Term Factorized Crashes In SWI-Prolog Exploring Alternatives And Solutions

Jul 18, 2025 by Jeany 75 views

Term Factorized Crashes in SWI-Prolog and Potential Alternatives

This article delves into a specific issue encountered in SWI-Prolog related to the term_factorized/3 predicate, which leads to stack overflow errors when dealing with cyclic terms. The discussion explores the root cause of the problem, which lies in the reliance on the compare/3 predicate within the implementation of term_factorized/3. It proposes an alternative approach to implement term_factorized/3 that circumvents the need for compare/3, potentially resolving the stack overflow issue. This article aims to provide a comprehensive understanding of the problem and explore viable solutions for SWI-Prolog developers.

Understanding the `term_factorized/3` Predicate

The term_factorized/3 predicate in SWI-Prolog is a crucial tool for term manipulation and analysis. Its primary purpose is to identify and represent shared subterms within a given term, effectively factorizing the term's structure. This factorization is essential for various applications, including term indexing, term comparison, and memory optimization. By identifying shared subterms, term_factorized/3 allows Prolog to represent terms more efficiently, reducing memory consumption and improving performance.

The predicate operates by traversing the input term and constructing a representation that captures the sharing relationships between subterms. This representation typically involves a table or dictionary that maps subterms to unique identifiers or handles. When a subterm is encountered for the first time, it is added to the table, and a new identifier is assigned. Subsequent occurrences of the same subterm are then represented by the same identifier, indicating that they are shared. This process effectively factorizes the term, replacing redundant subterms with references to a single shared instance.

Applications of term_factorized/3

The ability to factorize terms has significant implications for various aspects of Prolog programming. Some key applications of term_factorized/3 include:

Term Indexing: When indexing terms in a database or knowledge base, term_factorized/3 can be used to identify shared subterms, allowing for more efficient indexing and retrieval. By indexing only unique subterms, the index size can be reduced, and query performance can be improved.
Term Comparison: Comparing terms for equality or subsumption can be a computationally expensive operation, especially for large or complex terms. term_factorized/3 can facilitate term comparison by identifying shared subterms, allowing the comparison to focus on the unique parts of the terms. This can significantly speed up term comparison operations.
Memory Optimization: Sharing subterms through term_factorized/3 can lead to substantial memory savings, especially when dealing with terms that contain many repeated subterms. By representing shared subterms only once, the overall memory footprint of the program can be reduced.
Unification: The unification process, which is at the heart of Prolog's execution model, can benefit from term factorization. By identifying shared subterms, unification can be performed more efficiently, as only the unique parts of the terms need to be considered.

The Current Implementation and its Reliance on `compare/3`

The current implementation of term_factorized/3 in SWI-Prolog relies heavily on the compare/3 predicate. The compare/3 predicate is a fundamental tool for comparing two terms, determining their relative order according to the standard term ordering. This ordering is crucial for maintaining the integrity of data structures used within term_factorized/3, such as red-black trees (rbtrees), which are used for efficient lookup and insertion of subterms.

Within the term_factorized/3 implementation, compare/3 is used to check if a subterm has already been encountered and added to the factorization table. When a new subterm is encountered, compare/3 is used to compare it with existing subterms in the table. If a matching subterm is found, the existing identifier is used. Otherwise, the new subterm is added to the table, and a new identifier is assigned. This process ensures that shared subterms are represented by the same identifier.

The use of compare/3 within term_factorized/3 has proven to be effective in many cases. However, it also introduces a potential vulnerability when dealing with cyclic terms. Cyclic terms are terms that contain themselves as subterms, creating a circular reference. When compare/3 encounters cyclic terms, it can enter an infinite recursion, leading to a stack overflow error. This is because compare/3 attempts to traverse the entire term structure, including the cyclic references, which never terminate.

The Stack Overflow Issue with Cyclic Terms

The core problem arises when term_factorized/3 encounters cyclic terms. Cyclic terms, by their nature, create an infinite loop when traversed recursively. The current implementation's reliance on compare/3, which attempts to establish a total order between terms, exacerbates this issue. When compare/3 is called on cyclic terms, it enters a recursive loop, continuously comparing the terms without reaching a termination condition. This leads to the stack growing indefinitely until it exceeds the stack limit, resulting in a stack overflow error.

Illustrative Example

The following Prolog query demonstrates the issue:

?- X = s(s(X, Y), Z), Y = s(Y, X), term_factorized(X, _, _).

In this example, X and Y are defined as cyclic terms. When term_factorized/3 is called with X, the compare/3 predicate gets invoked recursively, leading to the stack overflow error. The error message clearly indicates that the stack limit is exceeded during the insertion operation within the red-black tree data structure used by term_factorized/3.

The error message:

ERROR: Stack limit (1.0Gb) exceeded
ERROR:   Stack sizes: local: 0.3Gb, global: 0.3Gb, trail: 81.8Mb
ERROR:     [6,038,429] rbtrees:insert2(<compound red/4>, 
<compound s/2>, 1, <compound black/4>, _76517588, _76517590)

This error highlights the fundamental limitation of the current approach when dealing with cyclic terms. The recursive nature of compare/3 in conjunction with the infinite structure of cyclic terms leads to the stack overflow. This issue needs to be addressed to ensure the robustness and reliability of term_factorized/3 when handling a wider range of Prolog terms.

Why `compare_with_stack/3` and `compare_extensive/3` are not Solutions

Kuniaki Mukai's compare_with_stack/3 and compare_extensive/3 were proposed as potential solutions to address the stack overflow issue with cyclic terms. However, as the original poster notes, these predicates are not suitable replacements for compare/3 within the context of term_factorized/3. The primary reason is that they don't provide the necessary transitive comparison behavior required by the underlying data structures, such as red-black trees, used in term_factorized/3.

