custom cases tactic

Game/Tactic/Cases.Lean

@@ -0,0 +1,68 @@
+import Game.MyNat.Definition
+import Mathlib.Tactic.Cases
+
+/-!
+# Modified `cases` tactic
+
+Modify `cases` 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 `cases'`.
+-/
+
+namespace MyNat
+
+/-- Modified `casesOn` principal to use `0` instead of `MyNat.zero`. -/
+def casesOn' {P : ℕ → Sort u} (t : ℕ) (zero : P 0)
+    (succ : (a : ℕ) → P (MyNat.succ a)) : P t := by
+  cases t with
+  | zero => assumption
+  | succ n =>
+    apply succ
+
+open Lean Meta Elab Parser Tactic Mathlib.Tactic
+open private getElimNameInfo from Lean.Elab.Tactic.Induction
+
+/-- Modified `cases` tactic for this game.
+
+Usage: `cases n with d` if `n : ℕ`; `cases h with h1 h2` if `h : P ∨ Q`; `cases h with c hc` if `h : a ≤ b`.
+
+*(This implementation mimics the `cases'` from mathlib. The actual `cases` tactic in mathlib has a more complex syntax)*
+-/
+elab (name := cases) "cases " tgts:(Parser.Tactic.casesTarget,+) usingArg:((" using " ident)?)
+    withArg:((" with" (ppSpace colGt binderIdent)+)?) : tactic => do
+  let targets ← elabCasesTargets tgts.1.getSepArgs
+  let g :: gs ← getUnsolvedGoals | throwNoGoalsToBeSolved
+  g.withContext do
+    let elimInfo ← getElimNameInfo usingArg targets (induction := false)
+
+    -- Edit: If `elimInfo.name` is `MyNat.casesOn` we want to use `MyNat.rec'` instead.
+    -- TODO: This seems extremely hacky. Especially that we need to get the `elimInfo` twice.
+    -- Please improve this.
+    let elimInfo ← match elimInfo.name with
+    | `MyNat.casesOn =>
+      let modifiedUsingArgs : TSyntax Name.anonymous := ⟨
+        match usingArg.raw with
+        | .node info kind #[] =>
+          -- TODO: How do you construct syntax in a semi-userfriendly way??
+          .node info kind #[.atom info "using", .ident info "MyNat.rec'".toSubstring `MyNat.casesOn' []]
+        | other => other ⟩
+      let newElimInfo ← getElimNameInfo modifiedUsingArgs targets (induction := false)
+      pure newElimInfo
+    | _ => pure elimInfo
+
+    let targets ← addImplicitTargets elimInfo targets
+    let result ← withRef tgts <| ElimApp.mkElimApp elimInfo targets (← g.getTag)
+    let elimArgs := result.elimApp.getAppArgs
+    let targets ← elimInfo.targetsPos.mapM (instantiateMVars elimArgs[·]!)
+    let motive := elimArgs[elimInfo.motivePos]!
+    let g ← generalizeTargetsEq g (← inferType motive) targets
+    let (targetsNew, g) ← g.introN targets.size
+    g.withContext do
+      ElimApp.setMotiveArg g motive.mvarId! targetsNew
+      g.assign result.elimApp
+      let subgoals ← ElimApp.evalNames elimInfo result.alts withArg
+         (numEqs := targets.size) (toClear := targetsNew)
+      setGoals <| subgoals.toList ++ gs
+
+end MyNat

Game/Tactic/Induction.lean

@@ -5,7 +5,6 @@ import Std.Data.List.Basic
 import Game.MyNat.Definition
 import Mathlib.Lean.Expr.Basic
 
-
 namespace MyNat
 
 /-!
@@ -79,34 +78,3 @@ elab (name := _root_.MyNat.induction) "induction " tgts:(casesTarget,+)
       let subgoals ← ElimApp.evalNames.MyNat elimInfo result.alts withArg
         (numGeneralized := fvarIds.size) (toClear := targetFVarIds)
       setGoals <| (subgoals ++ result.others).toList ++ gs
-
-open private getElimNameInfo generalizeTargets generalizeVars from Lean.Elab.Tactic.Induction
-
-/--
-Modified `cases` tactic for this game.
-
-Usage: `cases n with d` if `n : ℕ`; `cases h with h1 h2` if `h : P ∨ Q`; `cases h with c hc`
-if `h : a ≤ b`.
-
-*(This mimics Lean 3 `cases`. The Lean 4 `cases` tactic has a more complex syntax)*
--/
-elab (name := _root_.MyNat.cases) "cases " tgts:(Parser.Tactic.casesTarget,+) usingArg:((" using " ident)?)
-  withArg:((" with" (ppSpace colGt binderIdent)+)?) : tactic => do
-  let targets ← elabCasesTargets tgts.1.getSepArgs
-  let g :: gs ← getUnsolvedGoals | throwNoGoalsToBeSolved
-  g.withContext do
-    let elimInfo ← getElimNameInfo usingArg targets (induction := false)
-    -- I think I might want to say something like "if elimInfo = Mynat.rec then change it to MyNat.rec'"
-    let targets ← addImplicitTargets elimInfo targets
-    let result ← withRef tgts <| ElimApp.mkElimApp elimInfo targets (← g.getTag)
-    let elimArgs := result.elimApp.getAppArgs
-    let targets ← elimInfo.targetsPos.mapM (instantiateMVars elimArgs[·]!)
-    let motive := elimArgs[elimInfo.motivePos]!
-    let g ← generalizeTargetsEq g (← inferType motive) targets
-    let (targetsNew, g) ← g.introN targets.size
-    g.withContext do
-      ElimApp.setMotiveArg g motive.mvarId! targetsNew
-      g.assign result.elimApp
-      let subgoals ← ElimApp.evalNames.MyNat elimInfo result.alts withArg
-         (numEqs := targets.size) (toClear := targetsNew)
-      setGoals <| subgoals.toList ++ gs