feat: introduce NthRoot notation class
#7907
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This adds the notation `√r` for `Real.sqrt r`. The precedence is such that `√x⁻¹` is parsed as `√(x⁻¹)`; not because this is particularly desirable, but because it's the default and the choice doesn't really matter. This is extracted from #7907, which adds a more general nth root typeclass. The idea is to perform all the boring substitutions downstream quickly, so that we can play around with custom elaborators with a much slower rate of code-rot. This PR also won't rot as quickly, as it does not forbid writing `x.sqrt` as that PR does. While perhaps claiming `√` for `Real.sqrt` is greedy; it: * Is far more common thatn `NNReal.sqrt` and `Nat.sqrt` * Is far more interesting to mathlib than `sqrt` on `Float` * Can be overloaded anyway, so this does not prevent downstream code using the notation on their own types. * Will be replaced by a more general typeclass in a future PR. [Zulip](https://leanprover.zulipchat.com/#narrow/stream/287929-mathlib4/topic/.60Sqrt.60.20notation.20typeclass/near/400086502) Co-authored-by: Yury G. Kudryashov <urkud@urkud.name>
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This adds the notation `√r` for `Real.sqrt r`. The precedence is such that `√x⁻¹` is parsed as `√(x⁻¹)`; not because this is particularly desirable, but because it's the default and the choice doesn't really matter. This is extracted from #7907, which adds a more general nth root typeclass. The idea is to perform all the boring substitutions downstream quickly, so that we can play around with custom elaborators with a much slower rate of code-rot. This PR also won't rot as quickly, as it does not forbid writing `x.sqrt` as that PR does. While perhaps claiming `√` for `Real.sqrt` is greedy; it: * Is far more common thatn `NNReal.sqrt` and `Nat.sqrt` * Is far more interesting to mathlib than `sqrt` on `Float` * Can be overloaded anyway, so this does not prevent downstream code using the notation on their own types. * Will be replaced by a more general typeclass in a future PR. [Zulip](https://leanprover.zulipchat.com/#narrow/stream/287929-mathlib4/topic/.60Sqrt.60.20notation.20typeclass/near/400086502) Co-authored-by: Yury G. Kudryashov <urkud@urkud.name>
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This adds the notation `√r` for `Real.sqrt r`. The precedence is such that `√x⁻¹` is parsed as `√(x⁻¹)`; not because this is particularly desirable, but because it's the default and the choice doesn't really matter. This is extracted from #7907, which adds a more general nth root typeclass. The idea is to perform all the boring substitutions downstream quickly, so that we can play around with custom elaborators with a much slower rate of code-rot. This PR also won't rot as quickly, as it does not forbid writing `x.sqrt` as that PR does. While perhaps claiming `√` for `Real.sqrt` is greedy; it: * Is far more common thatn `NNReal.sqrt` and `Nat.sqrt` * Is far more interesting to mathlib than `sqrt` on `Float` * Can be overloaded anyway, so this does not prevent downstream code using the notation on their own types. * Will be replaced by a more general typeclass in a future PR. [Zulip](https://leanprover.zulipchat.com/#narrow/stream/287929-mathlib4/topic/.60Sqrt.60.20notation.20typeclass/near/400086502) Co-authored-by: Yury G. Kudryashov <urkud@urkud.name>
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This adds the notation `√r` for `Real.sqrt r`. The precedence is such that `√x⁻¹` is parsed as `√(x⁻¹)`; not because this is particularly desirable, but because it's the default and the choice doesn't really matter. This is extracted from #7907, which adds a more general nth root typeclass. The idea is to perform all the boring substitutions downstream quickly, so that we can play around with custom elaborators with a much slower rate of code-rot. This PR also won't rot as quickly, as it does not forbid writing `x.sqrt` as that PR does. While perhaps claiming `√` for `Real.sqrt` is greedy; it: * Is far more common thatn `NNReal.sqrt` and `Nat.sqrt` * Is far more interesting to mathlib than `sqrt` on `Float` * Can be overloaded anyway, so this does not prevent downstream code using the notation on their own types. * Will be replaced by a more general typeclass in a future PR. [Zulip](https://leanprover.zulipchat.com/#narrow/stream/287929-mathlib4/topic/.60Sqrt.60.20notation.20typeclass/near/400086502) Co-authored-by: Yury G. Kudryashov <urkud@urkud.name>
