Introduction to Parsers Part II: SLR(1),CLR(1),LALR(1)
Compiler Design and Construction | Tutorial
Abstract
Compiler design and construction is the process of building software that translates high-level code into machine-executable instructions. A parser is found in the syntax analysis of the compilation process. SLR(1) is the simplest but is limited in handling complex grammar. LALR(1) is more powerful as it merges states for better complexity management. CLR(1) is the most powerful, handling all unambiguous grammars with the largest parsing table. This article explores the tutorials and demonstrates some simple handwritten numerical examples on bottom-up parsers SLR(1), CLR(1), and LALR(1).
1. Introduction
SLR (Simple LR) is a basic LR parser that uses smaller tables. While it is less powerful, it is efficient for certain tasks. LALR (Look-Ahead LR) improves upon SLR by merging states to reduce the size of the parsing table, making it more powerful than SLR and commonly used in many compilers. CLR (Canonical LR(1)) represents the full LR(1) parsing approach; it is the most powerful of the three, but it requires more memory.
A Canonical Set in LR parsing is a collection of parsing steps (called items) that show how far we have read a grammar rule. Each item has a dot (·) marking progress and a lookahead symbol to guide decisions.
Example:
For the grammar:
S → A a
A → b | c
Some items in a Canonical Set could be:
S → A · a (We have read A, waiting for ‘a’)
A → · b (We expect ‘b’ next)
A → · c (We expect ‘c’ next) which is set and which are the items
Items are the individual rules with the dot (·) showing parsing progress. Each line below is an item:
Canonical Items:
S → A · a (We have read A, waiting for ‘a’)
A → · b (We expect ‘b’ next)
A → · c (We expect ‘c’ next)
Canonical Set:
{
S → A · a
A → · b
A → · c
}
2. Inadequate State in LR Parsing
A state in an LR parsing table is called inadequate if it contains at least one Reduce-Reduce (RR) conflict or Shift-Reduce (SR) conflict, making it impossible to determine the next parsing action uniquely.
2.1 Intuitive Examples of Inadequate States in LR Parsing
Let’s break it down with simple, real-world analogies and examples to make the idea of inadequate states (which cause parsing conflicts) more intuitive.
Reduce-Reduce (RR) Conflict: Two People Giving Conflicting Directions
Imagine someone is at a crossroads and asking two different people for directions.
Parsing Analogy:
Suppose a state has two reduction rules:
A→α⋅
B→β⋅
The parser doesn't know whether to reduce A → α or B → β.
💡 Example Grammar:
S→EF
E→ϵ
F→ϵ
2.2 Shift-Reduce (SR) Conflict: When a Cashier is Confused
Parsing Analogy:
Suppose a state has both:
S → A⋅a
A → α⋅
The parser doesn't know whether to shift (read more input) or reduce A to α.
💡 Example Grammar:
S→Aa
A→ϵ
When the parser reads A → ε, it has two choices:
Reduce A→ϵ mmediately.
Shift the next input symbol a.
The parser is confused, leading to an SR conflict → inadequate state.
Simplest Possible Example of Shift-Reduce (SR) Conflict 🚦
Imagine we are at a traffic light 🚦.
🔴 RED LIGHT (Stop!) → You should stop (Reduce). 🟢 GREEN LIGHT (Go!) → You should keep moving (Shift).
Now, what if BOTH LIGHTS are on at the same time? 😲
💡 We don’t know what to do!
This confusion is a Shift-Reduce Conflict!
3. Parsers Power Comparison
LL(1) < SLR(1) < LALR(1) < CLR(1) = LR(1)
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4. SLR(1) HandWritten Example
5. CLR(1) HandWritten Example
CLR(1) Example 1
CLR(1) Example 2
CLR(1) Example 3
5. LALR Handwritten and TextBook Examples
Conclusion
The Deterministic Finite Automata (DFA), along with the dot concept (item representation) and follow sets, play a crucial role in constructing these parsers by defining valid transitions and reducing conflicts(SR, RR). LALR(1) is the minimized version of CLR(1) because CLR(1) is a powerful parser that is computationally expensive. CLR(1) is the advanced and successor of SLR(1), LR(0) bottom-up parsers. LL(1) overpower SLR(1), LR(0) parser. With accurate algorithms and parser programs, the practical implementation of these parsing techniques can be effectively realized. Even though CLR(1) is the most real-world language parser, it can suffer from ambiguous grammar and Conflicts(SR-RR) in certain cases.
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