Related papers: Bidirectional Type Class Instances (Extended Versi…
In type theory, coinductive types are used to represent processes, and are thus crucial for the formal verification of non-terminating reactive programs in proof assistants based on type theory, such as Coq and Agda. Currently, programming…
We define a bi-directional embedding between hypersequent calculi and a subclass of systems of rules (2-systems). In addition to showing that the two proof frameworks have the same expressive power, the embedding allows for the recovery of…
In the calculus of dependent lambda eliminations (CDLE), it is possible to define inductive datatypes via lambda encodings that feature constant-time destructors and a course-of-values induction scheme. This paper begins to address the…
The expression problem describes a fundamental tradeoff between two types of extensibility: extending a type with new operations, such as by pattern matching on an algebraic data type in functional programming, and extending a type with new…
Large language model (LLM)-based embedding models, benefiting from large scale pre-training and post-training, have begun to surpass BERT and T5-based models on general-purpose text embedding tasks such as document retrieval. However, a…
Liquid Haskell's refinement-reflection feature augments the Haskell language with theorem proving capabilities, allowing programmers to retrofit their existing code with proofs. But many of these proofs require routine, boilerplate code…
At present, object recognition studies are mostly conducted in a closed lab setting with classes in test phase typically in training phase. However, real-world problem is far more challenging because: i) new classes unseen in the training…
Gradual dependent types can help with the incremental adoption of dependently typed code by providing a principled semantics for imprecise types and proofs, where some parts have been omitted. Current theories of gradual dependent types,…
While generalized algebraic datatypes (\GADTs) are now considered well-understood, adding them to a language with a notion of subtyping comes with a few surprises. What does it mean for a \GADT parameter to be covariant? The answer turns…
The research on gradual typing has led to many variations on the Gradually Typed Lambda Calculus (GTLC) of Siek and Taha (2006) and its underlying cast calculus. For example, Wadler and Findler (2009) added blame tracking, Siek et al.…
Examples in web API specifications can be essential for API testing, API understanding, and even building chat-bots for APIs. Unfortunately, most API specifications lack human-written examples. This paper introduces a novel technique for…
Type inference for dynamic programming languages such as Python is an important yet challenging task. Static type inference techniques can precisely infer variables with enough static constraints but are unable to handle variables with…
The random graph model has recently been extended to a random preferential attachment graph model, in order to enable the study of general asymptotic properties in network types that are better represented by the preferential attachment…
This study provides some results about two-level type-theoretic notions in a way that the proofs are fully formalizable in a proof assistant implementing two-level type theory such as Agda. The difference from prior works is that these…
We present a conservative extension ICaTT of the dependent type theory CaTT for weak $\omega$-categories with a type witnessing coinductive invertibility of cells. This extension allows for a concise description of the "walking equivalence"…
Graph Transformers (GTs) have shown strong empirical performance, yet current architectures vary widely in their use of attention mechanisms, positional embeddings (PEs), and expressivity. Existing expressivity results are often tied to…
We propose foundations for a synthetic theory of $(\infty,1)$-categories within homotopy type theory. We axiomatize a directed interval type, then define higher simplices from it and use them to probe the internal categorical structures of…
In recent years, various state of the art autonomous vehicle systems and architectures have been introduced. These methods include planners that depend on high-definition (HD) maps and models that learn an autonomous agent's controls in an…
In this paper, we describe our experience incorporating gradual types in a statically typed functional language with Hindley-Milner style type inference. Where most gradually typed systems aim to improve static checking in a dynamically…
Generic programming (GP) is an increasingly important trend in programming languages. Well-known GP mechanisms, such as type classes and the C++0x concepts proposal, usually combine two features: 1) a special type of interfaces; and 2)…