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@ -0,0 +1,83 @@
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import Mathlib.Lean.Expr.Basic
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import Lean.Elab.Tactic.Basic
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import Mathlib.Init.Data.Nat.Notation
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open Lean.Meta Lean.Elab.Tactic Lean.Parser.Tactic
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/-!
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# Modified `induction` tactic
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Modify `induction` tactic to use the cases `0` and `n + 1` (isnstead of `zero` and `succ n`)
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and support the lean3-style `with` keyword.
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This is mainly copied and modified from the mathlib-tactic `induction'`.
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-/
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/-- Custom induction principle that uses `0` and `n + 1` instead
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of `Nat.zero` and `Nat.succ n`. -/
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def CustomTactic.rec' {P : ℕ → Prop} (zero : P 0)
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(succ : (n : ℕ) → (n_ih : P n) → P (n + 1)) (t : ℕ) : P t := by
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induction t with
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| zero => assumption
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| succ n =>
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apply succ
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assumption
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namespace Lean.Parser.Tactic
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open Meta Elab Elab.Tactic
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open private getAltNumFields in evalCases ElimApp.evalAlts.go in
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def _root_.CustomTactic.ElimApp.evalNames (elimInfo : ElimInfo) (alts : Array ElimApp.Alt) (withArg : Syntax)
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(numEqs := 0) (numGeneralized := 0) (toClear : Array FVarId := #[]) :
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Lean.Elab.Term.TermElabM (Array MVarId) := do
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let mut names : List Syntax := withArg[1].getArgs |>.toList
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let mut subgoals := #[]
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for { name := altName, mvarId := g, .. } in alts do
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let numFields ← getAltNumFields elimInfo altName
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let (altVarNames, names') := names.splitAtD numFields (Unhygienic.run `(_))
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names := names'
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let (fvars, g) ← g.introN numFields <| altVarNames.map (getNameOfIdent' ·[0])
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let some (g, subst) ← Cases.unifyEqs? numEqs g {} | pure ()
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let (_, g) ← g.introNP numGeneralized
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let g ← liftM $ toClear.foldlM (·.tryClear) g
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for fvar in fvars, stx in altVarNames do
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g.withContext <| (subst.apply <| .fvar fvar).addLocalVarInfoForBinderIdent ⟨stx⟩
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subgoals := subgoals.push g
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pure subgoals
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open private getElimNameInfo generalizeTargets generalizeVars in evalInduction in
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/--
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Modified `induction` tactic for this game.
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Usage: `induction n with d hd`.
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For this game, `induction n` uses the cases `0` and `n + 1` instead of `Nat.zero` and
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`Nat.succ n`. These are defEq, but it's currently annoying that `ring` does not like the
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latter forms.
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*(The actual `induction` tactic has a more complex `with`-argument that works differently)*
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-/
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elab (name := _root_.MyNat.induction) "induction " tgts:(casesTarget,+)
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withArg:((" with " (colGt binderIdent)+)?)
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: tactic => do
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let targets ← elabCasesTargets tgts.1.getSepArgs
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let g :: gs ← getUnsolvedGoals | throwNoGoalsToBeSolved
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g.withContext do
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let elimInfo ← getElimInfo `CustomTactic.rec'
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let targets ← addImplicitTargets elimInfo targets
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evalInduction.checkTargets targets
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let targetFVarIds := targets.map (·.fvarId!)
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g.withContext do
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let forbidden ← mkGeneralizationForbiddenSet targets
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let mut s ← getFVarSetToGeneralize targets forbidden
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let (fvarIds, g) ← g.revert (← sortFVarIds s.toArray)
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let result ← withRef tgts <| ElimApp.mkElimApp elimInfo targets (← g.getTag)
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let elimArgs := result.elimApp.getAppArgs
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ElimApp.setMotiveArg g elimArgs[elimInfo.motivePos]!.mvarId! targetFVarIds
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g.assign result.elimApp
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let subgoals ← CustomTactic.ElimApp.evalNames elimInfo result.alts withArg
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(numGeneralized := fvarIds.size) (toClear := targetFVarIds)
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setGoals <| (subgoals ++ result.others).toList ++ gs
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end Lean.Parser.Tactic
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Jon Eugster
3 years ago