And this one

so that it can be used in pure code and that the error message can be
adjusted

src/Lean/Elab/PreDefinition/WF/Fix.lean

@@ -178,7 +178,8 @@ def groupGoalsByFunction (argsPacker : ArgsPacker) (numFuncs : Nat) (goals : Arr
     let type ← goal.getType
     let (.mdata _ (.app _ param)) := type
         | throwError "MVar does not look like a recursive call:{indentExpr type}"
-    let (funidx, _) ← argsPacker.unpack param
+    let some (funidx, _) := argsPacker.unpack param
+        | throwError "Cannot unpack param, unexpected expression:{indentExpr param}"
     r := r.modify funidx (·.push goal)
   return r
 

src/Lean/Elab/PreDefinition/WF/GuessLex.lean

@@ -352,8 +352,10 @@ def collectRecCalls (unaryPreDef : PreDefinition) (fixedPrefixSize : Nat)
         throwError "Insufficient arguments in recursive call"
       let arg := args[fixedPrefixSize]!
       trace[Elab.definition.wf] "collectRecCalls: {unaryPreDef.declName} ({param}) → {unaryPreDef.declName} ({arg})"
-      let (caller, params) ← argsPacker.unpack param
-      let (callee, args) ← argsPacker.unpack arg
+      let some (caller, params) := argsPacker.unpack param
+        | throwError "Cannot unpack param, unexpected expression:{indentExpr param}"
+      let some (callee, args) := argsPacker.unpack arg
+        | throwError "Cannot unpack arg, unexpected expression:{indentExpr arg}"
       RecCallWithContext.create (← getRef) caller (ys ++ params) callee (ys ++ args)
 
 /-- Is the expression a `<`-like comparison of `Nat` expressions -/
@@ -771,6 +773,8 @@ Main entry point of this module:
 
 Try to find a lexicographic ordering of the arguments for which the recursive definition
 terminates. See the module doc string for a high-level overview.
+
+The `preDefs` are used to determine arity and types of arguments; the bodies are ignored.
 -/
 def guessLex (preDefs : Array PreDefinition) (unaryPreDef : PreDefinition)
     (fixedPrefixSize : Nat) (argsPacker : ArgsPacker) :

src/Lean/Meta/ArgsPacker.lean

@@ -87,7 +87,7 @@ Unpacks a unary packed argument created with `Unary.pack`.
 
 Throws an error if the expression is not of that form.
 -/
-def unpack (arity : Nat) (e : Expr) : MetaM (Array Expr) := do
+def unpack (arity : Nat) (e : Expr) : Option (Array Expr) := do
   let mut e := e
   let mut args := #[]
   while args.size + 1 < arity do
@@ -95,11 +95,10 @@ def unpack (arity : Nat) (e : Expr) : MetaM (Array Expr) := do
       args := args.push (e.getArg! 2)
       e := e.getArg! 3
     else
-      throwError "Unexpected expression while unpacking n-ary argument"
+      none
   args := args.push e
   return args
 
-
 /--
   Given a (dependent) tuple `t` (using `PSigma`) of the given arity.
   Return an array containing its "elements".
@@ -258,7 +257,7 @@ argument and function index.
 
 Throws an error if the expression is not of that form.
 -/
-def unpack (numFuncs : Nat) (expr : Expr) : MetaM (Nat × Expr) := do
+def unpack (numFuncs : Nat) (expr : Expr) : Option (Nat × Expr) := do
   let mut funidx := 0
   let mut e := expr
   while funidx + 1 < numFuncs do
@@ -269,7 +268,7 @@ def unpack (numFuncs : Nat) (expr : Expr) : MetaM (Nat × Expr) := do
       e := e.getArg! 2
       break
     else
-      throwError "Unexpected expression while unpacking mutual argument:{indentExpr expr}"
+      none
   return (funidx, e)
 
