Uploaded August 2024 | Updated September 2026, 2 weeks ago
Topos Institute Colloquium, 29th of August 2024.
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This talk will review progress on the Hazel programming environment and its underlying theoretical developments. Hazel is the first totally live typed general-purpose programming environment, meaning that it deploys error localization and recovery mechanisms, rooted in language-theoretic developments, that ensure that every editor state is syntactically well-structured and statically and dynamically meaningful. The talk will review the underlying theory and include a live demonstration of various Hazel features, including its editor, training mode, and its stepper, which is forming the basis for ongoing work on a Hazel-based theorem prover. The talk will also discuss various other ongoing and future directions of interest to the community, including our vision for a "computational commons" that operates like a planetary-scale live program.
Topos Institute Colloquium, 29th of August 2024.
———
This talk will review progress on the Hazel programming environment and its underlying theoretical developments. Hazel is the first totally live typed general-purpose programming environment, meaning that it deploys error localization and recovery mechanisms, rooted in language-theoretic developments, that ensure that every editor state is syntactically well-structured and statically and dynamically meaningful. The talk will review the underlying theory and include a live demonstration of various Hazel features, including its editor, training mode, and its stepper, which is forming the basis for ongoing work on a Hazel-based theorem prover. The talk will also discuss various other ongoing and future directions of interest to the community, including our vision for a "computational commons" that operates like a planetary-scale live program.
![[Berkeley Seminar] Benjamin Brast McKie | The Construction of Possible Worlds](https://i.ytimg.com/vi/p-z4bhj7p-g/mqdefault.jpg "[Berkeley Seminar] Benjamin Brast McKie | The Construction of Possible Worlds
Title: The Construction of Possible Worlds
Abstract: Possible worlds are often taken to be complete histories of everything. Insofar as there are temporary sentences that are true at some times and false at other times, evaluating a sentence at a possible world does not fix its truth-value. Moreover, if possible worlds are taken to be primitive, evaluating sentences at world-time pairs invalidates a perpetuity principle that what is necessarily the case is always the case where imposing model constraints cannot validate these principles without undermining the significance of the truth-conditions for the language. Rather, this paper takes world states to be maximal possible ways for things to be at an instant where the task relation encodes the possible transitions between world states. Possible worlds are then defined as functions from times to world states as constrained by the task relation. Since sentences are assigned truth-values at world states, times are exogenous to the truth-conditions for the language, eliminating unnecessary degrees of freedom from the definition of a model. By evaluating sentences at world-time pairs, the resulting semantic theory validates a logic for tense and modality in which the perpetuity principles are theorems, providing a logical foundation for reasoning about future contingency.
Handout: https://benbrastmckie.com/wp-content/uploads/2025/11/talk.pdf
Paper: https://www.benbrastmckie.com/wp-content/uploads/2025/11/possible_worlds.pdf
Date: 11/25/2025")
![[Berkeley Seminar] Kris Brown | Categorical approaches to inferentialist semantics](https://i.ytimg.com/vi/pCUjgC5UKBQ/mqdefault.jpg "[Berkeley Seminar] Kris Brown | Categorical approaches to inferentialist semantics
Title: Categorical approaches to inferentialist semantics
Abstract: There are remarkable similarities between applied category theory and inferentialist semantics in the philosophy of language: a focus on making pre-existing structure explicit, sensemaking without rigid foundations, characterizing content in terms of external structure rather than internal structure, emphasis on open systems, and putting syntax and semantics in the same playing field. I will present some formalizations of inferentialism (a generalization of Girards phase semantics) due to Hlobil and Brandom and show some progress towards understanding what is taking place, categorically.
The accompanying slides are available at https://www.krisb.org/role/role-0034.xml, and a related blog post is available at https://topos.site/blog/2024-10-11-nonlogical-concepts/.
https://topos.site/events/berkeley-seminar/")
![[Oxford Seminar] David Jaz Myers | A modal proof of the nerve theorem](https://i.ytimg.com/vi/pKHjMXSfAX4/mqdefault.jpg "[Oxford Seminar] David Jaz Myers | A modal proof of the nerve theorem
Oxford Seminar, 24th of July 2025
Joint work with Mitchell Riley.
The nerve theorem is a classical result in homotopy theory,
usually attributed to Borsuk, which computes the homotopy type of a
(paracompact) topological space from a good open cover of it. An
open cover is good when finite intersections of opens in the cover
are contractible whenever they contain a point; the nerve of a good
open cover is the simplicial complex with a point for each open in the
cover, and an -simplex for each inhabited intersection of opens in the
cover. The nerve theorem states that the homotopy type of is the same
as the nerve of any good open cover of it.
In this talk, well prove the nerve theorem in the setting of modal
homotopy type theory. The key concepts in the nerve theorem — the
homotopy type of a space, the homotopy type presented by a simplicial
set, and even the Čech nerve itself — may all be understood as
modalities which act on simplicial, spatial homotopy types (that is,
simplicial stacks on a suitably topological site). Once we understand
the idea of modalities, well see that the nerve theorem is a
completely modal statement concerning the commutation of two sorts of
cohesion possible for types (in Lawveres sense): the combinatorial
cohesion of simplices, and the continuous cohesion of topology. As a
result, well actually be proving a nerve theorem for all spatial
stacks in a direct, conceptual way.")
![[DOTS Lectures] 10. LTL and specifications of behaviours](https://i.ytimg.com/vi/qpWD16mOwr0/mqdefault.jpg "[DOTS Lectures] 10. LTL and specifications of behaviours
*The paper referred to at the end was Temporal Landscapes: A Graphical Logic of Behavior by Brendan Fong, Alberto Speranzon and David I. Spivak.
This talk is part of a lecture series on the Double Operadic Theory of Systems (DOTS) presented by David Jaz Myers.
Some material from these lectures can be found in Davids book on categorical systems theory:
https://www.davidjaz.com/Papers/DynamicalBook.pdf")
