algebra-driven-design
Agda
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algebra-driven-design | Agda | |
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11 | 27 | |
129 | 2,371 | |
- | 1.5% | |
4.3 | 9.8 | |
6 months ago | 2 days ago | |
Haskell | Haskell | |
BSD 3-clause "New" or "Revised" License | MIT License |
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algebra-driven-design
- What are some useful techniques for designing in functional languages?
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Rust for projects that demand OOP type programming
You might want to read on Algebra-Driven Design and Data Oriented Design. If you are greedy, both books were pirated.
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Does anyone use formal methods to validate the behaviour of programs/software at their job?
I would like to do this more. At the moment I don't do formal verification. However, I often borrow methodology from the excellent book Algebra-Driven Design (text available on GitHub but support the author if you find it useful!) when designing systems. This means I define algebraic data types to describe the program and the laws that relate the different types, and use that to guide implementation in a language that doesn't support ADTs.
- Best books for Haskell
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Do you feel static types have "won the war", so to speak?
Their approach might be to express their business logic as a carefully selected collection of types and laws, as described in Algebra-Driven Design (the full text is available on GitHub, please support the author if you find it useful though). I recommend this book to everyone because, even if you don't use this approach to design your programs, it's an excellent way to think about problems and better understand the problem space.
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Can someone message me explaining category theory and representation theory? I’m trying to choose a topic for independent study and need some help.
If you have an interest in computer science, category theory is very useful there. Here's a good book on the topic (Algebra-Driven Design, by Sandy Maguire).
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Does anybody know a simple algorithm for generating unit tests given a function's code?
This reminds me of QuickSpec (different from QuickCheck) in Haskell. It takes Haskell code and finds the Mathematical laws that the code supports. It does this using a sort of smart random search. I learned about this as part of the Algebra Driven Design book.
- Source material for Algebra-Driven Design now available!
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Advice on designing algebras
Sorry probably worth pointing out that I'm not referring to an Algebra in the pure math sense. I'm more referring to specifying algebraic laws that an API would have to satisfy as talked about in this book https://leanpub.com/algebra-driven-design.
Agda
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Types versus sets (and what about categories?)
This was recently deemed inappropriate:
"Bye bye Set"
"Set and Prop are removed as keywords"
https://github.com/agda/agda/pull/4629
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If given a list of properties/definitions and relationship between them, could a machine come up with (mostly senseless, but) true implications?
Still, there are many useful tools based on these ideas, used by programmers and mathematicians alike. What you describe sounds rather like Datalog (e.g. Soufflé Datalog), where you supply some rules and an initial fact, and the system repeatedly expands out the set of facts until nothing new can be derived. (This has to be finite, if you want to get anywhere.) In Prolog (e.g. SWI Prolog) you also supply a set of rules and facts, but instead of a fact as your starting point, you give a query containing some unknown variables, and the system tries to find an assignment of the variables that proves the query. And finally there is a rich array of theorem provers and proof assistants such as Agda, Coq, Lean, and Twelf, which can all be used to help check your reasoning or explore new ideas.
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What can Category Theory do?
Haskell and Agda are probably the most obvious examples. Ocaml too, but it is much older, so its type system is not as categorical. There is also Idris, which is not as well-known but is very cool.
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What are the current hot topics in type theory and static analysis?
Most of the proof assistants out there: Lean, Coq, Dafny, Isabelle, F*, Idris 2, and Agda. And the main concepts are dependent types, Homotopy Type Theory AKA HoTT, and Category Theory. Warning: HoTT and Category Theory are really dense, you're going to really need to research them.
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Amendmend proposal: Changed syntax for Or patterns
Does this come with plans to separately unify the body with each of the contexts induced by matching on each of the respective patterns (similar to what’s discussed here), or will it behave like the _ pattern and use only the most general context?
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Functional Programming and Maths <|> How can a code monkey learn Agda?
That's absolutely untrue. From the horse's mouth:
- Doom emacs and agda-mode
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FP language idea - would this is possible to infer and type check?
Agda has the so-called mixfix operators (which are powerful enough to cover pre/in/postfix cases with an arbitrary number of arguments), check that out: - https://agda.readthedocs.io/en/v2.6.1/language/mixfix-operators.html - https://github.com/agda/agda/blob/master/examples/Introduction/Operators.agda - https://github.com/agda/agda-stdlib/blob/master/src/Data/Product/Base.agda
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Best Programming Language for Computational Proof
Coq, Agda, Lean, Isabelle, and probably some others which are not coming to my mind at the moment, but those would be considered the major ones.
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Do you use Idris or Coq, and why?
Funny that you say this, because there are some obvious long standing open feature requests with looking up the type of the term under cursor — № 4295 and № 516. I am not blaming anyone in particular — this is the way it is. I wish I could find time to rewrite the proof search engine (how hard can it be), but I am already buried under a pile of other commitments and a good chunk of overwhelming sadness.
What are some alternatives?
learn-you-a-haskell - “Learn You a Haskell for Great Good!” by Miran Lipovača
lean - Lean Theorem Prover
pynguin - The PYthoN General UnIt Test geNerator is a test-generation tool for Python
coq - Coq is a formal proof management system. It provides a formal language to write mathematical definitions, executable algorithms and theorems together with an environment for semi-interactive development of machine-checked proofs.
FsCheck - Random Testing for .NET
open-typerep - Open type representations and dynamic types
methods2test - methods2test is a supervised dataset consisting of Test Cases and their corresponding Focal Methods from a set of Java software repositories
HoleyMonoid - Automatically exported from code.google.com/p/monoid-cont
tcases - A model-based test case generator
distributive - Dual Traversable
austin-sbst - Automatically exported from code.google.com/p/austin-sbst
lean4 - Lean 4 programming language and theorem prover