Focusing on Refinement Typing - A Logically Principled Foundation
Explore a logically principled foundation for SMT constraint generation in refinement type systems, combining focalized call-by-push-value, bidirectional typing, and value-determined indexes.
The Complex(ity) Landscape of Checking Infinite Descent
Explore the complexity of checking Infinite Descent in cyclic proof systems, examining various criteria and their parameterized time complexities to improve automatic verification techniques.
Proof Theory Impressionism - Blurring the Curry-Howard Line
Exploring approaches to bridge the gap between proof assistants and production languages, focusing on Rust and its potential for incorporating provable system capabilities.
Explicit Refinement Types - A Type Theory with Embedded Proofs
Explore λert, a type theory with explicit proof refinement types. Learn about its soundness, denotational semantics, and formalization in Lean 4.
Recursive Inequalities in Applied Proof Theory
Explore recursive inequalities in applied proof theory, delving into advanced mathematical concepts and their practical applications.
From Axioms to Synthetic Inference Rules via Focusing
Explore the connection between axioms and synthetic inference rules through focusing, as presented by Dale Miller in this mathematical conference talk.
Inductive Definitions, Predicativity, and the Mahlo Universe
Explore inductive definitions, predicativity, and the Mahlo universe in type theory with Peter Dybjer. Gain insights into advanced mathematical concepts and their applications.
Structural Rules and Algebraic Properties of Intersection Types
Explore structural rules and algebraic properties of intersection types in lambda calculus, examining their impact on type assignment systems and programming language theory.
Challenges in Formalising Recent Results in Formal Language Theory
Explore challenges in formalizing recent results linking formal language theory and computational group theory, with insights on making proofs more amenable to formalization.
Data Parallel Proof Verification in APL - Using Metamath for Mathematical Databases
Discover how APL enables data-parallel verification of mathematical proofs using Metamath, exploring formal verification methods, proof structures, and efficient processing of large mathematical databases.