Merge branch 'son/update-lean' into has-int-pred

3 files changed, 45 insertions, 35 deletions

diff --git a/backends/lean/Base/Arith/Base.lean b/backends/lean/Base/Arith/Base.lean
index 8ada4171..fb6b12e5 100644
--- a/backends/lean/Base/Arith/Base.lean
+++ b/backends/lean/Base/Arith/Base.lean
@@ -1,6 +1,5 @@
 import Lean
-import Std.Data.Int.Lemmas
-import Mathlib.Tactic.Linarith
+import Mathlib.Tactic.Linarith -- Introduces a lot of useful lemmas
 
 namespace Arith
 
@@ -21,12 +20,12 @@ theorem ne_is_lt_or_gt {x y : Int} (hne : x ≠ y) : x < y ∨ x > y := by
   have hne : x - y ≠ 0 := by
     simp
     intro h
-    have: x = y := by linarith
+    have: x = y := by omega
     simp_all
   have h := ne_zero_is_lt_or_gt hne
   match h with
-  | .inl _ => left; linarith
-  | .inr _ => right; linarith
+  | .inl _ => left; omega
+  | .inr _ => right; omega
 
 -- TODO: move?
 theorem add_one_le_iff_le_ne (n m : Nat) (h1 : m ≤ n) (h2 : m ≠ n) : m + 1 ≤ n := by
@@ -66,7 +65,7 @@ theorem to_int_to_nat_lt (x y : ℤ) (h0 : 0 ≤ x) (h1 : x < y) :
 theorem to_int_sub_to_nat_lt (x y : ℤ) (x' : ℕ)
   (h0 : ↑x' ≤ x) (h1 : x - ↑x' < y) :
   ↑(x.toNat - x') < y := by
-  have : 0 ≤ x := by linarith
+  have : 0 ≤ x := by omega
   simp [Int.toNat_sub_of_le, *]
 
 end Arith
diff --git a/backends/lean/Base/Arith/Int.lean b/backends/lean/Base/Arith/Int.lean
index a1cb9da3..ab6dd4ab 100644
--- a/backends/lean/Base/Arith/Int.lean
+++ b/backends/lean/Base/Arith/Int.lean
@@ -27,7 +27,7 @@ class HasIntPred {a: Sort u} (x: a) where
   prop : concl
 
 /- Proposition with implications: if we find P we can introduce Q in the context -/
-class PropHasImp (x : Prop) where
+class PropHasImp (x : Sort u) where
   concl : Prop
   prop : x → concl
 
@@ -199,7 +199,7 @@ def introInstances (declToUnfold : Name) (lookup : Expr → MetaM (Option Expr))
     -- Add a declaration
     let nval ← Utils.addDeclTac name e type (asLet := false)
     -- Simplify to unfold the declaration to unfold (i.e., the projector)
-    Utils.simpAt true [declToUnfold] [] [] (Location.targets #[mkIdent name] false)
+    Utils.simpAt true {} #[] [declToUnfold] [] [] (Location.targets #[mkIdent name] false)
     -- Return the new value
     pure nval
 
@@ -242,7 +242,7 @@ def intTacPreprocess (extraPreprocess :  Tactic.TacticM Unit) : Tactic.TacticM U
   extraPreprocess
   -- Reduce all the terms in the goal - note that the extra preprocessing step
   -- might have proven the goal, hence the `Tactic.allGoals`
-  Tactic.allGoals do tryTac (dsimpAt false [] [] [] Tactic.Location.wildcard)
+  Tactic.allGoals do tryTac (dsimpAt false {} #[] [] [] [] Tactic.Location.wildcard)
 
 elab "int_tac_preprocess" : tactic =>
   intTacPreprocess (do pure ())
@@ -259,10 +259,10 @@ def intTac (tacName : String) (splitGoalConjs : Bool) (extraPreprocess :  Tactic
   -- the goal. I think before leads to a smaller proof term?
   Tactic.allGoals (intTacPreprocess extraPreprocess)
   -- More preprocessing
-  Tactic.allGoals (Utils.tryTac (Utils.simpAt true [] [``nat_zero_eq_int_zero] [] .wildcard))
+  Tactic.allGoals (Utils.tryTac (Utils.simpAt true {} #[] [] [``nat_zero_eq_int_zero] [] .wildcard))
   -- Split the conjunctions in the goal
   if splitGoalConjs then Tactic.allGoals (Utils.repeatTac Utils.splitConjTarget)
-  -- Call linarith
+  -- Call omega
   Tactic.allGoals do
     try do Tactic.Omega.omegaTactic {}
     catch _ =>
diff --git a/backends/lean/Base/Arith/Scalar.lean b/backends/lean/Base/Arith/Scalar.lean
index 86b2e216..ecc5acaf 100644
--- a/backends/lean/Base/Arith/Scalar.lean
+++ b/backends/lean/Base/Arith/Scalar.lean
@@ -8,30 +8,31 @@ open Lean Lean.Elab Lean.Meta
 open Primitives
 
