81 lines
3.0 KiB
Lean4
81 lines
3.0 KiB
Lean4
import Lean.Elab.Tactic.Basic
|
||
import Lean.Elab.Tactic.Induction
|
||
import Std.Tactic.OpenPrivate
|
||
import Std.Data.List.Basic
|
||
import Game.MyNat.Definition
|
||
import Mathlib.Lean.Expr.Basic
|
||
|
||
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
|