2120883307
@Kha I had some unexpected surprises, but it is a good change.
Here is the summary.
1- We could get rid of `a %ₙ b` and `ModN` class. We can use `HMod`
instead. It was a positive surprise since I didn't remember we had
this `ModN` class.
2- Coercions are never used in heterogeneous operators. This is
expected since `a * b` is now notation for `HMul.hMul a b`, and
`a` and `b` may have different types. I manually added instances such
as `HMul Nat Int Int`. However, I did not try to add generic instances
such as
```
instance [Coe a b] [Mul b] : HMul a b b where
hMul x y := mul (coe x) y
```
I will try later.
3- Give `h : cs.size > 0`, I got a type error at
```
let idx : Fin cs.size := ⟨cs.size - 1, Nat.predLt h⟩
```
`Nat.predLt h` has type `Nat.pred cs.size < cs.size`
However, `Nat.pred cs.size` doesn't unify with `cs.size - 1`.
The problem is that we can't synthesize the `HSub` instance until
we apply the default instances.
It worked before because `isDefEq` would force the pending TC
problem `Sub Nat` to be resolved, and after that we would be able
to reduce `cs.size - 1` and establish that it is definitionally
equal to `Nat.pred cs.size`.
I considered two possible workarounds
a) `let idx : Fin cs.size := ⟨cs.size - (1:Nat), Nat.predLt h⟩`
b) `let idx : Fin cs.size := ⟨cs.size - 1, by exact Nat.predLt h⟩`
The first one works because we are not providing enough information
for synthesizing the `HSub` instance. The second works because it
postpones the elaboration of `Nat.predLt h`. The default instances
will be applied before we start applying tactics.
4- The `.` notation is affected too. For example, `(x + 1).toUInt8`
doesn't work since we don't know the type of `x+1` until we apply
default instances. I fixed it by using `(x + (1:Nat)).toUInt8`.
Another possible fix is `Nat.toUInt8 (x + 1)`.
Similarly, `(x+1).fold ...` doesn't work.
5- The following code failed to be elaborated
```
indent (push s!"{ss'}\n") (some (0 - Format.getIndent (← getOptions)))
```
It was working before, but it relied on how the expected type is
propagated. The elaborator process
```
some (0 - Format.getIndent (← getOptions))
```
with expected type `(Option Int)`. So, the `-` is interpreted as
`Int.sub` although `Format.getIndent (← getOptions)` has type `Nat`.
In the new `HSub`, the expected type doesn't really influence TC
resolution since it is an `outparam`. So, we failed with the error
failed to synthesize `HSub Nat Nat Int`.
One possible fix was to add the instance `HSub Nat Nat Int` with
`Int.sub`, but I used the following fix
```
some ((0 : Int) - Format.getIndent (← getOptions))
```
which makes it clear that we want the `Int.sub` operator instead of
`Nat.sub`.
28 lines
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28 lines
3 KiB
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"`Nat.one._@.UnhygienicMain._hyg.1"
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"<missing>"
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"<missing>"
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"<missing>"
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"(_kind.term._@.Init.Notation._hyg.637 <missing> \"+\" (numLit \"1\"))"
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"(_kind.term._@.Init.Notation._hyg.637 <missing> \"+\" (numLit \"1\"))"
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"(_kind.term._@.Init.Notation._hyg.637 (numLit \"1\") \"+\" (numLit \"1\"))"
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"(Term.fun \"fun\" (Term.basicFun [`a._@.UnhygienicMain._hyg.1] \"=>\" `a._@.UnhygienicMain._hyg.1))"
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"(Command.declaration\n (Command.declModifiers [] [] [] [] [] [])\n (Command.def\n \"def\"\n (Command.declId `foo._@.UnhygienicMain._hyg.1 [])\n (Command.optDeclSig [] [])\n (Command.declValSimple \":=\" (numLit \"1\") [])))"
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"[(Command.declaration\n (Command.declModifiers [] [] [] [] [] [])\n (Command.def\n \"def\"\n (Command.declId `foo._@.UnhygienicMain._hyg.1 [])\n (Command.optDeclSig [] [])\n (Command.declValSimple \":=\" (numLit \"1\") [])))\n (Command.declaration\n (Command.declModifiers [] [] [] [] [] [])\n (Command.def\n \"def\"\n (Command.declId `bar._@.UnhygienicMain._hyg.1 [])\n (Command.optDeclSig [] [])\n (Command.declValSimple \":=\" (numLit \"2\") [])))]"
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"`Nat.one._@.UnhygienicMain._hyg.1"
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"(Term.app `f._@.UnhygienicMain._hyg.1 [`Nat.one._@.UnhygienicMain._hyg.1 `Nat.one._@.UnhygienicMain._hyg.1])"
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"(_kind.term._@.Init.Notation._hyg.12477\n `f._@.UnhygienicMain._hyg.1\n \"$\"\n (Term.app `f._@.UnhygienicMain._hyg.1 [`Nat.one._@.UnhygienicMain._hyg.1 (numLit \"1\")]))"
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"(Term.app `f._@.UnhygienicMain._hyg.1 [`Nat.one._@.UnhygienicMain._hyg.1])"
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"(Term.proj `Nat.one._@.UnhygienicMain._hyg.1 \".\" `b._@.UnhygienicMain._hyg.1)"
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"(_kind.term._@.Init.Notation._hyg.637 (numLit \"2\") \"+\" (numLit \"1\"))"
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"(Command.declaration\n (Command.declModifiers [] [] [] [] [] [])\n (Command.def\n \"def\"\n (Command.declId `foo._@.UnhygienicMain._hyg.1 [])\n (Command.optDeclSig [] [])\n (Command.declValSimple \":=\" (numLit \"1\") [])))"
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"[(Command.declaration\n (Command.declModifiers [] [] [] [] [] [])\n (Command.def\n \"def\"\n (Command.declId `bar._@.UnhygienicMain._hyg.1 [])\n (Command.optDeclSig [] [])\n (Command.declValSimple \":=\" (numLit \"2\") [])))\n (Command.declaration\n (Command.declModifiers [] [] [] [] [] [])\n (Command.def\n \"def\"\n (Command.declId `foo._@.UnhygienicMain._hyg.1 [])\n (Command.optDeclSig [] [])\n (Command.declValSimple \":=\" (numLit \"1\") [])))]"
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"0"
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"1"
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"(Term.fun\n \"fun\"\n (Term.basicFun\n [`a._@.UnhygienicMain._hyg.1\n (Term.paren \"(\" [`b._@.UnhygienicMain._hyg.1 [(Term.typeAscription \":\" `Nat._@.UnhygienicMain._hyg.1)]] \")\")]\n \"=>\"\n (numLit \"1\")))"
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"#[(Term.paren \"(\" [`a._@.UnhygienicMain._hyg.1 [(Term.typeAscription \":\" `Nat._@.UnhygienicMain._hyg.1)]] \")\"), `b._@.UnhygienicMain._hyg.1]"
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"`a._@.UnhygienicMain._hyg.1"
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"(Term.forall \"∀\" [(Term.simpleBinder [(Term.hole \"_\")] [])] \",\" `c._@.UnhygienicMain._hyg.1)"
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"(Term.simpleBinder [(Term.hole \"_\")] [])"
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"`a._@.UnhygienicMain._hyg.1"
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"(Term.explicitUniv `a._@.UnhygienicMain._hyg.1 \".{\" [(numLit \"0\")] \"}\")"
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"#[]"
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