# Re: Difficulties getting equality working with higher-kinded types

```Forgot to paste the code for 'eq' that I used:

implement
{a}{b}
eq_either_either (x, y) =
case+ (x, y) of
| (right (_), left (_)) => false
| (left (_), right (_)) => false
| (left (x), left (y)) => gequal_val_val<a>(x, y)
| (right (x), right (y)) => gequal_val_val<b>(x, y)```
```

On Monday, February 12, 2018 at 12:07:33 AM UTC-5, gmhwxi wrote:
>
> There are several issues here.
>
> First, eq and neq should be function templates (rather than polymorphic
> functions):
>
> datatype either(a: t@ype, b: t@ype+) =
>   | left of a
>   | right of b
>
> fun
> {a:t@ype}
> {b:t@ype}
> eq_either_either(x : either(a, INV(b)), y : either(a, b)) : bool
>
> fun
> {a:t@ype}
> {b:t@ype}
> neq_either_either(x : either(a, INV(b)), y : either(a, b)) : bool
>
>
>
>
> Since the second argument of 'either' is declared to be co-variant, INV(b)
> is used in the interface for eq and neq
>
> The function of test_eq1 needs to be modified slightly:
>
>
> fn test_eq1() : bool =
>     let
>       val rhs = right{string,string}("eq")
>       val lhs = right{string,string}("eq")
>     in
>       rhs = lhs
>     end
>
> If you write rhs:either(string, string) = right("eq"), then the
> typechecker only knows that the type assigned to rhs is either(string, X)
> for some X <= string.
>
> Now your code can be compiled to an executable. I saw the following when
> trying it:
>
>   succeeded: eq (1/2)
>   succeeded: eq (2/2)
>
> Test suite complete (2/2)
>
> A more serious issue with your code is the following one:
>
> assume monad_type(b : t0p) = [a:t0p] either(a, b)
>
> This is unlikely to work. I think what you need is monad(a, b) where 'a'
> serves
> as a parameter:
>
> assume monad_type(a:t0p, b:t0p) = either(a, b)
>
> On Sunday, February 11, 2018 at 8:27:15 PM UTC-5
>
>> Hi all,
>>
>> I have been trying to implement something like Haskell's Data.Either
>> module in ATS. I'd like to be able to test equality generically. This is my
>> .sats file:
>>
>>
>> datatype either(a: t@ype, b: t@ype+) =
>>   | left of a
>>   | right of b
>>
>> fun eq_either_either {a:t@ype}{b:t@ype+} (x : either(a, b), y : either(a,
>> b)) : bool
>>
>> fun neq_either_either {a:t@ype}{b:t@ype+} (x : either(a, b), y : either(a
>> , b)) : bool
>>
>>
>>
>> fun lefts {a:t@ype}{b:t@ype+}{n:int} (x : list(either(a,b), n)) :
>>   [ m : int | m <= n ] list(a, m)
>>
>> fun rights {a:t@ype}{b:t@ype+}{n:int} (x : list(either(a,b), n)) :
>>   [ m : int | m <= n ] list(b, m)
>>
>> fun either_ {a:t@ype}{b:t@ype+}{c:t@ype} (f : a -> c, g : b -> c, x :
>> either(a, b)) : c
>>
>> fun is_left {a:t@ype}{b:t@ype+} (x : either(a, b)) : bool
>>
>> fun is_right {a:t@ype}{b:t@ype+} (x : either(a, b)) : bool
>>
>> fun from_right {a:t@ype}{b:t@ype+} (x : b, y : either(a, b)) : b
>>
>> fun from_left {a:t@ype}{b:t@ype+} (x : a, y : either(a, b)) : a
>>
>>
>> and this is my .dats file:
>>
>>
>> #include "prelude/DATS/basics.dats"
>> #include "prelude/DATS/list.dats"
>>
>> assume monad_type(b : t0p) = [a:t0p] either(a, b)
>>
>> implement eq_either_either (x, y) =
>>   case+ (x, y) of
>>     | (right (_), left (_)) => false
>>     | (left (_), right (_)) => false
>>     | (left (x), left (y)) => gequal_val_val(x, y)
>>     | (right (x), right (y)) => gequal_val_val(x, y)
>>
>> implement neq_either_either (x, y) =
>>   not(eq_either_either(x, y))
>>
>> datasort list =
>>   | NIL
>>   | CONS of list
>>
>> dataprop LENGTH(list, int) =
>>   | L_NIL(NIL, 0)
>>   | {l:list}{len:nat} L_CONS(CONS(l), 1 + len) of (LENGTH(l, len))
>>
>> implement lefts (ys) =
>>   case- ys of
>>     | list_nil() => list_nil()
>>     | list_cons (right (x), xs) => lefts(xs)
>>
>> // | list_cons (left (x), xs) => list_cons(x, lefts(xs))
>> // functorial proof functions?
