@MichaelHomer Did you learn about Cartesian Closed Category from Categories for the Working Mathematician or some other books?

Where did you learn about modelling the type system of Haskell in Catersian Closed Category

@Tim I have not read that book

The description of the category "Hask" is pretty widespread and I don't know where I first encountered it. My understanding is that there's a bit of hand-waving over its actually being a category in the strictest sense

Or there's a hypothetical subset of the language that fits, without bottom and non-terminating functions, I guess, and the rest is either an open question or definitively falsified, I'm not sure which

People manage to write Haskell programs without thinking about any of those things

I suppose it depends what you mean by "encounter"

The gist of my question is: are type theory and typed lambda calculus explicitly visible to programmers in Haskell language? (not implicitly hidden in its implementation).

There are types and there are functions

category and lambda calculus are visible to programmers

so I have to understand them

In as much as visible types are visible type theory, and first-class (typed) functions are visible typed lambda calculus, sure

I don't think you do.

I found the following book, which seem to be simplified and easier to access: Pierce's Basic Category Theory for Computer Scientist. It is less than 100 pages, define the concepts of cartesian closed category in a different way from the book for mathematician

its definitions seem to require less advanced concepts

If you want to learn Haskell, I suggest you... learn Haskell

Yes I am reading the Haskell book you recommended, and also put more emphaisis on another Haskell book by Hutton

I am stuck at applicatives and monads in the books. So I refered back to your comment and have asked a few questions on math.se and SO

Lambda calculus and category theory are not reasonable paths into Haskell

I think category is necessary to understand functor, applicative and monad

Not really

I can't relate from concrete examples directly to concrete examples, I can only apply concepts to concrete examples

I can't see why the lambda calculus is going to be any more useful on that front than Haskell is

lambda calclus helps to understand operations on functions

at conceptual level

I guess

Sorry for being even more horrible learner. My eventual goal is to learn Scala, by learning FP by Haskell first.

I am scared to learn Scala from the beginning

Functors are things that can be mapped over. Applicative functors are functors where operations can be sequenced (which isn't honestly all that important most of the time).

Then you should just learn Scala

The path you've described only serves to insert more obstacles in the way of getting where you're going

:) tell that to @StephenKitt

fmap (*) (Just 4) gives Just (4*). An applicative functor lets you use (Just (4*)) <*> Just 3 to get Just 12 (and does the right thing for Nothing). Occasionally something like that is useful

Sorry, I misunderstood StephenKitt

I'm not saying you should learn Scala at all, but if that's the goal then picking the most convoluted roundabout way of getting there that you can seems like an indicator that you're not really expecting to get there

If I don't have a specific goal, which language(s) do you recommend to learn?

I don't know, what do you want to learn it for?

I want to learn Scala, because of Spark and Akka appearing in some job descriptions. But if Scala is a language with less future than its alternatives, then probably I will switch to learn its alternatives

The OO part of Scala is said to be a better Java. I guess Scala borrows OO features not from Java but some other langauges? I wonder if that is Smalltalk. So I was wondering if it is better to learn Smalltalk.

Scala got all its OO from Java because it was built specifically for the JVM

Then how can it be a better Java?

If you just want a job, Java and C#

Probably some sort of qualification would help to get in the door too

They bolted on all the features they could manage and declared it better

what does "bolted on" mean?

Attached

select the Java features they can manage, and don't select those they can't?

Just take everything from everywhere and throw it in

Is it true that jobs in Java and C# are almost all about web services or web appllcations?

I haven't get my head around MVC and RESTful yet

Jobs in everything are largely websites now

The thing about a job is your employer will tell you what to do. You don't have to understand every related detail before you start