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.
130 lines
3.5 KiB
Text
130 lines
3.5 KiB
Text
/-!
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Tests around the special case of well-founded recursion on Nat.
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-/
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set_option warn.sorry false
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namespace T1
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@[semireducible]
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def foo : List α → Nat
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| [] => 0
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| _::xs => 1 + (foo xs)
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termination_by xs => xs.length
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-- Closed terms should evaluate
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example : foo ([] : List Unit) = 0 := rfl
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example : foo ([] : List Unit) = 0 := by decide
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example : foo ([] : List Unit) = 0 := by decide +kernel
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example : foo [1,2,3,4,5] = 5 := rfl
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example : foo [1,2,3,4,5] = 5 := by decide
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example : foo [1,2,3,4,5] = 5 := by decide +kernel
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-- Open terms should not (these wouldn't even without the provisions with `WellFounded.Nat.eager`,
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-- the fuel does not line up)
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example : foo (x::xs) = 1 + foo xs := by (fail_if_success rfl); simp [foo]
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example : foo (x::y::z::xs) = 1+ (1+(1+ foo xs)) := by (fail_if_success rfl); simp [foo]
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end T1
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-- Variant where the fuel does not line up
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namespace T2
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@[semireducible] def foo : List α → Nat
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| [] => 0
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| _::xs => 1 + (foo xs)
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termination_by xs => 2 * xs.length
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example : foo ([] : List Unit) = 0 := rfl
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example : foo ([] : List Unit) = 0 := by decide
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example : foo ([] : List Unit) = 0 := by decide +kernel
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example : foo [1,2,3,4,5] = 5 := rfl
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example : foo [1,2,3,4,5] = 5 := by decide
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example : foo [1,2,3,4,5] = 5 := by decide +kernel
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-- Open terms should not (these wouldn't even without the provisions, the fuel does not line up)
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example : foo (x::xs) = 1 + foo xs := by (fail_if_success rfl); simp [foo]
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example : foo (x::y::z::xs) = 1+ (1 + ( 1+ foo xs)) := by (fail_if_success rfl); simp [foo]
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end T2
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-- Idiom to switch to `WellFounded.fix`
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namespace T3
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def foo : List α → Nat
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| [] => 0
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| _::xs => 1 + (foo xs)
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termination_by xs => (xs.length, 0)
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example : foo ([] : List Unit) = 0 := by (fail_if_success rfl); simp [foo]
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example : foo ([] : List Unit) = 0 := by (fail_if_success decide); simp [foo]
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example : foo ([] : List Unit) = 0 := by (fail_if_success decide +kernel); simp [foo]
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example : foo [1,2,3,4,5] = 5 := by (fail_if_success rfl); simp [foo]
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example : foo [1,2,3,4,5] = 5 := by (fail_if_success decide); simp [foo]
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example : foo [1,2,3,4,5] = 5 := by (fail_if_success decide +kernel); simp [foo]
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-- Open terms should not (these wouldn't even without the provisions, the fuel does not line up)
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example : foo (x::xs) = 1 + foo xs := by (fail_if_success rfl); simp [foo]
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example : foo (x::y::z::xs) = 1+ (1 + ( 1+ foo xs)) := by (fail_if_success rfl); simp [foo]
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end T3
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-- Defeq between similar functions
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namespace T4
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@[semireducible] def foo (b : Bool) : Nat → Nat
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| 0 => 0
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| n+1 => 1 + foo b n
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termination_by n => n
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@[semireducible] def bar (b : Bool) : Nat → Nat
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| 0 => 0
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| n+1 => cond b 1 2 + bar b n
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termination_by n => n
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@[semireducible] def baz : Nat → Nat
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| 0 => 0
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| n+1 => 1 + baz n
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termination_by n => n
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example : foo true n = bar true n := rfl
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example : foo true n = baz n := rfl
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example : bar true n = baz n := rfl
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end T4
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-- For comparison: with wfrec
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namespace T4wfrec
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def foo (b : Bool) : Nat → Nat
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| 0 => 0
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| n+1 => 1 + foo b n
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termination_by n => (n, 0)
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def bar (b : Bool) : Nat → Nat
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| 0 => 0
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| n+1 => cond b 1 2 + bar b n
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termination_by n => (n, 0)
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def baz : Nat → Nat
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| 0 => 0
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| n+1 => 1 + baz n
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termination_by n => (n, 0)
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example : foo true n = bar true n := by (fail_if_success rfl); sorry
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example : foo true n = baz n := by (fail_if_success rfl); sorry
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example : bar true n = baz n := by (fail_if_success rfl); sorry
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unseal foo bar baz
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example : foo true n = bar true n := rfl
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example : foo true n = baz n := rfl
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example : bar true n = baz n := rfl
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end T4wfrec
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