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.
71 lines
3 KiB
Text
71 lines
3 KiB
Text
inductive Term where
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| const : String → Term
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| app : String → List Term → Term
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namespace Term
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mutual
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def numConsts : Term → Nat
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| const _ => 1
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| app _ cs => numConstsLst cs
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def numConstsLst : List Term → Nat
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| [] => 0
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| c :: cs => numConsts c + numConstsLst cs
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end
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mutual
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-- Since #4733 this function can be compiled using structural recursion,
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-- but then the construction of the functional induction principle falls over
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-- TODO: Fix funind, and then omit the `termination_by` here (or test both variants)
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def replaceConst (a b : String) : Term → Term
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| const c => if a == c then const b else const c
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| app f cs => app f (replaceConstLst a b cs)
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termination_by t => sizeOf t
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def replaceConstLst (a b : String) : List Term → List Term
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| [] => []
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| c :: cs => replaceConst a b c :: replaceConstLst a b cs
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termination_by ts => sizeOf ts
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end
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/--
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info: Term.replaceConst.induct (a : String) (motive1 : Term → Prop) (motive2 : List Term → Prop)
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(case1 : ∀ (a_1 : String), (a == a_1) = true → motive1 (const a_1))
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(case2 : ∀ (a_1 : String), ¬(a == a_1) = true → motive1 (const a_1))
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(case3 : ∀ (a : String) (cs : List Term), motive2 cs → motive1 (app a cs)) (case4 : motive2 [])
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(case5 : ∀ (c : Term) (cs : List Term), motive1 c → motive2 cs → motive2 (c :: cs)) (a✝ : Term) : motive1 a✝
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-/
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#guard_msgs in
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#check replaceConst.induct
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theorem numConsts_replaceConst (a b : String) (e : Term) : numConsts (replaceConst a b e) = numConsts e := by
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apply replaceConst.induct (a := a)
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(motive1 := fun e => numConsts (replaceConst a b e) = numConsts e)
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(motive2 := fun es => numConstsLst (replaceConstLst a b es) = numConstsLst es)
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case case1 => intro c h; guard_hyp h :ₛ (a == c) = true; simp [replaceConst, numConsts, *]
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case case2 => intro c h; guard_hyp h :ₛ ¬(a == c) = true; simp [replaceConst, numConsts, *]
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case case3 =>
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intro f cs ih
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guard_hyp ih :ₛnumConstsLst (replaceConstLst a b cs) = numConstsLst cs
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simp [replaceConst, numConsts, *]
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case case4 => simp [replaceConstLst, numConstsLst, *]
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case case5 =>
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intro c cs ih₁ ih₂
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guard_hyp ih₁ :ₛ numConsts (replaceConst a b c) = numConsts c
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guard_hyp ih₂ :ₛ numConstsLst (replaceConstLst a b cs) = numConstsLst cs
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simp [replaceConstLst, numConstsLst, *]
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theorem numConsts_replaceConst' (a b : String) (e : Term) : numConsts (replaceConst a b e) = numConsts e := by
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apply replaceConst.induct (a := a)
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(motive1 := fun e => numConsts (replaceConst a b e) = numConsts e)
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(motive2 := fun es => numConstsLst (replaceConstLst a b es) = numConstsLst es)
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<;> intros <;> simp [replaceConst, numConsts, replaceConstLst, numConstsLst, *]
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theorem numConsts_replaceConst'' (a b : String) (e : Term) : numConsts (replaceConst a b e) = numConsts e := by
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induction e using replaceConst.induct (a := a)
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(motive2 := fun es => numConstsLst (replaceConstLst a b es) = numConstsLst es) <;>
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simp [replaceConst, numConsts, replaceConstLst, numConstsLst, *]
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end Term
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