
if (y!=0) z=true;
Else w = true;
Disambiguating Rule
• Leave the grammar ambiguous, but
create a rule (outside the grammar) that
determines which competing parse is
“correct”
• Examples:
– Multiplication has precedence over addition
– Subtraction is left-associative
– Else matches the closest “if”
Modifying the Grammar
• Create additional non-terminals and
rules that prevent ambiguity
• In this case, the syntax is (again)
reflected only by the grammar
Exp Grammar with Precedence
•
•
•
•
•
Exp -> Exp Adop Exp | Term
Term -> Term Mulop Factor | Factor
Factor -> ( Exp ) | number
Adop -> + | –
Mulop -> *
• * evaluation forced “deeper” into the tree!
If Grammar with “Closest else”
• Stmt -> MatchedStmt | UnmStmt
• MatchedStmt -> if (Exp) MatchedStmt
else MatchedStmt | Other
• UnmStmt -> if (Exp) Stmt | if (Exp)
MatchedStmt else UnmStmt
• Other -> { Stmt-list } | … | 
• Stmt-list -> Stmt Stmt-list | Stmt
Avoiding the IF ambiguity
• Require the else part in all if’s
– This is the LISP solution
• Require bracketing keywords
– If-stmt -> if Exp Stmt endif | if Exp Stmt
else Stmt endif
– In some languages “fi” is used instead of
“endif”
Abstract Parse Trees
• Design trees that include only essential
aspects of the language (for semantics);
remove “syntactic sugar” and
intermediate non-terminals
Parse Tree vs. Abstract Parse
Tree
Exp
Exp Op
Exp
Exp Op
+
Exp
*
number + number * number
number
number
number
Extended BNF
• “Ordinary BNF” is simply a CFG
– Non-terminals named like: <expression>
– Terminals are bare sequences of
characters
• Extensions
–{x}
–[x]
Repeat x 0 or more times ( x*)
x is optional (x | )