## 33 Citations

Formalizing computability theory via partial recursive functions

- Computer Science, MathematicsITP
- 2019

An extension to the $\mathtt{mathlib}$ library of the Lean theorem prover formalizing the foundations of computability theory is presented, which includes the construction of a universal partial recursive function and a proof of the undecidability of the halting problem.

An Analysis of Tennenbaum's Theorem in Constructive Type Theory

- MathematicsFSCD
- 2022

Tennenbaum’s theorem states that the only countable model of Peano arithmetic (PA) with computable arithmetical operations is the standard model of natural numbers. In this paper, we use constructive…

Partial Elements and Recursion via Dominances in Univalent Type Theory

- MathematicsCSL
- 2017

We begin by revisiting partiality in univalent type theory via the notion of dominance. We then perform first steps in constructive computability theory, discussing the consequences of working with…

Parametric Church's Thesis: Synthetic Computability Without Choice

- PhilosophyLFCS
- 2022

This work introduces various parametric strengthenings of CTφ, which are equivalent to assuming CT φ and an S n operator for φ like in the S n theorem, and explains the novel axioms and proofs of Rice’s theorem.

On fixed-point theorems in synthetic computability

- Mathematics
- 2017

Abstract Lawvere’s fixed point theorem captures the essence of diagonalization arguments. Cantor’s theorem, Gödel’s incompleteness theorem, and Tarski’s undefinability of truth are all instances of…

Partial functions and recursion in univalent type theory

- MathematicsArXiv
- 2020

This work investigates partial functions and computability theory from within a constructive, univalent type theory, using the notion of dominance, which is used in synthetic domain theory to discuss classes of partial maps, and suggests an alternative notion of partial function the authors call disciplined maps.

An intrinsic treatment of ubiquity phenomena in higher-order computability models ( Part I , draft version )

- Mathematics
- 2017

We introduce some simple conditions on typed partial combinatory algebras (viewed as models of higher-order computability) which suffice for an axiomatic development of some non-trivial computability…

Computational Back-And-Forth Arguments in Constructive Type Theory

- MathematicsITP
- 2022

The back-and-forth method is a well-known technique to establish isomorphisms of countable structures. In this proof pearl, we formalise this method abstractly in the framework of constructive type…

A Brief Critique of Pure Hypercomputation

- Computer ScienceMinds and Machines
- 2009

Hypercomputation—the hypothesis that Turing-incomputable objects can be computed through infinitary means—is ineffective, as the unsolvability of the halting problem for Turing machines depends just…

On synthetic undecidability in Coq, with an application to the Entscheidungsproblem

- Computer ScienceCPP
- 2019

Developing a basic framework for synthetic computability theory in Coq, this work proves the equivalence of Post's theorem with Markov's principle and provides a convenient technique for establishing the enumerability of inductive predicates such as the considered proof systems and PCP.

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- Mathematics
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- 1999

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- MathematicsJournal of Symbolic Logic
- 1998

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