Update lean to v4.6.0-rc1 and start fixing the proofs

3 files changed, 36 insertions, 28 deletions

diff --git a/backends/lean/Base/Diverge/Base.lean b/backends/lean/Base/Diverge/Base.lean
index 9458c926..e40432bd 100644
--- a/backends/lean/Base/Diverge/Base.lean
+++ b/backends/lean/Base/Diverge/Base.lean
@@ -21,7 +21,7 @@ namespace Lemmas
     else
       f ⟨ m, by simp_all [Nat.lt_iff_le_and_ne] ⟩ ∧
       for_all_fin_aux f (m + 1) (by simp_all [Arith.add_one_le_iff_le_ne])
-  termination_by for_all_fin_aux n _ m h => n - m
+  termination_by n - m
   decreasing_by
     simp_wf
     apply Nat.sub_add_lt_sub <;> try simp
@@ -240,8 +240,8 @@ namespace Fix
           simp [fix]
           -- By property of the least upper bound
           revert Hd Hl
-          -- TODO: there is no conversion to select the head of a function!
-          conv => lhs; apply congr_fun; apply congr_fun; apply congr_fun; simp [fix_fuel_P, div?]
+          conv => lhs; rw [fix_fuel_P]
+          simp [div?]
           cases fix_fuel (least (fix_fuel_P f x)) f x <;> simp
         have Hmono := fix_fuel_mono Hmono Hineq x
         simp [result_rel] at Hmono
@@ -255,7 +255,7 @@ namespace Fix
     intros x n Hf
     have Hfmono := fix_fuel_fix_mono Hmono n x
     -- TODO: there is no conversion to select the head of a function!
-    conv => apply congr_fun; simp [fix_fuel_P]
+    rw [fix_fuel_P]
     simp [fix_fuel_P] at Hf
     revert Hf Hfmono
     simp [div?, result_rel, fix]
@@ -268,9 +268,7 @@ namespace Fix
     fix f x = f (fix f) x := by
     have Hl := fix_fuel_P_least Hmono He
     -- TODO: better control of simplification
-    conv at Hl =>
-      apply congr_fun
-      simp [fix_fuel_P]
+    rw [fix_fuel_P] at Hl; simp at Hl
     -- The least upper bound is > 0
     have ⟨ n, Hsucc ⟩ : ∃ n, least (fix_fuel_P f x) = Nat.succ n := by
       revert Hl
@@ -618,12 +616,16 @@ namespace FixI
   @[simp] theorem is_valid_p_same
     (k : ((i:id) → (x:a i) → Result (b i x)) → (i:id) → (x:a i) → Result (b i x)) (x : Result c) :
     is_valid_p k (λ _ => x) := by
-    simp [is_valid_p, k_to_gen, e_to_gen]
+    simp [is_valid_p]
+    unfold k_to_gen e_to_gen
+    simp
 
   @[simp] theorem is_valid_p_rec
      (k : ((i:id) → (x:a i) → Result (b i x)) → (i:id) → (x:a i) → Result (b i x)) (i : id) (x : a i) :
     is_valid_p k (λ k => k i x) := by
-    simp [is_valid_p, k_to_gen, e_to_gen, kk_to_gen, kk_of_gen]
+    simp [is_valid_p]
+    unfold k_to_gen e_to_gen kk_to_gen kk_of_gen
+    simp
 
   theorem is_valid_p_ite
     (k : ((i:id) → (x:a i) → Result (b i x)) → (i:id) → (x:a i) → Result (b i x))
@@ -826,12 +828,16 @@ namespace FixII
   @[simp] theorem is_valid_p_same
     (k : ((i:id) → (t:ty i) → a i t → Result (b i t)) → (i:id) → (t:ty i) → a i t → Result (b i t)) (x : Result c) :
     is_valid_p k (λ _ => x) := by
-    simp [is_valid_p, k_to_gen, e_to_gen]
+    simp [is_valid_p]
+    unfold k_to_gen e_to_gen
+    simp
 
   @[simp] theorem is_valid_p_rec
      (k : ((i:id) → (t:ty i) → a i t → Result (b i t)) → (i:id) → (t:ty i) → a i t → Result (b i t)) (i : id) (t : ty i) (x : a i t) :
     is_valid_p k (λ k => k i t x) := by
-    simp [is_valid_p, k_to_gen, e_to_gen, kk_to_gen, kk_of_gen]
+    simp [is_valid_p]
+    unfold k_to_gen e_to_gen kk_to_gen kk_of_gen
+    simp
 
   theorem is_valid_p_ite
     (k : ((i:id) → (t:ty i) → a i t → Result (b i t)) → (i:id) → (t:ty i) → a i t → Result (b i t))
@@ -1531,10 +1537,11 @@ namespace Ex9
     intro k a x
     simp only [id_body]
     split <;> try simp
-    apply is_valid_p_bind <;> try simp [*]
-    -- We have to show that `map k tl` is valid
-    -- Remark: `map_is_valid` doesn't work here, we need the specialized version
-    apply map_is_valid_simple
+    . apply is_valid_p_same
+    . apply is_valid_p_bind <;> try simp [*]
+      -- We have to show that `map k tl` is valid
+      -- Remark: `map_is_valid` doesn't work here, we need the specialized version
+      apply map_is_valid_simple
 
