[lkitching]

> First, Why does this even matter?

The reason you can't write my version using yours is that the types are less precise and you can't recover the imprecision in the output type after the fact. The only safe way to obtain an Int from an Optional[Int] is by providing a default value which doesn't exist in this case.

> The Optional[Int] doesn't exist so how do you create it?? You CAST

By casting I mean an unchecked narrowing conversion e.g. of the type Optional[Int] -> Int. There's no casting in my version.

> if you want to talk about "Well Established" then Optional is more well established

This is a false dichotomy, contracts are still used in static languages where you can't or don't want to try represent properties at the type level. You could for example define a function

    lookup: Map -> Key -> Optional[Value]

and still add preconditions that the map and key were non-null. The failure to uphold these represent a different kind of 'failure' than the key not being found so it wouldn't make sense to lift them into the return type.

> The safe version suffers from your same problem just moved

It didn't 'just' move, it moved to the point in the program you actually need to deal with the possibility of a zero divisor i.e. before calling div. Where does the divisor come from in the first place? You seem to be assuming there is necessarily some call to NonZero.fromInt at each call site to div but this is wrong. The non-zeroness of the divisor could be established at some prior point in the program and used in multiple places. In contrast your version has to deal with the possibility of returning None everwhere even if you've already established the property of the divisor beforehand.

[deltaonefour]

>The reason you can't write my version using yours is that the types are less precise and you can't recover the imprecision in the output type after the fact.

Irrelevant to my statement. I said why does it even matter not why can't you do it. The answers are it doesn't matter at all AND you can't do it for EITHER case.

>The only safe way to obtain an Int from an Optional[Int] is by providing a default value which doesn't exist in this case.

No the safe way is through exhaustive type checking via pattern matching. If you're not sure what this is, look it up. Suffice to say it's static safety on all sum types including Optionals prior to execution.

>By casting I mean an unchecked narrowing conversion e.g. of the type Optional[Int] -> Int. There's no casting in my version.

There is 100% casting in your version. 100% percent. There is no narrow conversion here you're just making that shit up. The inverse of what you wrote is THIS:

       def convertDiv(f: (Int, NonZero[Int]) -> Int ): (Int, Int) -> Optional[Int]:

There is no way to create an Optional[Int] WITHOUT a typecast. I'm sorry, but your statement is definitively wrong no need to build some scaffold of strange logic around it and "narrow" the definition of a cast. I get your point though (even though I disagree). However, this does not change the fact that your example is completely wrong from a logical standpoint and completely off base.

>and still add preconditions that the map and key were non-null. The failure to uphold these represent a different kind of 'failure' than the key not being found so it wouldn't make sense to lift them into the return type.

Uh no. You can do Exactly what you did with NonZero[Int] with Key in your example. Imagine a map with RGB colors as keys.

   type KEY = Red | Green | Blue
   type VALUE = ...
   lookup: Map[KEY, VALUE] -> KEY -> VALUE

Like I said it's just your preference here. There is a false dichotomy when it comes to things being more correct when "Well Established" and that false dichotomy isn't coming from me. It's coming from you.

>It didn't 'just' move, it moved to the point in the program you actually need to deal with the possibility of a zero divisor i.e. before calling div. Where does the divisor come from in the first place? You seem to be assuming there is necessarily some call to NonZero.fromInt at each call site to div but this is wrong.

Ok let me reframe this. I completely AM not Assuming NonZero.fromInt at the call point AT all. Once you realize that your assumption is wrong, maybe you should consider the fact that you're NOT understanding me.

>The non-zeroness of the divisor could be established at some prior point in the program and used in multiple places.

The above is 100% what I am assuming. This prior point involves the creation of the type NonZero[Int] which involves: NonZero.fromInt. Every other mathematical operation (+,-,x^y,/,) returns an Int not a NonZero[Int] so this cast must occur. And that is my point. Think about it.

> In contrast your version has to deal with the possibility of returning None everwhere even if you've already established the property of the divisor beforehand.

This is where you're getting hung up. Let's clarify something your NonZero.fromInt is of the type:

   Int -> Optional[NonZero[Int]]

With that out of the way let us continue:

Yeah so my division returns an Optional which could be a None. I can either handle the None immediately or let it propagate all the way to IO and handle it just before it hits this wall. This is a bad thing I get it.

But your NonZero.fromInt Also returns an Optional which could be None. I can either handle the None immediately or let it propagate all the way to IO and handle it just before it hits this wall. This is a bad thing I get it.

Notice how the above two sentences are the same? That is what I mean when I say you're just moving the problem to another place but the problem essentially remains the SAME THING.

As I stated before and I'll repeat it again. The only reason why you prefer NonZero[Int] over Optional[Int] is the same reason why someone would prefer blue over red. There is no logic, rhyme or reason behind it. It is just your style and your personal taste.

