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