Transitive Comparison: Transitive comparison means that if A < B and B < C, then A < C. Data structures like red-black trees rely on this property to maintain their internal ordering and ensure efficient search and insertion operations. If the comparison predicate does not guarantee transitivity, the data structure can become corrupted, leading to incorrect results or crashes.

compare_with_stack/3 and compare_extensive/3 might avoid stack overflows by limiting the depth of recursion or using alternative comparison strategies. However, they do not guarantee a transitive ordering for all terms, which makes them unsuitable for use with red-black trees or other data structures that require transitive comparisons.

Alternative Approaches to Implement `term_factorized/3`

Given the limitations of the current implementation when dealing with cyclic terms, it's essential to explore alternative approaches that can address the stack overflow issue. The key idea is to implement term_factorized/3 without relying on the problematic compare/3 predicate. Instead, we can leverage alternative techniques that are better suited for handling cyclic terms.

Hashing with Depth Limit

One promising approach is to use a hash lookup structure in conjunction with a hash function that is robust to cyclic terms. Unlike compare/3, which attempts to establish a total order between terms, hashing provides a way to quickly identify potential matches based on a calculated hash value. A well-designed hash function can map terms to hash values in a way that avoids collisions for most practical cases.

Hash Function with Depth Limit: To handle cyclic terms effectively, the hash function should incorporate a depth limit. This means that the hash value is calculated based on the term's structure up to a certain depth. Beyond this depth, the hash function ignores the term's subterms, effectively breaking the cyclic dependency. This prevents the hash function from entering an infinite recursion when calculating the hash value for a cyclic term.
Hash Lookup Structure: A hash lookup structure, such as a hash table or a hash map, can be used to store the mapping between subterms and their unique identifiers. When a new subterm is encountered, its hash value is calculated, and the lookup structure is consulted. If a matching hash value is found, the corresponding subterms are compared using a simpler equality check, such as (==)/2. If the subterms are identical, the existing identifier is used. Otherwise, the new subterm is added to the lookup structure with a new identifier.

Benefits of Hashing

Efficiency: Hashing provides a very efficient way to look up subterms, as the average time complexity for hash table operations is O(1).
Handling Cyclic Terms: The depth limit in the hash function prevents infinite recursion when dealing with cyclic terms.
Simpler Comparison: The comparison of subterms can be done using (==)/2, which is a simpler and more efficient operation than compare/3.

Drawbacks of Hashing

Hash Collisions: Hash collisions can occur when different subterms have the same hash value. While well-designed hash functions minimize collisions, they cannot be entirely avoided. Collision resolution strategies, such as chaining or open addressing, need to be employed to handle collisions.
Depth Limit: The depth limit in the hash function introduces a trade-off between accuracy and performance. A shallow depth limit can lead to more hash collisions, while a deep depth limit can increase the computational cost of hash calculation.

Using `(==)/2` for Equality Check

In the proposed alternative approach, the (==)/2 predicate plays a crucial role in determining the equality of subterms. Unlike compare/3, which establishes a total order between terms, (==)/2 simply checks if two terms are identical. This is a much simpler and more efficient operation, especially for cyclic terms.

(==)/2 and Cyclic Terms: The (==)/2 predicate can handle cyclic terms without entering an infinite recursion. It compares the terms' structures up to the point where a cycle is detected and then considers the terms to be identical if the cycles match.
Role in the Hashing Approach: In the hashing approach, (==)/2 is used to compare subterms that have the same hash value. This ensures that only truly identical subterms are considered shared, even if they have the same hash value due to a collision.

Fuzzy Testing and the Discovery of the Test Case

The test case that triggers the stack overflow in term_factorized/3 was discovered using fuzzy testing. Fuzzy testing is a software testing technique that involves feeding a program with a large number of randomly generated inputs to uncover unexpected behavior, such as crashes or errors.

Effectiveness of Fuzzy Testing: Fuzzy testing is particularly effective at finding edge cases and corner cases that might not be covered by traditional testing methods. It can automatically generate a wide variety of inputs, including those that are malformed, invalid, or unexpected, which can expose vulnerabilities in the program's logic.
Discovery of the Cyclic Term Issue: In this case, fuzzy testing generated a Prolog query with cyclic terms that triggered the stack overflow in term_factorized/3. This demonstrates the power of fuzzy testing in uncovering subtle bugs that might otherwise go unnoticed.
Less than 1000 Trials: The fact that the test case was found in less than 1000 trials highlights the severity of the issue. It suggests that the vulnerability is relatively easy to trigger, making it important to address it promptly.

Conclusion

The stack overflow issue in term_factorized/3 when dealing with cyclic terms is a significant problem that needs to be addressed. The current implementation's reliance on compare/3 makes it vulnerable to infinite recursion when encountering cyclic terms. Alternative approaches, such as hashing with a depth limit and using (==)/2 for equality checks, offer promising solutions that can circumvent the need for compare/3 and handle cyclic terms more effectively.

The discovery of the test case through fuzzy testing underscores the importance of robust testing techniques in software development. Fuzzy testing can help identify subtle bugs and vulnerabilities that might otherwise go unnoticed, ensuring the reliability and stability of software systems.

By implementing a more robust term_factorized/3 predicate, SWI-Prolog can better handle cyclic terms and provide a more reliable foundation for Prolog programming. This will benefit a wide range of applications that rely on term manipulation and analysis, including term indexing, term comparison, memory optimization, and unification.