08eb78a5b2
This PR sets up the new integrated test/bench suite. It then migrates all benchmarks and some related tests to the new suite. There's also some documentation and some linting. For now, a lot of the old tests are left alone so this PR doesn't become even larger than it already is. Eventually, all tests should be migrated to the new suite though so there isn't a confusing mix of two systems.
60 lines
1.9 KiB
Text
60 lines
1.9 KiB
Text
namespace SillyParam
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set_option linter.unusedVariables false in
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theorem nat_rec_with_string (some_param : String) {motive : Nat → Prop}
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(zero : motive .zero) (succ : ∀ n, motive n → motive (.succ n)) : ∀ n, motive n :=
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@Nat.rec motive zero succ
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example (n m : Nat) (h : n ≠ zero) : Nat.add m n ≠ zero := by
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induction n using nat_rec_with_string
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case some_param =>
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show String
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exact "heh"
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case zero => sorry
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case succ => sorry
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end SillyParam
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namespace RestrictedMotive
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axiom Restriction : (Nat → Prop) → Prop
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axiom restricted_induction {motive : Nat → Prop} (h : Restriction motive)
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(zero : motive .zero) (succ : ∀ n, motive n → motive (.succ n)) : ∀ n, motive n
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example (n m : Nat) (h : n ≠ zero) : Nat.add m n ≠ zero := by
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induction n using restricted_induction
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case h =>
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show Restriction _
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sorry
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case zero => sorry
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case succ => sorry
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end RestrictedMotive
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namespace DownInduction
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axiom down_induction {motive : Nat → Prop} (u : Nat) (x : Nat)
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(le_u : x ≤ u) (start : motive u) (step : ∀ x, x < u → motive (x + 1) → motive x) : motive x
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example (n m : Nat) (h : m * m < 100) (h2 : n ≤ m) : n * n < 100 := by
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induction n using down_induction
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case u => exact m -- (could have used `using down_induction (u := m)` of course)
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case le_u =>
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-- This does not work as hoped for yet: `induction` will revert `h2`, because it mentions `n`,
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-- but we’d like to keep it outside of the motive here.
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sorry
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case start => exact h
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case step x hlt IH =>
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have IH := IH hlt
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sorry
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-- Unfortunately, this doesn’t work either:
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-- example (n m : Nat) (h : m * m < 100) (h2 : n ≤ m) : n * n < 100 := by
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-- induction n using down_induction (le_u := h2)
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-- because after this, the target `n` is no longer a universally qualified variable
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--
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-- This probably could be made to work with a bit more refactoring.
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end DownInduction
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