f771dea78b
This PR fixes an issue where the "eta feature" in the app elaborator, which is invoked when positional arguments are skipped due to named arguments, results in variables that can be captured by those named arguments. Now the temporary local variables that implement this feature get fresh names. The names used for the closed lambda expression still use the original parameter names. Closes #6373
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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