[lkitching]

> I said why does it even matter not why can't you do it

I've explained why it matters - the types are more precise in my version and if you start from that you can always throw away the extra precision if desired to get to your version. You can't go in the other direction, so starting from your version makes it impossible to safely recover an Int from the returned type of Optional[Int], even if you've already established the precondtion beforehand.

> There is 100% casting in your version

Creating an Optional[Int] from an Int is a conversion, not a cast. I thought it was obvious from the context but for the avoidance of any doubt, by 'casting' I mean an unsafe narrowing conversion. Optional[Int] is a larger type than Int, so it's trivial to create one from an Int:

    def pure(x: Int): Optional[Int] = Just(x)

you clearly can't safely go in the other direction, whether using pattern matching or otherwise. If you disagree, just complete the following definition:

    def fromOptional(o: Optional[Int]): Int =
        match o with
        | Some(i) => i
        | Nothing => ...

eventually you need to provide a default value for the case of no value.

> Imagine a map with RGB colors as keys.

Your example doesn't make sense, what would you expect (lookup Map.empty Red) to return? The optional return value is used to represent the key being missing in the map. Nonetheless the point I was making is that you wouldn't return Nothing from such a function in the event of a precondition failure e.g.

    def lookup(m: Map[K, V], v: K): Optional[V] =
        if m is None return Nothing
        ...

you would instead throw an exception if the input map is null and force the caller to handle it. The majority of static type systems are not powerful enough to encode arbitrary properties about values, so you have to decide which ones to check dynamically and which statically. Checking preconditions dynamically is reasonable if encodng them in the type system is too cumbersome.

> This prior point involves the creation of the type NonZero[Int] which involves: NonZero.fromInt

No, this is not necessarily the only way to create instances of NonZero. You could have a PosNat subtype with members one: PosNat and succ: PosNat -> PosNat. You could have a non-empty list type with a length member.

> Every other mathematical operation (+,-,x^y,/,) returns an Int not a NonZero[Int]

They don't return Optional[Int] either so I don't see how this is relevant. There's no reason the input has to come from some application of a different operator, it could come from configuration, user input, a property from some other type etc. The question is whether and how to model the constraints in the type. The constraint exists in the argument so it makes sense to constrain the input type, not widen the output.

> Notice how the above two sentences are the same?

Yes, if all you want to do is avoid establishing the property you care about and silently propagate some information-free 'failure' value to the top level, then you can do it either way. But the entire point of encoding properties in the types is to force you to establish them. These statements highlight the difference:

1. I've established the divisor is non-zero, called myDiv, received an Int and continue

2. I've established the divisor is non-zero, discarded that information to call yourDiv, recieved an Optional[Int] which cannot be empty, but which must be propagated. You could immediately unwrap the value but now you're just re-creating the dynamic behaviour of a function (Int, Int) -> Int which you've already rejected.

[deltaonefour]

>Creating an Optional[Int] from an Int is a conversion, not a cast.

Ok man, take a look at this: https://en.wikipedia.org/wiki/Type_conversion

There is no garbage redefining of a well known word to fit your convenient argument. We are using English and well known terms. This is not obvious to anyone.

Let me illustrate what happened. YOu used a well known term INCORRECTLY, then redefined later claiming that your redefinition was obvious. That is a comedy excuse. No.

You were using a term incorrectly. You man handled the term and you are wrong in that regard.

> eventually you need to provide a default value for the case of no value.

So? It's still type safe. My point is you can't get rid of this problem at all, not even with NonZero int. But via an optional type you guarantee that it's handled. The Rest of your composition needs to live in the Context of that optional. This problem isn't solved by moving it to a post condition.

>Your example doesn't make sense, what would you expect (lookup Map.empty Red) to return?

Ok this I admit I'm wrong. I wasn't thinking detailed enough in that respect so my example was wrong . But this doesn't prove your case at all. There is nothing wrong with using a Maybe monad here. There is zero reason why you need to throw an exception.

>No, this is not necessarily the only way to create instances of NonZero. You could have a PosNat subtype with members one: PosNat and succ: PosNat -> PosNat. You could have a non-empty list type with a length member.

This level of pedantism is too extreme. Nobody uses that type of arithmetic. But if you want to go there fine. You now have a hole in subtraction as 3 - 3 would be a singularity. Your program can no longer use subtraction or addition.

Division and all other mathematical operations have incompatible types. Type casting is 100% necessary to use all operations. The only way I see your Peanno NonZero safetly working is to restrict division to be the exact First set of operations. Then a safe cast can be done without an optional from NonZero to Int for subsequent operations. This is the expansive type casting that is safe and what you're referring to earlier. Either way such an ordering restriction is highly unreasonable but it does offer total safety at the type level.

