Bottom-up parsing encompasses various techniques, each with its unique strengths and characteristics. Canonical LR, LALR, SLR, and LR(1) parsing algorithms provide options to balance power, efficiency, and ease of implementation in different contexts. Understanding the differences and trade-offs among these types of bottom-up parsing is crucial in choosing the most suitable technique for specific compiler design scenarios.
1.
Introduction to Bottom-Up
Parsing
2.
Shift-Reduce Parsing
a.
LR(0) Parsing
b.
SLR(1) Parsing
c.
CLR(1) Parsing
d.
LALR(1) Parsing
3.
Operator-Precedence Parsing
4.
LR(1) Parsing
5.
GLR Parsing
6.
Comparison of Bottom-Up
Parsing Techniques
7.
Advantages and
Disadvantages of Bottom-Up Parsing
8.
Frequently Asked Questions
Bottom-Up Parsing
Bottom-up parsing, also known as shift-reduce parsing, is a
parsing technique that builds a parse tree from the leaves to the root. It
starts with the input symbols and applies grammar rules in a bottom-up manner
until it reaches the start symbol. This approach allows for a wide range of
grammars to be parsed efficiently and is commonly used in various applications,
including compiler design and natural language processing.
Shift-Reduce Parsing
Shift-reduce parsing is a type of bottom-up parsing where
the parser repeatedly performs two actions: shift and reduce. During the shift
operation, the parser shifts the next input symbol onto the stack. In the
reduce operation, the parser applies a production rule to replace a sequence of
symbols on the stack with a non-terminal symbol.
1.
LR(0) Parsing
LR(0) parsing is a simple bottom-up parsing technique that
uses a deterministic finite automaton (DFA) to parse the input. It employs a
lookahead of 0, meaning it only considers the current input symbol when making
parsing decisions. LR(0) parsing is powerful enough to handle a wide range of
grammars, but it may suffer from shift-reduce and reduce-reduce conflicts.
LR Parsing Algorithm
// Get the next token from the input
token = next_token()
// Main parsing loop
while true:
// Get the top of
the stack
s = top of stack
// Check the
action for the current stack symbol and token
if action[s,
token] = "shift si" then:
// Shift the
token onto the stack
PUSH token
PUSH si
// Get the
next token from the input
token =
next_token()
else if action[s, token] = "reduce A::=
β" then:
// Reduce by
applying the production A::= β
POP 2 * |β|
symbols
// Get the new
top of the stack
s = top of
stack
// Push the
nonterminal A onto the stack
PUSH A
// Perform the
goto operation
PUSH goto[s,
A]
else if action[s,
token] = "accept" then:
// Parsing is
complete, return
return
else:
// Handle
syntax error
error()
2.
SLR(1) Parsing
SLR(1) parsing, which stands for Simple LR(1) parsing, is an
enhanced version of LR(0) parsing that uses a lookahead of 1. By considering
one additional symbol of lookahead, SLR(1) parsing can resolve many
shift-reduce conflicts that LR(0) parsing encounters. However, it still has
limitations and may not handle all grammars correctly.
SLR (Simple LR) parsing is a bottom-up parsing technique
that uses a simplified version of the LR parsing algorithm. It combines the
ease of LR(0) items and the power of a lookahead symbol to construct a parsing
table. Here's an overview of the SLR parsing algorithm and an example code snippet:
SLR Parsing Algorithm:
1. Construct the augmented grammar by adding a new start
symbol and production:
S' -> S
2. Compute the closure of the initial item, [S' -> .S].
3. Create an empty set of LR(0) items, C, and add the
closure of the initial item to C.
4. Repeat until no new sets can be added:
a. For each set of
items, C_i, in C, and for each grammar symbol, X, do the following:
i. Compute the
GOTO(C_i, X), which represents the items that can be reached from C_i by X.
ii. If GOTO(C_i,
X) is not empty and not already in C, add it to C.
5. Create the SLR parsing table:
a. For each set of
items, C_i, in C:
i. For each
item, [A -> α.Xβ], in C_i, do the following:
- If X is a
nonterminal:
- For each
production, A -> γ, in the grammar, add a "reduce A -> γ" entry
to the parsing table for each terminal symbol in FOLLOW(A).
- If X is a
terminal and X != epsilon:
- Add a "shift GOTO(C_i, X)"
entry to the parsing table.
- If X ==
epsilon and A == S', add an "accept" entry to the parsing table.
3.
CLR(1) Parsing
CLR(1) parsing, or Canonical LR(1) parsing, is a more
powerful technique that can handle a broader class of grammars than SLR(1)
parsing. It constructs a more detailed parsing table by augmenting LR(0) items
with lookahead information. CLR(1) parsing resolves more conflicts and is
capable of parsing a larger set of grammars accurately.
CLR (Canonical LR) parsing is a bottom-up parsing technique
that combines the power of LR(1) items and the efficiency of LR(0) items. It
uses a canonical collection of LR(1) items to construct a parsing table. Here's
an overview of the CLR parsing algorithm and an example code snippet:
CLR Parsing Algorithm:
1. Construct the augmented grammar by adding a new start
symbol and production:
S' -> S
2. Compute the closure of the initial item, [S' -> .S,
$].
3. Create an empty set of LR(1) items, C, and add the
closure of the initial item to C.
