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.
122 lines
3.6 KiB
Text
122 lines
3.6 KiB
Text
namespace MutualCoinduction
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mutual
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def f : Prop :=
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g
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coinductive_fixpoint
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def g : Prop :=
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f
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coinductive_fixpoint
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end
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/--
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info: MutualCoinduction.f.coinduct (pred_1 pred_2 : Prop) (hyp_1 : pred_1 → pred_2) (hyp_2 : pred_2 → pred_1) : pred_1 → f
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-/
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#guard_msgs in
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#check MutualCoinduction.f.coinduct
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/--
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info: MutualCoinduction.f.mutual_induct (pred_1 pred_2 : Prop) (hyp_1 : pred_1 → pred_2) (hyp_2 : pred_2 → pred_1) :
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(pred_1 → f) ∧ (pred_2 → g)
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-/
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#guard_msgs in
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#check MutualCoinduction.f.mutual_induct
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/--
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info: MutualCoinduction.g.coinduct (pred_1 pred_2 : Prop) (hyp_1 : pred_1 → pred_2) (hyp_2 : pred_2 → pred_1) : pred_2 → g
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-/
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#guard_msgs in
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#check MutualCoinduction.g.coinduct
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end MutualCoinduction
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namespace MutualInduction
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mutual
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def f : Prop :=
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g
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inductive_fixpoint
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def g : Prop :=
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f
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inductive_fixpoint
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end
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/--
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info: MutualInduction.f.induct (pred_1 pred_2 : Prop) (hyp_1 : pred_2 → pred_1) (hyp_2 : pred_1 → pred_2) : f → pred_1
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-/
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#guard_msgs in
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#check MutualInduction.f.induct
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/--
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info: MutualInduction.f.mutual_induct (pred_1 pred_2 : Prop) (hyp_1 : pred_2 → pred_1) (hyp_2 : pred_1 → pred_2) :
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(f → pred_1) ∧ (g → pred_2)
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-/
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#guard_msgs in
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#check MutualInduction.f.mutual_induct
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/--
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info: MutualInduction.g.induct (pred_1 pred_2 : Prop) (hyp_1 : pred_2 → pred_1) (hyp_2 : pred_1 → pred_2) : g → pred_2
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-/
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#guard_msgs in
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#check MutualInduction.g.induct
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end MutualInduction
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namespace MixedInductionCoinduction
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mutual
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def f : Prop :=
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g → f
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inductive_fixpoint
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def g : Prop :=
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f → g
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coinductive_fixpoint
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end
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/--
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info: MixedInductionCoinduction.f.induct (pred_1 pred_2 : Prop) (hyp_1 : (pred_2 → pred_1) → pred_1)
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(hyp_2 : pred_2 → pred_1 → pred_2) : f → pred_1
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-/
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#guard_msgs in
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#check f.induct
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/--
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info: MixedInductionCoinduction.f.mutual_induct (pred_1 pred_2 : Prop) (hyp_1 : (pred_2 → pred_1) → pred_1)
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(hyp_2 : pred_2 → pred_1 → pred_2) : (f → pred_1) ∧ (pred_2 → g)
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-/
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#guard_msgs in
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#check f.mutual_induct
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/--
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info: MixedInductionCoinduction.g.coinduct (pred_1 pred_2 : Prop) (hyp_1 : (pred_2 → pred_1) → pred_1)
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(hyp_2 : pred_2 → pred_1 → pred_2) : pred_2 → g
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-/
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#guard_msgs in
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#check g.coinduct
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end MixedInductionCoinduction
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namespace DifferentPredicateTypes
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mutual
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def f (n : Nat) : Prop :=
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g (n+1) (n+2)
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coinductive_fixpoint
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def g (n m : Nat): Prop :=
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f (n + 2) ∨ g (m + 1) m
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coinductive_fixpoint
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end
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/--
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info: DifferentPredicateTypes.f.coinduct (pred_1 : Nat → Prop) (pred_2 : Nat → Nat → Prop)
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(hyp_1 : ∀ (n : Nat), pred_1 n → pred_2 (n + 1) (n + 2))
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(hyp_2 : ∀ (n m : Nat), pred_2 n m → pred_1 (n + 2) ∨ pred_2 (m + 1) m) (n : Nat) : pred_1 n → f n
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-/
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#guard_msgs in
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#check f.coinduct
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/--
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info: DifferentPredicateTypes.f.mutual_induct (pred_1 : Nat → Prop) (pred_2 : Nat → Nat → Prop)
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(hyp_1 : ∀ (n : Nat), pred_1 n → pred_2 (n + 1) (n + 2))
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(hyp_2 : ∀ (n m : Nat), pred_2 n m → pred_1 (n + 2) ∨ pred_2 (m + 1) m) :
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(∀ (n : Nat), pred_1 n → f n) ∧ ∀ (n m : Nat), pred_2 n m → g n m
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-/
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#guard_msgs in
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#check f.mutual_induct
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/--
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info: DifferentPredicateTypes.g.coinduct (pred_1 : Nat → Prop) (pred_2 : Nat → Nat → Prop)
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(hyp_1 : ∀ (n : Nat), pred_1 n → pred_2 (n + 1) (n + 2))
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(hyp_2 : ∀ (n m : Nat), pred_2 n m → pred_1 (n + 2) ∨ pred_2 (m + 1) m) (n m : Nat) : pred_2 n m → g n m
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-/
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#guard_msgs in
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#check g.coinduct
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end DifferentPredicateTypes
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