dafny
NumPy
dafny | NumPy | |
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31 | 272 | |
2,763 | 26,360 | |
4.4% | 0.9% | |
9.7 | 10.0 | |
2 days ago | 6 days ago | |
C# | Python | |
GNU General Public License v3.0 or later | GNU General Public License v3.0 or later |
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dafny
- Dafny is a verification-aware programming language
- Candy – a minimalistic functional programming language
- Dafny – a verification-aware programming language
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Lean4 helped Terence Tao discover a small bug in his recent paper
Code correctness is a lost art. I requirement to think in abstractions is what scares a lot of devs to avoid it. The higher abstraction language (formal specs) focus on a dedicated language to describe code, whereas lower abstractions (code contracts) basically replace validation logic with a better model.
C# once had Code Contracts[1]; a simple yet powerful way to make formal specifications. The contracts was checked at compile time using the Z3 SMT solver[2]. It was unfortunately deprecated after a few years[3] and once removed from the .NET Runtime it was declared dead.
The closest thing C# now have is probably Dafny[4] while the C# dev guys still try to figure out how to implement it directly in the language[5].
[1] https://www.microsoft.com/en-us/research/project/code-contra...
[2] https://github.com/Z3Prover/z3
[3] https://github.com/microsoft/CodeContracts
[4] https://github.com/dafny-lang/dafny
[5] https://github.com/dotnet/csharplang/issues/105
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The Deep Link Equating Math Proofs and Computer Programs
I don't think something that specific exists. There are a very large number of formal methods tools, each with different specialties / domains.
For verification with proof assistants, [Software Foundations](https://softwarefoundations.cis.upenn.edu/) and [Concrete Semantics](http://concrete-semantics.org/) are both solid.
For verification via model checking, you can check out [Learn TLA+](https://learntla.com/), and the more theoretical [Specifying Systems](https://lamport.azurewebsites.net/tla/book-02-08-08.pdf).
For more theory, check out [Formal Reasoning About Programs](http://adam.chlipala.net/frap/).
And for general projects look at [F*](https://www.fstar-lang.org/) and [Dafny](https://dafny.org/).
- Dafny
- The Dafny Programming and Verification Language
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In Which I Claim Rich Hickey Is Wrong
Dafny and Whiley are two examples with explicit verification support. Idris and other dependently typed languages should all be rich enough to express the required predicate but might not necessarily be able to accept a reasonable implementation as proof. Isabelle, Lean, Coq, and other theorem provers definitely can express the capability but aren't going to churn out much in the way of executable programs; they're more useful to guide an implementation in a more practical functional language but then the proof is separated from the implementation, and you could also use tools like TLA+.
https://dafny.org/
https://whiley.org/
https://www.idris-lang.org/
https://isabelle.in.tum.de/
https://leanprover.github.io/
https://coq.inria.fr/
http://lamport.azurewebsites.net/tla/tla.html
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Programming Languages Going Above and Beyond
> I think we can assume it won't be as efficient has hand written code
Actually, surprisingly, not necessarily the case!
If you'll refer to the discussion in https://github.com/dafny-lang/dafny/issues/601 and in https://github.com/dafny-lang/dafny/issues/547, Dafny can statically prove that certain compiler branches are not possible and will never be taken (such as out-of-bounds on index access, logical assumptions about whether a value is greater than or less than some other value, etc). This lets you code in the assumptions (__assume in C++ or unreachable_unchecked() under rust) that will allow the compiler to optimize the codegen using this information.
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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.
NumPy
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Dot vs Matrix vs Element-wise multiplication in PyTorch
In NumPy with @, dot() or matmul():
- NumPy 2.0.0 Beta1
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Element-wise vs Matrix vs Dot multiplication
In NumPy with * or multiply(). ` or multiply()` can multiply 0D or more D arrays by element-wise multiplication.
- JSON dans les projets data science : Trucs & Astuces
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JSON in data science projects: tips & tricks
Data science projects often use numpy. However, numpy objects are not JSON-serializable and therefore require conversion to standard python objects in order to be saved:
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Introducing Flama for Robust Machine Learning APIs
numpy: A library for scientific computing in Python
- help with installing numpy, please
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A Comprehensive Guide to NumPy Arrays
Python has become a preferred language for data analysis due to its simplicity and robust library ecosystem. Among these, NumPy stands out with its efficient handling of numerical data. Let’s say you’re working with numbers for large data sets—something Python’s native data structures may find challenging. That’s where NumPy arrays come into play, making numerical computations seamless and speedy.
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Why do all the popular projects use relative imports in __init__ files if PEP 8 recommends absolute?
I was looking at all the big projects like numpy, pytorch, flask, etc.
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NumPy 2.0 development status & announcements: major C-API and Python API cleanup
I wish the NumPy devs would more thoroughly consider adding full fluent API support, e.g. x.sqrt().ceil(). [Issue #24081]
What are some alternatives?
tlaplus - TLC is a model checker for specifications written in TLA+. The TLA+Toolbox is an IDE for TLA+.
SymPy - A computer algebra system written in pure Python
FStar - A Proof-oriented Programming Language
Pandas - Flexible and powerful data analysis / manipulation library for Python, providing labeled data structures similar to R data.frame objects, statistical functions, and much more
rust - Rust for the xtensa architecture. Built in targets for the ESP32 and ESP8266
blaze - NumPy and Pandas interface to Big Data
koka - Koka language compiler and interpreter
SciPy - SciPy library main repository
Rust-for-Linux - Adding support for the Rust language to the Linux kernel.
Numba - NumPy aware dynamic Python compiler using LLVM
interactive - .NET Interactive combines the power of .NET with many other languages to create notebooks, REPLs, and embedded coding experiences. Share code, explore data, write, and learn across your apps in ways you couldn't before.
Nim - Nim is a statically typed compiled systems programming language. It combines successful concepts from mature languages like Python, Ada and Modula. Its design focuses on efficiency, expressiveness, and elegance (in that order of priority).