4. Repeat until no new sets can be added:
a. For each set of
items, C_i, in C, and for each grammar symbol, X, do the following:
i. Compute the
GOTO(C_i, X), which represents the items that can be reached from C_i by X.
ii. If GOTO(C_i,
X) is not empty and not already in C, add it to C.
5. Create the CLR parsing table:
a. For each set of
items, C_i, in C:
i. For each
item, [A -> α.Xβ, a], in C_i, do the following:
- If X is a
nonterminal:
- For each
production, A -> γ, in the grammar, add a "reduce A -> γ" entry
to the parsing table for each terminal symbol in FOLLOW(A).
- If X is a terminal and X != epsilon:
- Add a
"shift GOTO(C_i, X)" entry to the parsing table.
- If X ==
epsilon and A == S', add an "accept" entry to the parsing table.
ii. For each
item, [A -> α.Xβ, a], in C_i where a is a lookahead symbol, add a
"reduce A -> α.Xβ" entry to the parsing table.
4.
LALR(1) Parsing
LALR(1) parsing, or Look-Ahead LR(1) parsing, is a
compromise between SLR(1) and CLR(1) parsing. It constructs a compact parsing
table like SLR(1) but resolves more conflicts like CLR(1). LALR(1) parsing is
widely used in practice due to its balance between efficiency and expressive
power.
LALR (Look-Ahead LR) parsing is a bottom-up parsing
technique that combines the efficiency of SLR (Simple LR) parsing with the
power of LR(1) parsing. It constructs a parsing table using a compact
representation of LR(1) items. Here's an overview of the LALR parsing algorithm
and an example code snippet:
LALR Parsing Algorithm:
1. Construct the augmented grammar by adding a new start
symbol and production:
S' -> S.
2. Compute the sets of LR(1) items for the augmented grammar
using the LR(1) item construction algorithm.
3. Merge the sets of LR(1) items that have the same core,
combining their lookahead symbols.
4. Create the LALR(1) parsing table:
a. For each merged
set of items, C_i:
i. For each
item, [A -> α.Xβ, a], in C_i, do the following:
- If X is a nonterminal:
- For each
production, A -> γ, in the grammar, add a "reduce A -> γ" entry
to the parsing table for each terminal symbol in LOOKAHEAD(A, α.Xβ, a).
- If X is a
terminal and X != epsilon:
- Add a
"shift GOTO(C_i, X)" entry to the parsing table.
- If X ==
epsilon and A == S', add an "accept" entry to the parsing table.
Operator-Precedence Parsing
Operator-precedence parsing is a different approach to
bottom-up parsing that relies on the precedence and associativity of operators
to guide the parsing process. It uses a precedence table to determine whether
to shift or reduce based on the relative priorities of operators.
Operator-precedence parsing is often used in simple arithmetic expressions and can
handle left-recursive grammars effectively.
LR(1) Parsing
LR(1) parsing is a more general technique than LR(0) parsing
that uses a lookahead of 1 symbol to make parsing decisions. It handles a
broader class of grammars by taking into account more information about the
input. LR(1) parsing constructs a deterministic finite automaton with a
lookahead, which allows it to resolve shift-reduce and reduce-reduce conflicts
effectively.
GLR Parsing
GLR parsing, or Generalized LR parsing, is a powerful technique
that can handle ambiguous grammars and produce multiple parse trees when
necessary. It uses a nondeterministic finite automaton and explores all
possible parsing paths simultaneously. GLR parsing is useful for languages with
complex syntactic structures and is often employed in natural language
processing applications.
Comparison of Bottom-Up Parsing Techniques
Let's compare the different bottom-up parsing techniques
discussed so far:
-
LR(0) parsing is simple but
may suffer from conflicts.
-
SLR(1) parsing resolves
some conflicts but has limitations.
-
CLR(1) parsing handles more
grammars accurately but is more complex.
-
LALR(1) parsing strikes a
balance between efficiency and expressive power.
-
Operator-precedence parsing
is suitable for simple expressions and left-recursive grammars.
-
LR(1) parsing handles a
broader class of grammars effectively.
-
GLR parsing can handle
ambiguous grammars and produce multiple parse trees.
Advantages and Disadvantages of Bottom-Up Parsing
Bottom-up parsing offers several advantages, such as:
-
Ability to handle a wide
range of grammars.
-
Efficient parsing
algorithm.
-
Accommodation of
left-recursive grammars.
-
Suitable for error
recovery.
However, bottom-up parsing also has some disadvantages:
-
Potentially complex parsing
tables.
-
Possible conflicts and
ambiguities in the grammar.
-
Increased computational
overhead in some cases.
Frequently Asked Questions: Types of Bottom-up Parsing
1. What is bottom-up parsing?
Bottom-up parsing is a technique that builds a parse tree from
the leaves to the root by applying grammar rules in a bottom-up manner.
2. What are the advantages of bottom-up parsing?
Bottom-up parsing can handle a wide range of grammars, is
efficient, accommodates left-recursive grammars, and supports error recovery.
3. Which bottom-up parsing technique is suitable for
simple arithmetic expressions?
Operator-precedence parsing is commonly used for simple
arithmetic expressions.
4. Can bottom-up parsing handle ambiguous grammars?
Yes, GLR parsing, a type of bottom-up parsing, can handle
ambiguous grammars and produce multiple parse trees.
5. How do LR(1) parsing and LR(0) parsing differ?
LR(1) parsing uses a lookahead of 1 symbol, while LR(0)
parsing uses a lookahead of 0, allowing LR(1) parsing to handle a broader class
of grammars.
