Related papers: The RedPRL Proof Assistant (Invited Paper)
We contribute a general apparatus for dependent tactic-based proof refinement in the LCF tradition, in which the statements of subgoals may express a dependency on the proofs of other subgoals; this form of dependency is extremely useful…
This article introduces Globular, an online proof assistant for the formalization and verification of proofs in higher-dimensional category theory. The tool produces graphical visualizations of higher-dimensional proofs, assists in their…
We present three projects concerned with applications of proof assistants in the area of programming language theory and mathematics. The first project is about a certified compilation technique for a domain-specific programming language…
This paper improves the treatment of equality in guarded dependent type theory (GDTT), by combining it with cubical type theory (CTT). GDTT is an extensional type theory with guarded recursive types, which are useful for building models of…
We define a computational type theory combining the contentful equality structure of cartesian cubical type theory with internal parametricity primitives. The combined theory supports both univalence and its relational equivalent, which we…
This paper proposes a way of doing type theory informally, assuming a cubical style of reasoning. It can thus be viewed as a first step toward a cubical alternative to the program of informalization of type theory carried out in the…
This paper improves the treatment of equality in guarded dependent type theory (GDTT), by combining it with cubical type theory (CTT). GDTT is an extensional type theory with guarded recursive types, which are useful for building models of…
Partial label learning is a type of weakly supervised learning, where each training instance corresponds to a set of candidate labels, among which only one is true. In this paper, we introduce ProPaLL, a novel probabilistic approach to this…
Preference-based reward learning is widely used for shaping agent behavior to match a user's preference, yet its sparse binary feedback makes it especially vulnerable to causal confusion. The learned reward often latches onto spurious…
We present the proof assistant homotopy.io for working with finitely-presented semistrict higher categories. The tool runs in the browser with a point-and-click interface, allowing direct manipulation of proof objects via a graphical…
We discuss the homotopy type theory library in the Lean proof assistant. The library is especially geared toward synthetic homotopy theory. Of particular interest is the use of just a few primitive notions of higher inductive types, namely…
Partial Label Learning (PLL) is a type of weakly supervised learning where each training instance is assigned a set of candidate labels, but only one label is the ground-truth. However, this idealistic assumption may not always hold due to…
When working in a proof assistant, automation is key to discharging routine proof goals such as equations between algebraic expressions. Homotopy type theory allows the user to reason about higher structures, such as topological spaces,…
Martin-L\"of's Intuitionistic Theory of Types is becoming popular for formal reasoning about computer programs. To handle recursion schemes other than primitive recursion, a theory of well-founded relations is presented. Using primitive…
Reinforcement learning with verifiable rewards (RLVR) has advanced reasoning capabilities in multimodal large language models. However, existing methods typically treat visual inputs as deterministic, overlooking the perceptual ambiguity…
Verifying relations between programs arises as a task in various verification contexts such as optimizing transformations, relating new versions of programs with older versions (regression verification), and noninterference. However,…
Proust is a small Racket program offering rudimentary interactive assistance in the development of verified proofs for propositional and predicate logic. It is constructed in stages, some of which are done by students before using it to…
Reinforcement Learning (RL) is increasingly adopted to train agents that can deal with complex sequential tasks, such as driving an autonomous vehicle or controlling a humanoid robot. Correspondingly, novel approaches are needed to ensure…
Proof assistants are getting more widespread use in research and industry to provide certified and independently checkable guarantees about theories, designs, systems and implementations. However, proof assistant implementations themselves…
Cubical type theory provides a constructive justification to certain aspects of homotopy type theory such as Voevodsky's univalence axiom. This makes many extensionality principles, like function and propositional extensionality, directly…