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.
70 lines
1.9 KiB
Text
70 lines
1.9 KiB
Text
inductive PFormula (α: Type): Type where
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| And: Array (PFormula α) → PFormula α
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| Or: Array (PFormula α) → PFormula α
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| Not: (PFormula α) → PFormula α
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| Atom: α → PFormula α
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| FF: PFormula α
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| TT: PFormula α
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namespace PFormula
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@[simp]
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def is_atom (f: PFormula α): Prop :=
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match f with
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| .Atom _ => True
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| _ => False
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-- set_option trace.Elab.definition.eqns true
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def is_nnf (f: PFormula α): Prop :=
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match f with
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| .And a | .Or a => all_nnf a
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| .Not g => g.is_atom
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| .Atom _ | .TT | .FF => True
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termination_by sizeOf f
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where
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all_nnf (a: Array (PFormula α)): Prop := ∀ i, (h: i < a.size) → a[i].is_nnf
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termination_by sizeOf a
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-- This is irreducible
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/-- info: @[irreducible] def PFormula.is_nnf : {α : Type} → PFormula α → Prop -/
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#guard_msgs in
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#print sig is_nnf
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-- So this should not be defeq!
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/-- info: theorem PFormula.is_nnf.eq_4 : ∀ {α : Type} (a : α), (Atom a).is_nnf = True -/
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#guard_msgs(pass trace, all) in
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#print sig is_nnf.eq_4
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-- If we try to prove it manually, it the irreducibility of `is_nnf` prevents that:
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theorem eq_4 : ∀ {α : Type} (a : α), (Atom a).is_nnf = True := by
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intros
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fail_if_success rfl -- Should not work
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apply is_nnf.eq_4
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def to_nnf (f: PFormula α): PFormula α :=
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match f with
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| .And a => And (a.mapFinIdx (fun i _ _ => a[i].to_nnf))
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| .Or a => Or (a.mapFinIdx (fun i _ _ => a[i].to_nnf))
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| .Not g =>
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match g with
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| .And a => Or (a.mapFinIdx
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(fun i _ _ =>
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have : sizeOf a[i] < sizeOf a := by simp
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(Not a[i]).to_nnf))
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| .Or a => And (a.mapFinIdx
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(fun i _ _ =>
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have : sizeOf a[i] < sizeOf a := by simp
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(Not a[i]).to_nnf))
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| .Not h => h.to_nnf
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| .Atom x => Not (.Atom x)
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| .TT => .FF
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| .FF => .TT
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| g => g
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theorem test: (TT: PFormula α).Not.to_nnf.is_nnf := by
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simp [is_nnf, to_nnf]
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end PFormula
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