>> // want to prove: if length(f(xs)) <= n, length(xs) = n, length(cons(x,
>> xs)) <= length(cons(x, f(xs)))
>> implement {a} monad_return (x) =
>>   right(x)
>>
>> implement {a} monad_join (x) =
>>   case+ x of
>>     | left (y) => left(y)
>>     | right (left (y)) => left(y)
>>     | right (right (x)) => right(x)
>>
>> implement {a}{b} monad_fmap (fopr, x) =
>>   case+ x of
>>     | left (y) => left(y)
>>     | right (x) => right(fopr(x))
>>
>> implement {a}{b} monad_bind (x, fopr) =
>>   case+ x of
>>     | left (y) => left(y)
>>     | right (y) => fopr(y)
>>
>>
>> my .hats file:
>>
>>
>>
>> and finally the actual test suite:
>>
>> #include "either.hats"
>>
>>
>> #define nil list_vt_nil
>>
>> #define :: list_vt_cons
>>
>> fn test_eq1() : bool =
>>   let
>>     val rhs: either(string, string) = right("eq")
>>     val lhs: either(string, string) = right("eq")
>>   in
>>     rhs = lhs
>>   end
>>
>> fn test_eq2() : bool =
>>   true
>>
>> vtypedef named = @{ fst = string, snd = bool }
>> vtypedef test_tree = @{ group = string, leaves = List_vt(named) }
>>
>> fn fail_incomplete(i : int, n : int) : void =
>>   {
>>     val _ = prerr!("\nTest suite complete (" + tostring_int(i) + "/" +
>> tostring_int(n) + ")\n")
>>     val _ = if n != i then
>>       (exit(1) ; ())
>>     else
>>       ()
>>   }
>>
>> fnx iterate_list(t : test_tree, i : int, n : int) : void =
>>   let
>>     val _ = if i = 0 then
>>       println!(t.group + ":")
>>     else
>>       ()
>>
>>     fun handle_loop(s : string, b : bool, xs : test_tree) : void =
>>       if b then
>>         (println!("  \33[32msucceeded:\33[0m " + s) ; iterate_list(xs, i
>> + 1, n))
>>       else
>>         (println!("  \33[31mfailed:\33[0m " + s) ; iterate_list(xs, i, n
>> ))
>>   in
>>     case+ t.leaves of
>>       | ~list_vt_nil() => fail_incomplete(i, n)
>>       | ~list_vt_cons (x, xs) => handle_loop(x.fst, x.snd, @{ group = t.
>> group, leaves = xs })
>>   end
>>
>> implement main0 () =
>>   {
>>     var n0 = @{ fst = "eq (1/2)", snd = test_eq1() }
>>     var n1 = @{ fst = "eq (2/2)", snd = test_eq2() }
>>     var xs = n0 :: n1 :: nil
>>     var total = list_vt_length(xs)
>>     val g = @{ group = "monad_join", leaves = xs } : test_tree
>>     val _ = iterate_list(g, 0, total)
>>   }
>>
>>
>> which fails to build with the following error:
>>
>> /tmp/ccrn6Wjd.o: In function `mainats_void_0':
>> test_dats.c:(.text+0x391): undefined reference to `
>> _057_home_057_vanessa_057__056_atspkg_057_0_056_3_056_9_057_lib_057_ats2_055_postiats_055_0_056_3_056_9_057_either_056_sats__eq_either_either'
>>
>> collect2: error: ld returned 1 exit status )
>>
>>
>> Am I doing something wrong here? I tried to get generic equality on lists
>> working as well, but I couldn't seem to figure out how. I tried this with
>> ATS 0.3.9 as well as ATS 0.3.10. Any insight would be much appreciated!
>>
>> Thanks!
>>
>

--
You received this message because you are subscribed to the Google Groups
"ats-lang-users" group.
To unsubscribe from this group and stop receiving emails from it, send an email