相关论文: Constructing the Propositional Truncation using No…

The monomial basis for polynomials in N variables is labeled by compositions. To each composition there is associated a hook-length product, which is a product of linear functions of a parameter. The zeroes of this product are related to…

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…

Learning high-quality oblique decision trees remains a significant challenge due to the discrete and non-convex nature of split optimization. We present the Hinge Regression Tree (HRT) framework, which reframes each oblique split as a…

We give a model of set theory based on multisets in homotopy type theory. The equality of the model is the identity type. The underlying type of iterative sets can be formulated in Martin-L\"of type theory, without Higher Inductive Types…

We present an extension to the $\mathtt{mathlib}$ library of the Lean theorem prover formalizing the foundations of computability theory. We use primitive recursive functions and partial recursive functions as the main objects of study, and…

There are several paradigms for integrating interactive and automated theorem provers, combining the convenience of powerful automation with strong soundness guarantees. We introduce a new approach for reconstructing proofs found by SMT…

An introduction and survey of homotopy type theory in honor of W.W. Tait.

With the recent success of pre-trained models in NLP, a significant focus was put on interpreting their representations. One of the most prominent approaches is structural probing (Hewitt and Manning, 2019), where a linear projection of…

We show that the type $\mathrm{T}\mathbb{Z}$ of $\mathbb{Z}$-torsors has the dependent universal property of the circle, which characterizes it up to a unique homotopy equivalence. The construction uses Voevodsky's Univalence Axiom and…

Short-circuit evaluation denotes the semantics of propositional connectives in which the second argument is evaluated only if the first argument does not suffice to determine the value of the expression. In programming, short-circuit…

We give a new constructive proof of homotopy canonicity for homotopy type theory (HoTT). Canonicity proofs typically involve gluing constructions over the syntax of type theory. We instead use a gluing construction over a "strict Rezk…

Clocked Type Theory (CloTT) is a type theory for guarded recursion useful for programming with coinductive types, allowing productivity to be encoded in types, and for reasoning about advanced programming language features using an abstract…

We prove a conservativity result for extensional type theories over propositional ones, i.e. dependent type theories with propositional computation rules, or computation axioms, using insights from homotopy type theory. The argument…

The goal of this dissertation is to present results from synthetic homotopy theory based on homotopy type theory (HoTT). After an introduction to Martin-L\"of's dependent type theory and homotopy type theory, key results include a synthetic…

This paper builds on our earlier proposal for construction of a positive inner product for pseudo-Hermitian Hamiltonians and we give several examples to clarify our method. We show through the example of the harmonic oscillator how our…

Hamiltonian truncation is a non-perturbative numerical method for calculating observables of a quantum field theory. The starting point for this method is to truncate the interacting Hamiltonian to a finite-dimensional space of states…

Present Hermitian Quantum Theory, i.e. Quantum Mechanics and Quantum Field Theory, is revised and replaced by a consistent non-Hermitian formalism called non-Hermitian Quantum Theory (NHQT) or (Anti)Causal Quantum Theory ((A)CQT) after…

We work over an arbitrary ring R. Given two truncated projective resolutions of equal length for the same module we consider their underlying chain complexes. We show they may be stabilized by projective modules to obtain a pair of…

Resolution lies at the foundation of both logic programming and type class context reduction in functional languages. Terminating derivations by resolution have well-defined inductive meaning, whereas some non-terminating derivations can be…

This paper describes new, simple, recursive methods of construction for orientable sequences, i.e. periodic binary sequences in which any n-tuple occurs at most once in a period in either direction. As has been previously described, such…