TypeSim: Semantic Type Similarity Metric

• TypeSim is a continuous, semantically informed metric that measures functional equivalence between predicted and human-annotated type annotations in Python.
• It calculates similarity using set-theoretic overlaps and recursive comparisons of type attributes, accommodating both simple and complex generics.
• Empirical evaluations show that while TypeSim grants partial credit for near matches, it also highlights challenges in handling deeply nested and complex type structures.

TypeSim is a continuous, semantically informed similarity metric developed to evaluate the degree of functional equivalence between predicted and human-annotated type annotations in Python codebases. Unlike strict exact-matching metrics, which penalize otherwise reasonable type predictions for structural or superficial deviations (such as interchangeability between List and Sequence), TypeSim quantifies nuanced similarities using set-theoretic and recursive measures over type operations, arguments, and structure. Emerging from the TypyBench benchmark for LLM type inference, TypeSim addresses the evaluation needs of modern AI-assisted programming, especially in the context of complex or gradually typed codebases (Dong et al., 28 Jul 2025).

1. Definition and Rationale

TypeSim is defined as a metric for measuring the functional similarity between a predicted type annotation and its ground truth counterpart. It is grounded in the observation that many type annotations admit partial substitutability—e.g., Sequence in place of List or numeric generalization from int to float—and thus evaluating type inference models using only exact matches does not capture practical utility in software engineering tasks.

By quantifying overlap in supported methods and interfaces (i.e., attributes) as well as structural type compatibility (including for parametric types and unions), TypeSim produces a normalized score in the interval [0, 1], where higher values indicate closer functional equivalence.

This approach departs from binary correctness, recognizing that semantic similarity often trumps surface form when assessing type prediction models for their utility in large, dynamic codebases (Dong et al., 28 Jul 2025).

2. Formal Methodology

TypeSim operates recursively to accommodate both simple and complex types—including nested generics and composition via Union. For two non-generic types $t$ and $t'$, TypeSim computes a base similarity score as follows:

$$s(t, t') = \frac{|\text{attrs}(t) \cap \text{attrs}(t')|}{|\text{attrs}(t) \cup \text{attrs}(t')|}$$

where $\text{attrs}(t)$ is the set of methods and properties supported by type $t$.

For parametric types (e.g., List[int] vs. Sequence[float]), the comparison proceeds as:

$$S(T, T') = \frac{1}{2} \left[ s(\text{root}, \text{root}') + S_{\text{list}}(\text{args}(T), \text{args}(T')) \right]$$

where $\text{root}$ and $\text{root}'$ denote the base type, and $S_{\text{list}}$ compares the sequences of type arguments (supporting leniency when parameters are omitted, as in gradual typing).

When types use Union constructs, the metric decomposes the type into a set of member types and seeks an optimal matching under the setwise version of the metric (“SetCompare”), handling the permutation-invariant nature of union membership.

The metric’s implementation includes explicit pseudocode algorithms (TypeSim, ListCompare, SetCompare) and corresponding LaTeX equations to assure soundness and reproducibility (Dong et al., 28 Jul 2025).

3. Empirical Evaluation and Observed Performance

TypeSim was applied to evaluate type inference from several LLMs on the TypyBench dataset, a curated corpus of 50 diverse Python repositories. Key findings include:

• Leading models attained TypeSim scores around 0.80, a metric that reflects strong, but not perfect, functional similarity to ground truth annotations.
• TypeSim is more forgiving than exact match, granting partial credit when predictions align on “root” types or generalize type parameters.
• The metric revealed a distinct drop in performance for complex, deeply nested types compared to shallower (“depth-1”) types, with performance gaps widening compared to exact match as structural complexity increases.
• A comparison with repository-level consistency metrics (e.g., “TypeCheck,” which detects static type errors via Mypy) demonstrated that high local similarity (TypeSim) does not guarantee consistency across an entire codebase.

These results suggest that existing LLM-based inference systems perform adequately on local, surface-level typing but face persistent challenges as compositional and structural complexity increase (Dong et al., 28 Jul 2025).

4. Limitations and Open Challenges

Despite its finer granularity, TypeSim exposes several important limitations in practical LLM-inference performance:

• LLMs tend to underperform on rare types and complex, high-depth nested structures, as indicated by lower TypeSim scores in these regimes.
• Long repository contexts, while important for global type consistency, present a challenge for LLMs due to input/output length constraints, potentially increasing inconsistency and lowering TypeSim across longer files or modules.
• An inherent trade-off is observed between optimizing for local type similarity (TypeSim) and ensuring type correctness and consistency at repository scale. High TypeSim does not eliminate type consistency errors detectable by static checkers.

These challenges reaffirm the necessity for distinct, complementary evaluation metrics: TypeSim for local semantic similarity, and repository-level checks (such as TypeCheck) for global consistency (Dong et al., 28 Jul 2025).

5. Practical Implications for Software Engineering

TypeSim’s semantic grading aligns with practical developer workflows in several respects:

• It enables more realistic evaluation and deployment of AI-assisted type inference tools, since many code maintenance and refactoring scenarios favor functionally similar types (for instance, substituting Iterable for List in input processing).
• High TypeSim scores correlate with enhanced code clarity, improved error detection, and superior IDE support, even when full human equivalence is not achieved.
• The metric provides a robust criterion for tool and model development, facilitating rapid, nuanced benchmarking of type prediction systems against the evolving needs of dynamic language codebases.

In practical usage, TypeSim reveals that even incomplete annotations can meaningfully support downstream tooling when they semantically approximate the ground truth (Dong et al., 28 Jul 2025).

6. Resources and Community Usage

TypeSim and its implementation are publicly released as part of the TypyBench toolkit, available at https://github.com/typybench/typybench (Dong et al., 28 Jul 2025). The benchmark provides code and datasets for reproducible evaluation of type inference models using both TypeSim and complementary metrics.

This resource provides a foundation for future research into both metric design and type inference modeling in dynamic languages, with particular relevance for benchmarking LLMs operating on large code repositories.

7. Future Research Directions

The development and empirical paper of TypeSim underscore several avenues for subsequent investigation:

• Prioritizing research on repository-level type consistency, moving beyond pointwise type similarity that TypeSim measures.
• Developing advanced techniques for LLMs that robustly handle rare types and deeply nested structures, as TypeSim scores reveal these as persistent weak points.
• Exploring algorithmic advances to mitigate the context length bottleneck, thereby improving both local and global type inference in large-scale repositories.
• Refining TypeSim and related metrics by incorporating finer-grained behavioral or operational profiles for types, aligning model evaluation even more closely with software engineering best practices.

Shifting evaluation toward these complex codebase-level capabilities is projected to lead to better integrated, semantically robust type inference systems suitable for deployment in industry-scale, dynamically typed codebases (Dong et al., 28 Jul 2025).