>They don't return Optional[Int] either so I don't see how this is relevant. There's no reason the input has to come from some application of a different operator, it could come from configuration, user input, a property from some other type etc. The question is whether and how to model the constraints in the type. The constraint exists in the argument so it makes sense to constrain the input type, not widen the output.

If it comes from user input are you saying there's a terminal where the user can never input a zero? If it comes from IO anything goes, you have to be prepared for Anything. Usually the input is String and String -> Int has a shitload of holes.

>Yes, if all you want to do is avoid establishing the property you care about and silently propagate some information-free 'failure' value to the top level, then you can do it either way. But the entire point of encoding properties in the types is to force you to establish them. These statements highlight the difference:

>1. I've established the divisor is non-zero, called myDiv, received an Int and continue

Number 1 cannot be established without creating a singularity or creating strange restrictions as I explained above. If all your program ever does is do division without accepting terms from IO then fine, you win, but let's be real. This is not a realistic expectation and that is my point.

[lkitching]

Sorry for the confusion, but regardless of whether you call it casting, conversion, or something else, it's still trivial to do safely in one directly and impossible to do safely in the other. Given your fixation on the terminology I assume you've now accepted this.

> But via an optional type you guarantee that it's handled

It's not 'handled', which is the point. There's no default value so you have no option but to propagate the missing value. Callers that establish the precondition still have to deal with an Optional value even though it can't be empty. Callers which establish the precondtion through the types receive a more precise type and don't have this problem. Callers that establish the precondition in the more simply-typed version (Int, Int) -> Int also receive an Int. Only your version imposes the imprecision on the return type.

> There is nothing wrong with using a Maybe monad here. There is zero reason why you need to throw an exception.

The Optional[Value] returned from a map lookup is used to incidicate the possibility of a missing key, which is an expected outcome of the operation itself. Passing a null map represents a structural error in the construction of the program at the point the call is made. If you represent both in the same type you can't distinguish these two cases.

> You now have a hole in subtraction as 3 - 3 would be a singularity.

There's no hole here, subtraction on NonZero just has to return Int instead.

> If it comes from IO anything goes, you have to be prepared for Anything

Yes, if it comes from user input you have to establish the property dynamically. Encoding the property in the argument type forces you to actually do it (whether statically or dynamically), and help you push the constraint to the highest level. Putting the optionality in the return type doesn't force you do do this, and imposes a cost on every call that actually does.

[deltaonefour]

>Given your fixation on the terminology I assume you've now accepted this.

I would call it fixation if it was some obscure reference. But it's not. You're calling a cat a dog. Literally everyone knows what type casting is. I'm saying hey buddy I know what you're talking about, but a cat IS NOT a dog.

I've always accepted the intent of what you're saying. You're just not understanding my intent. You literally didn't even address division coming before all other mathematical operations. I don't think you understood.

>It's not 'handled', which is the point.

It is handled. Otherwise it won't compile.

>There's no default value so you have no option but to propagate the missing value.

Understood. Let me put it this way an "=" represents a section of a program with no Optionals a "-" represents a section of a program with Optionals and an F represents a section of a program with a function that does division. A program is can be represented by a serial list of these characters. To you a program is bad if it looks like this:

-------------------F====================

After the division call the output is polluted with optionals because F returns an optional. You think this is bad.

You think a program should look like this:

-------------------F---------------------

And you think this is achievable with division if you use a NonZero Int type.

What I am saying is that it is not generally possible. To create a NonZero type your program will be polluted before the function call simply because Int->Optional[NonZero[Int]]:

===================F----------------------

>There's no hole here, subtraction on NonZero just has to return Int instead.

First of all this a type cast. subtraction and addition are defined on sets, not between two different sets.

Second off this defeats your whole point. You wanted to create a NonZero int for safety subtraction just made it unsafe again.

Third off does it return an int for 3 -3 and a nonzero for 4 - 2? So your subtraction returns a variant type. That basically opens up the same singularity as your null once you try to evaluate this sum type via pattern matching.

Wasn't your point this:

   f(x: NonZero, y: NonZero) -> int

If I do a subtraction operation BEFORE this function you can't even use the resulting zero value. So basically I have to turn subtraction into this which is identical from a cardinality stand point to returning a variant of a Int or NonZero:

   minus(x: NonZero, y: NonZero) -> Optional[NonZero]

> Encoding the property in the argument type forces you to actually do it (whether statically or dynamically), and help you push the constraint to the highest level.

As I said above nothing is pushed to a higher level you're just moving the singularity around. Making it happen at the type cast rather then the division.

>and imposes a cost on every call that actually does.

You either pay the cost before division or after. Pick your poison, that is what I am saying.

The only way your methodology works is if Division is the first thing that happens. Then your program looks like this:

F--------------------------------------

That's the only time a nonzero type makes better sense then a function that returns an optional.