 def scalarTacExtraPreprocess : Tactic.TacticM Unit := do
-   Tactic.withMainContext do
-   -- Inroduce the bounds for the isize/usize types
-   let add (e : Expr) : Tactic.TacticM Unit := do
-     let ty ← inferType e
-     let _ ← Utils.addDeclTac (← Utils.mkFreshAnonPropUserName) e ty (asLet := false)
-   add (← mkAppM ``Scalar.cMin_bound #[.const ``ScalarTy.Isize []])
-   add (← mkAppM ``Scalar.cMax_bound #[.const ``ScalarTy.Usize []])
-   add (← mkAppM ``Scalar.cMax_bound #[.const ``ScalarTy.Isize []])
-   -- Reveal the concrete bounds, simplify calls to [ofInt]
-   Utils.simpAt true
-                -- Unfoldings
-                [``Scalar.min, ``Scalar.max, ``Scalar.cMin, ``Scalar.cMax,
-                 ``I8.min, ``I16.min, ``I32.min, ``I64.min, ``I128.min,
-                 ``I8.max, ``I16.max, ``I32.max, ``I64.max, ``I128.max,
-                 ``U8.min, ``U16.min, ``U32.min, ``U64.min, ``U128.min,
-                 ``U8.max, ``U16.max, ``U32.max, ``U64.max, ``U128.max,
-                 ``Usize.min
-                 ]
-                 -- Simp lemmas
-                 [``Scalar.ofInt_val_eq, ``Scalar.neq_to_neq_val,
-                  ``Scalar.lt_equiv, ``Scalar.le_equiv, ``Scalar.eq_equiv]
-                 -- Hypotheses
-                 [] .wildcard
-   
+  Tactic.withMainContext do
+  -- Inroduce the bounds for the isize/usize types
+  let add (e : Expr) : Tactic.TacticM Unit := do
+    let ty ← inferType e
+    let _ ← Utils.addDeclTac (← Utils.mkFreshAnonPropUserName) e ty (asLet := false)
+  add (← mkAppM ``Scalar.cMin_bound #[.const ``ScalarTy.Isize []])
+  add (← mkAppM ``Scalar.cMax_bound #[.const ``ScalarTy.Usize []])
+  add (← mkAppM ``Scalar.cMax_bound #[.const ``ScalarTy.Isize []])
+  -- Reveal the concrete bounds, simplify calls to [ofInt]
+  Utils.simpAt true {}
+               -- Simprocs
+               #[]
+               -- Unfoldings
+               [``Scalar.min, ``Scalar.max, ``Scalar.cMin, ``Scalar.cMax,
+                ``I8.min, ``I16.min, ``I32.min, ``I64.min, ``I128.min,
+                ``I8.max, ``I16.max, ``I32.max, ``I64.max, ``I128.max,
+                ``U8.min, ``U16.min, ``U32.min, ``U64.min, ``U128.min,
+                ``U8.max, ``U16.max, ``U32.max, ``U64.max, ``U128.max,
+                ``Usize.min
+                ]
+                -- Simp lemmas
+                [``Scalar.ofInt_val_eq, ``Scalar.neq_to_neq_val,
+                 ``Scalar.lt_equiv, ``Scalar.le_equiv, ``Scalar.eq_equiv]
+                -- Hypotheses
+                [] .wildcard
 
 elab "scalar_tac_preprocess" : tactic =>
   intTacPreprocess scalarTacExtraPreprocess
@@ -81,4 +82,14 @@ example (x : Int) (h0 : 0 ≤ x) (h1 : x ≤ U32.max) :
 example (x : U32) (h0 : ¬ x = U32.ofInt 0) : 0 < x.val := by
   scalar_tac
 
+/- See this: https://aeneas-verif.zulipchat.com/#narrow/stream/349819-general/topic/U64.20trouble/near/444049757
+
+   We solved it by removing the instance `OfNat` for `Scalar`.
+   Note however that we could also solve it with a simplification lemma.
+   However, after testing, we noticed we could only apply such a lemma with
+   the rewriting tactic (not the simplifier), probably because of the use
+   of typeclasses. -/
+example {u: U64} (h1: (u : Int) < 2): (u : Int) = 0 ∨ (u : Int) = 1 := by
+  scalar_tac
+
 end Arith