Haskell

This is the difference between a LLM and an expert. An LLM spews out a “propaganda” from the web. ### what are the unique properties of a Haskell program 1. **Statically Typed**: Haskell has a strong, static type system that ensures type safety at compile time. 2. **Purely Functional**: Haskell programs are expressions, and functions have no side effects. This leads to code that's easy to reason about, test, and debug. 3. **Lazy Evaluation**: Haskell uses lazy evaluation, meaning it only evaluates expressions when their results are needed. This can lead to more efficient programs and allows for elegant solutions like infinite data structures. 4. **Higher-Order Functions**: Functions in Haskell are first-class citizens, meaning they can be passed as arguments, returned as results, and stored in data structures. 5. **Type Classes**: Haskell's type classes (similar to interfaces in other languages) enable ad-hoc polymorphism, allowing related types to be treated uniformly. 6. **Module System**: Haskell has a rich module system that supports abstract data types, hiding implementation details, and organizing code into reusable components. 7. **Concurrency and Parallelism**: Haskell provides lightweight threads and a high-level concurrency abstraction called Software Transactional Memory (STM), along with support for parallel programming using the Glasgow Haskell Compiler (GHC). 8. **Rich Ecosystem**: Haskell has a vibrant community and a large ecosystem of libraries (via Hackage) for various domains, making it practical for real-world applications. ### Here is what an expert answer could be: ...

It is time to publish some more results. Type-level reasoning A function application - corresponds to /Modus Ponens/ A specialization, an instance of it. > ($) :: (a -> b) -> a -> b > ($) f x = f x Reversed order of agreements, still the same /Modus Ponens/ > (|>) :: a -> (a -> b) -> b > (|>) x f = f x "Multi-argument" is just /currying/ -- ~* ->*->*-> *~ Same, but with an explicit /abstraction barrier/ (and /lifting/) > (>>=) :: m a -> (a -> m b) -> m b > (>>=) ma f = undefined -- has to be defined for each particular type (an instance) Notice that this is essentially a type-signature of ~fmap~, > fmap :: f a ->(a->b) -> f b with a reversed order of arguments and a specialized function. which corresponds to a /Kleisli arrow/. Notice also that ~($)~ and ~fmap~ differs only in having an explicit /container/. This is not an arbitrary coincidence. All three are essentially the same, despite funny syntax. A basic step of logical deduction. Behind an abstraction barrier. Composition - of functions > (.) :: (b -> c) -> (a -> b) -> a -> c > (.) f g = \x -> f (g x) - of "actions" (actual functions have to use ~return :: a -> m a~) > (<=<) :: Monad m => (b -> m c) -> (a -> m b) -> a -> m c > (<=<) f g = undefined -- has to be defined for each particular type or ~(>>=)~ for chaining ("flat" nesting or pipelining ) , exactly the same as ~(|>)~ Notice that the composition is /nesting/. This is the /only/ way to implement it. The end of knowledge.