Evil plan to turn #Agda into a tactic-based proof assistant:
1. Resurrect/repurpose the REPL as a place to input editor commands, particularly with commands local to a hole. (https://github.com/agda/agda/issues/5778)
2. Expand the collection of editor commands to facilitate more specific refinements of the proof term.
3. Add edit-time tacticals like`repeat` and `;`, allowing for more unprincipled proof term synthesis.
4. Allow sequences of editor commands to be embedded in files, and to be run (without changing the buffer, but updating the proof state) at load time.
5. Allow interactive stepping through of editor commands embedded in files.

Quite a lot of these steps are already in #Idris, but I don't know how well used they are, and how usable they are without the other steps.

I think categorical composition is oversold in functional programming hype, but I'm still a fan of #Agda #Idris #Haskell and #Purescript

This is probably really easy but is the variant of LEM (forall a, not a or not not a) equivalent to vanilla LEM (for all a, a or not a) constructively?
Bonus points if you can give me a runnable example
#logic #agda #coq #idris

A topological counterpart of well-founded trees in dependent type theory. ~ Maria Emilia Maietti, Pietro Sabelli. https://arxiv.org/abs/2308.08404 #ITP #Agda

#multiplication #recursion preposition , proof #agda
A (diy thread )

Denotationally correct computer arithmetic. ~ Atticus Kuhn. https://atticuskuhn.github.io/papers/denotationalCircuits.pdf #ITP #Agda

@i_dabble You should try #Agda and incredible.pm

Formalizing π4(S3) ∼= Z/2Z and computing a Brunerie number in Cubical Agda. ~ Axel Ljungström, Anders Mörtberg. \0https://lics.siglog.org/lics23/Slides/s086.pdf #ITP #Agda #Math

Смотрю лекцию по слабым моделям памяти https://youtu.be/P4AnGeVFbzo и тут опять касаются формальной верификации, даже сюда хочется #Agda тащить.

#ФормальнаяВерификация #ТеорияТипов #Программирование

Teoría homotópica de tipos. ~ Fernando Rafael Chu Rivera. https://cybertesis.unmsm.edu.pe/bitstream/handle/20.500.12672/19939/Chu_rf.pdf #ITP #Agda #HoTT

Slice nondeterminism. ~ Niels F. W. Voorneveld. https://drops.dagstuhl.de/opus/volltexte/2023/18374/pdf/lipics-vol268-itp2023-complete.pdf#page=527 #ITP #Agda

A new #formalmethods community was just created on the Lemmy instance programming.dev: https://programming.dev/c/formal_methods@programming.dev

I’ve seen lots of interesting discussion on Mathstodon about #FormaMathematics, #TheoremProving and #ProofAssistants such as #Lean4, #Coq, #agda, #isabelle, and others. In addition to the fascinating discussion here on Mathstodon, I would love to see an active home on Lemmy for aggregating resources on formal methods and formal mathematics!

Parts of my new stdlib PR have more lines devoted to module parameters than to the proof. #Agda

On trees and their topological realisations in homotopy type theory. ~ Jonathan Prieto-Cubides. https://jonaprieto.github.io/drafts/Jonathan-Prieto-Cubides-On-Trees-and-Their-Topological-Realisation-in-HoTT.pdf #ITP #Agda #HoTT

Всё пытаюсь придумать что такого покодить на #Agda , но я не очень умный поэтому балуюсь со всякой хренью, вот недавно для меня стало открытием, что можно доказывать существование и единственность чего-либо:

```
2+x=5 : ∃! (_≡_) (λ x → 2 + x ≡ 5)
2+x=5 = 3 , ( refl , λ {y} 2+y=5 → 2+y=5⇒y=3 y 2+y=5 )
where
2+y=5⇒y=3 : ∀ y → 2 + y ≡ 5 → 3 ≡ y
2+y=5⇒y=3 0 ()
2+y=5⇒y=3 1 ()
2+y=5⇒y=3 2 ()
2+y=5⇒y=3 3 refl = refl
2+y=5⇒y=3 (suc (suc (suc (suc _)))) ()
```

Полноценное осознание, что в этот момент происходит правда так и не пришло...

Getting ready for the thesis defense of Ivar de Bruin on Improving Agda's Module System!

Read the full thesis now at http://resolver.tudelft.nl/uuid:98b8fbf5-33f0-4470-88b0-39a9d526b115

#TUDelft #Agda #Modules

Refactoring with confidence: Creating and proving the correctness of a refactoring to add arguments to a function in a functional language. ~ Kalle Struik. https://repository.tudelft.nl/islandora/object/uuid:c82c7a45-632d-4451-8ae2-4e77d2509c88 #ITP #Agda #Haskell #FunctionalProgramming

Proving correctness of refactoring tuples to records: A correct-by-construction approach on a Haskell-like language. ~ Jeroen Bastenhof. https://repository.tudelft.nl/islandora/object/uuid:e61b0972-175e-42d3-bb10-d7ee9f2584ea #ITP #Agda #Haskell #FunctionalProgramming

module plfa.backmatter.Fonts where
#agda #nix
just saying

https://stackoverflow.com/questions/63861218/opening-the-top-level-module-applied-on-arguments
This or cubicle #agda for that matter
https://github.com/carnotweat/morning-agda