 
@@ -377,14 +376,17 @@ and `(z : C) → R₂[z]`, returns an expression of type
 (x : A ⊕' C) → (match x with | .inl x => R₁[x] | .inr R₂[z])
 ```
 -/
-def uncurry (es : Array Expr) : MetaM Expr := do
-  let types ← es.mapM inferType
-  let resultType ← uncurryType types
+def uncurryWithType (resultType : Expr) (es : Array Expr) : MetaM Expr := do
   forallBoundedTelescope resultType (some 1) fun xs codomain => do
     let #[x] := xs | unreachable!
     let value ← casesOn x codomain es.toList
     mkLambdaFVars #[x] value
 
+def uncurry (es : Array Expr) : MetaM Expr := do
+  let types ← es.mapM inferType
+  let resultType ← uncurryType types
+  uncurryWithType resultType es
+
 /--
 Given unary expressions `e₁`, `e₂` with types `(x : A) → R`
 and `(z : C) → R`, returns an expression of type
@@ -414,7 +416,7 @@ def curryType (n : Nat) (type : Expr) : MetaM (Array Expr) := do
 
 end Mutual
 
--- Now for the main definitions in this moduleo
+-- Now for the main definitions in this module
 
 /-- The number of functions being packed -/
 def numFuncs (argsPacker : ArgsPacker) : Nat := argsPacker.varNamess.size
@@ -422,6 +424,10 @@ def numFuncs (argsPacker : ArgsPacker) : Nat := argsPacker.varNamess.size
 /-- The arities of the functions being packed -/
 def arities (argsPacker : ArgsPacker) : Array Nat := argsPacker.varNamess.map (·.size)
 
+def onlyOneUnary (argsPacker : ArgsPacker) :=
+  argsPacker.varNamess.size = 1 &&
+  argsPacker.varNamess[0]!.size = 1
+
 def pack (argsPacker : ArgsPacker) (domain : Expr) (fidx : Nat) (args : Array Expr)
     : MetaM Expr := do
   assert! fidx < argsPacker.numFuncs
@@ -436,14 +442,13 @@ return the function index that is called and the arguments individually.
 
 We expect precisely the expressions produced by `pack`, with manifest
 `PSum.inr`, `PSum.inl` and `PSigma.mk` constructors, and thus take them apart
-rather than using projectinos.
+rather than using projections.
 -/
-def unpack (argsPacker : ArgsPacker) (e : Expr) : MetaM (Nat × Array Expr) := do
+def unpack (argsPacker : ArgsPacker) (e : Expr) : Option (Nat × Array Expr) := do
   let (funidx, e) ← Mutual.unpack argsPacker.numFuncs e
   let args ← Unary.unpack argsPacker.varNamess[funidx]!.size e
   return (funidx, args)
 
-
 /--
 Given types `(x : A) → (y : B[x]) → R₁[x,y]` and `(z : C) → R₂[z]`, returns the type uncurried type
 ```
@@ -465,6 +470,10 @@ def uncurry (argsPacker : ArgsPacker) (es : Array Expr) : MetaM Expr := do
   let unary ← (Array.zipWith argsPacker.varNamess es Unary.uncurry).mapM id
   Mutual.uncurry unary
 
+def uncurryWithType (argsPacker : ArgsPacker) (resultType : Expr) (es : Array Expr) : MetaM Expr := do
+  let unary ← (Array.zipWith argsPacker.varNamess es Unary.uncurry).mapM id
+  Mutual.uncurryWithType resultType unary
+
 /--
 Given expressions `e₁`, `e₂` with types `(x : A) → (y : B[x]) → R`
 and `(z : C) → R`, returns an expression of type

src/Lean/Meta/Tactic/FunInd.lean

@@ -810,7 +810,8 @@ def cleanPackedArgs (eqnInfo : WF.EqnInfo) (value : Expr) : MetaM Expr := do
       let args := e.getAppArgs
       if eqnInfo.fixedPrefixSize + 1 ≤ args.size then
         let packedArg := args.back!
-          let (i, unpackedArgs) ← eqnInfo.argsPacker.unpack packedArg
+          let some (i, unpackedArgs) := eqnInfo.argsPacker.unpack packedArg
+            | throwError "Unexpected packedArg:{indentExpr packedArg}"
           let e' := .const eqnInfo.declNames[i]! e.getAppFn.constLevels!
           let e' := mkAppN e' args.pop
           let e' := mkAppN e' unpackedArgs