I am trying to write a declaration of two mutually inductive datatypes that both take a type parameter as arguments as follows:
noeq
type foo 'a =
| FooA: x: 'a -> foo 'a
| Foob: y: bar 'a -> foo 'a
and bar 'b =
| BarA: x: int -> bar 'b
| BarF: y: foo 'b -> bar 'b
I get an error message that is as follows:
LabeledStates.fst(59,0-64,31): (Error 67) Failed to solve universe inequalities for inductives 1 error was reported (see above)
(where line 59 is the line that includes "type foo 'a")
What does this error mean and what can I do to fix it?
If I remove the type parameters (and give foo.x the type of int, for example) I do not get errors anymore. Similarly, if I just give one of the types a type parameter but not the other, I also do not have errors.
F* isn't capable of inferring universes in cases like this. You can provide explicit universe instantiations, however. For example, here are three possible solutions:
First, a doubly universe polymorphic one, most general but also possibly quite cumbersome to use
noeq
type foo (a:Type u#a) : Type u#(max a b) =
| FooA: x: a -> foo a
| Foob: y: bar u#b u#a a -> foo a
and bar (b:Type u#b) : Type u#(max a b) =
| BarA: x: int -> bar b
| BarF: y: foo u#b u#a b -> bar b
A singly universe polymorphic solution, perhaps a bit simpler, though less general:
noeq
type foo1 (a:Type u#a) : Type u#a =
| Foo1A: x: a -> foo1 a
| Foo1b: y: bar1 u#a a -> foo1 a
and bar1 (b:Type u#a) : Type u#a =
| Bar1A: x: int -> bar1 b
| Bar1F: y: foo1 u#a b -> bar1 b
And, finally, a version specialized to universe 0, probably the easiest to use if it fits your needs, but also least general:
noeq
type foo0 (a:Type u#0) : Type u#0 =
| Foo0A: x: a -> foo0 a
| Foo0b: y: bar0 a -> foo0 a
and bar0 (b:Type u#0) : Type u#0 =
| Bar0A: x: int -> bar0 b
| Bar0F: y: foo0 b -> bar0 b