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This adds the notation `√r` for `Real.sqrt r`. The precedence is such that `√x⁻¹` is parsed as `√(x⁻¹)`; not because this is particularly desirable, but because it's the default and the choice doesn't really matter. This is extracted from #7907, which adds a more general nth root typeclass. The idea is to perform all the boring substitutions downstream quickly, so that we can play around with custom elaborators with a much slower rate of code-rot. This PR also won't rot as quickly, as it does not forbid writing `x.sqrt` as that PR does. While perhaps claiming `√` for `Real.sqrt` is greedy; it: * Is far more common thatn `NNReal.sqrt` and `Nat.sqrt` * Is far more interesting to mathlib than `sqrt` on `Float` * Can be overloaded anyway, so this does not prevent downstream code using the notation on their own types. * Will be replaced by a more general typeclass in a future PR. [Zulip](https://leanprover.zulipchat.com/#narrow/stream/287929-mathlib4/topic/.60Sqrt.60.20notation.20typeclass/near/400086502) Co-authored-by: Yury G. Kudryashov <urkud@urkud.name>
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This adds the notation `√r` for `Real.sqrt r`. The precedence is such that `√x⁻¹` is parsed as `√(x⁻¹)`; not because this is particularly desirable, but because it's the default and the choice doesn't really matter. This is extracted from #7907, which adds a more general nth root typeclass. The idea is to perform all the boring substitutions downstream quickly, so that we can play around with custom elaborators with a much slower rate of code-rot. This PR also won't rot as quickly, as it does not forbid writing `x.sqrt` as that PR does. While perhaps claiming `√` for `Real.sqrt` is greedy; it: * Is far more common thatn `NNReal.sqrt` and `Nat.sqrt` * Is far more interesting to mathlib than `sqrt` on `Float` * Can be overloaded anyway, so this does not prevent downstream code using the notation on their own types. * Will be replaced by a more general typeclass in a future PR. [Zulip](https://leanprover.zulipchat.com/#narrow/stream/287929-mathlib4/topic/.60Sqrt.60.20notation.20typeclass/near/400086502) Co-authored-by: Yury G. Kudryashov <urkud@urkud.name>
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This adds the notation `√r` for `Real.sqrt r`. The precedence is such that `√x⁻¹` is parsed as `√(x⁻¹)`; not because this is particularly desirable, but because it's the default and the choice doesn't really matter. This is extracted from #7907, which adds a more general nth root typeclass. The idea is to perform all the boring substitutions downstream quickly, so that we can play around with custom elaborators with a much slower rate of code-rot. This PR also won't rot as quickly, as it does not forbid writing `x.sqrt` as that PR does. While perhaps claiming `√` for `Real.sqrt` is greedy; it: * Is far more common thatn `NNReal.sqrt` and `Nat.sqrt` * Is far more interesting to mathlib than `sqrt` on `Float` * Can be overloaded anyway, so this does not prevent downstream code using the notation on their own types. * Will be replaced by a more general typeclass in a future PR. [Zulip](https://leanprover.zulipchat.com/#narrow/stream/287929-mathlib4/topic/.60Sqrt.60.20notation.20typeclass/near/400086502) Co-authored-by: Yury G. Kudryashov <urkud@urkud.name>
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I pushed some more changes, this now looks great.
@kmill, could you check the unexpander / use of default_instance is reasonable?
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| @[app_unexpander NthRoot.nthRoot] | ||
| def NthRoot.unexpander : Lean.PrettyPrinter.Unexpander | ||
| | `($_ $n $a) => | ||
| match n with | ||
| | `(2) => `(√$a) | ||
| | `(3) => `(∛$a) | ||
| | `(4) => `(∜$a) | ||
| | _ => `($n:superscript √$a) | ||
| | _ => throw () |
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If the superscript is complicated (even with just NthRoot.nthRoot (2*n) x) it won't pretty print correctly. I think restricting to just number literals and identifiers should handle the common cases:
Suggested change
| @[app_unexpander NthRoot.nthRoot] | |
| def NthRoot.unexpander : Lean.PrettyPrinter.Unexpander | |
| | `($_ $n $a) => | |
| match n with | |
| | `(2) => `(√$a) | |
| | `(3) => `(∛$a) | |
| | `(4) => `(∜$a) | |
| | _ => `($n:superscript √$a) | |
| | _ => throw () | |
| @[app_unexpander NthRoot.nthRoot] | |
| def NthRoot.unexpander : Lean.PrettyPrinter.Unexpander | |
| | `($_ 2 $a) => `(√$a) | |
| | `($_ 3 $a) => `(∛$a) | |
| | `($_ 4 $a) => `(∜$a) | |
| | `($_ $n:num $a) | `($_ $n:ident $a) => `($n:superscript √$a) | |
| | _ => throw () |
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Also use it for
Real.sqrt, and replace the few occurrences ofsqrtthat do not already use the notation.Zulip