   def body (k : (i : Fin 1) → (t : ty i) → (x : input_ty i t) → Result (output_ty i t)) (i: Fin 1) :
     (t : ty i) → (x : input_ty i t) → Result (output_ty i t) := get_fun bodies i k
diff --git a/backends/lean/Base/Diverge/Elab.lean b/backends/lean/Base/Diverge/Elab.lean
index 6115b13b..3c2ea877 100644
--- a/backends/lean/Base/Diverge/Elab.lean
+++ b/backends/lean/Base/Diverge/Elab.lean
@@ -383,10 +383,7 @@ def mkFin (n : Nat) : Expr :=
 def mkFinVal (n i : Nat) : MetaM Expr := do
   let n_lit : Expr := .lit (.natVal (n - 1))
   let i_lit : Expr := .lit (.natVal i)
-  -- We could use `trySynthInstance`, but as we know the instance that we are
-  -- going to use, we can save the lookup
-  let ofNat ← mkAppOptM ``Fin.instOfNatFinHAddNatInstHAddInstAddNatOfNat #[n_lit, i_lit]
-  mkAppOptM ``OfNat.ofNat #[none, none, ofNat]
+  mkAppOptM ``Fin.ofNat #[.some n_lit, .some i_lit]
 
 /- Information about the type of a function in a declaration group.
 
@@ -654,8 +651,8 @@ partial def proveExprIsValid (k_var kk_var : Expr) (e : Expr) : MetaM Expr := do
   -- Normalize to eliminate the lambdas - TODO: this is slightly dangerous.
   let e ← do
     if e.isLet ∧ normalize_let_bindings then do
-      let updt_config config :=
-        { config with transparency := .reducible, zetaNonDep := false }
+      let updt_config (config : Lean.Meta.Config) :=
+        { config with transparency := .reducible }
       let e ← withConfig updt_config (whnf e)
       trace[Diverge.def.valid] "e (after normalization): {e}"
       pure e
@@ -929,7 +926,7 @@ partial def proveAppIsValidApplyThms (k_var kk_var : Expr) (e : Expr)
           -- We sometimes need to reduce the term - TODO: this is really dangerous
           let e ← do
             let updt_config config :=
-              { config with transparency := .reducible, zetaNonDep := false }
+              { config with transparency := .reducible }
             withConfig updt_config (whnf e)
           trace[Diverge.def.valid] "e (after normalization): {e}"
           let e_valid ← proveExprIsValid k_var kk_var e
diff --git a/backends/lean/Base/Diverge/ElabBase.lean b/backends/lean/Base/Diverge/ElabBase.lean
index 0d33e9d2..08ef96f7 100644
--- a/backends/lean/Base/Diverge/ElabBase.lean
+++ b/backends/lean/Base/Diverge/ElabBase.lean
@@ -27,12 +27,12 @@ initialize registerTraceClass `Diverge.attr
 -- divspec attribute
 structure DivSpecAttr where
   attr : AttributeImpl
-  ext  : DiscrTreeExtension Name true
+  ext  : DiscrTreeExtension Name
   deriving Inhabited
 
 /- The persistent map from expressions to divspec theorems. -/
 initialize divspecAttr : DivSpecAttr ← do
-  let ext ← mkDiscrTreeExtention `divspecMap true
+  let ext ← mkDiscrTreeExtention `divspecMap
   let attrImpl : AttributeImpl := {
     name := `divspec
     descr := "Marks theorems to use with the `divergent` encoding"
@@ -44,7 +44,7 @@ initialize divspecAttr : DivSpecAttr ← do
       -- Lookup the theorem
       let env ← getEnv
       let thDecl := env.constants.find! thName
-      let fKey : Array (DiscrTree.Key true) ← MetaM.run' (do
+      let fKey : Array (DiscrTree.Key) ← MetaM.run' (do
         /- The theorem should have the shape:
            `∀ ..., is_valid_p k (λ k => ...)`
 
@@ -59,7 +59,9 @@ initialize divspecAttr : DivSpecAttr ← do
         let (_, _, fExpr) ← lambdaMetaTelescope fExpr.consumeMData
         trace[Diverge] "Registering divspec theorem for {fExpr}"
         -- Convert the function expression to a discrimination tree key
-        DiscrTree.mkPath fExpr)
+        -- We use the default configuration
+        let config : WhnfCoreConfig := {}
+        DiscrTree.mkPath fExpr config)
       let env := ext.addEntry env (fKey, thName)
       setEnv env
       trace[Diverge] "Saved the environment"
@@ -69,9 +71,11 @@ initialize divspecAttr : DivSpecAttr ← do
   pure { attr := attrImpl, ext := ext }
 
 def DivSpecAttr.find? (s : DivSpecAttr) (e : Expr) : MetaM (Array Name) := do
-  (s.ext.getState (← getEnv)).getMatch e
+  -- We use the default configuration
+  let config : WhnfCoreConfig := {}
+  (s.ext.getState (← getEnv)).getMatch e config
 
-def DivSpecAttr.getState (s : DivSpecAttr) : MetaM (DiscrTree Name true) := do
+def DivSpecAttr.getState (s : DivSpecAttr) : MetaM (DiscrTree Name) := do
   pure (s.ext.getState (← getEnv))
 
 def showStoredDivSpec : MetaM Unit := do