Merge pull request #241 from AeneasVerif/son/tactics

Do minor improvements to the Lean backend

5 files changed, 118 insertions, 45 deletions

diff --git a/backends/lean/Base/Arith/Int.lean b/backends/lean/Base/Arith/Int.lean
index 4a3db5f8..59cdca25 100644
--- a/backends/lean/Base/Arith/Int.lean
+++ b/backends/lean/Base/Arith/Int.lean
@@ -180,7 +180,7 @@ 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
 
@@ -214,7 +214,7 @@ 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 ())
@@ -231,7 +231,7 @@ 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
diff --git a/backends/lean/Base/Arith/Scalar.lean b/backends/lean/Base/Arith/Scalar.lean
index 86b2e216..8793713b 100644
--- a/backends/lean/Base/Arith/Scalar.lean
+++ b/backends/lean/Base/Arith/Scalar.lean
@@ -8,30 +8,29 @@ 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 {}
+               -- 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 +80,14 @@ 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
diff --git a/backends/lean/Base/Primitives/Scalar.lean b/backends/lean/Base/Primitives/Scalar.lean
index 8fb067e1..157ade2c 100644
--- a/backends/lean/Base/Primitives/Scalar.lean
+++ b/backends/lean/Base/Primitives/Scalar.lean
@@ -351,10 +351,17 @@ instance [Decide (Scalar.cMin ty ≤ v ∧ v ≤ Scalar.cMax ty)] : InBounds ty
 @[simp] abbrev Scalar.check_bounds (ty : ScalarTy) (x : Int) : Bool :=
   (Scalar.cMin ty ≤ x || Scalar.min ty ≤ x) ∧ (x ≤ Scalar.cMax ty || x ≤ Scalar.max ty)
 
+/- Discussion:
+   This coercion can be slightly annoying at times, because if we write
+   something like `u = 3` (where `u` is, for instance, as `U32`), then instead of
+   coercing `u` to `Int`, Lean will lift `3` to `U32`).
+   For now we deactivate it.
+
 -- TODO(raitobezarius): the inbounds constraint is a bit ugly as we can pretty trivially
 -- discharge the lhs on ≥ 0.
 instance {ty: ScalarTy} [InBounds ty (Int.ofNat n)]: OfNat (Scalar ty) (n: ℕ) where
   ofNat := Scalar.ofInt n
+-/
 
 theorem Scalar.check_bounds_imp_in_bounds {ty : ScalarTy} {x : Int}
   (h: Scalar.check_bounds ty x) :
diff --git a/backends/lean/Base/Progress/Progress.lean b/backends/lean/Base/Progress/Progress.lean
index f2a56e50..03d464d7 100644
--- a/backends/lean/Base/Progress/Progress.lean
+++ b/backends/lean/Base/Progress/Progress.lean
@@ -58,17 +58,13 @@ def progressWith (fExpr : Expr) (th : TheoremOrLocal)
      We also make sure that all the meta variables which appear in the
      function arguments have been instantiated
    -/
-  let env ← getEnv
   let thTy ← do
     match th with
     | .Theorem thName =>
-      let thDecl := env.constants.find! thName
-      -- We have to introduce fresh meta-variables for the universes already
-      let ul : List (Name × Level) ←
-        thDecl.levelParams.mapM (λ x => do pure (x, ← mkFreshLevelMVar))
-      let ulMap : HashMap Name Level := HashMap.ofList ul
-      let thTy := thDecl.type.instantiateLevelParamsCore (λ x => ulMap.find! x)
-      pure thTy
+      -- Lookup the theorem and introduce fresh meta-variables for the universes
+      let th ← mkConstWithFreshMVarLevels thName
+      -- Retrieve the type
+      inferType th
     | .Local asmDecl => pure asmDecl.type
   trace[Progress] "Looked up theorem/assumption type: {thTy}"
   -- TODO: the tactic fails if we uncomment withNewMCtxDepth
@@ -135,7 +131,7 @@ def progressWith (fExpr : Expr) (th : TheoremOrLocal)
     Tactic.focus do
     let _ ←
       tryTac
-        (simpAt true []
+        (simpAt true {} []
                [``Primitives.bind_tc_ok, ``Primitives.bind_tc_fail, ``Primitives.bind_tc_div]
                [hEq.fvarId!] (.targets #[] true))
     -- It may happen that at this point the goal is already solved (though this is rare)
@@ -144,7 +140,7 @@ def progressWith (fExpr : Expr) (th : TheoremOrLocal)
     else
        trace[Progress] "goal after applying the eq and simplifying the binds: {← getMainGoal}"
        -- TODO: remove this (some types get unfolded too much: we "fold" them back)
-       let _ ← tryTac (simpAt true [] scalar_eqs [] .wildcard_dep)
+       let _ ← tryTac (simpAt true {} [] scalar_eqs [] .wildcard_dep)
        trace[Progress] "goal after folding back scalar types: {← getMainGoal}"
        -- Clear the equality, unless the user requests not to do so
        let mgoal ← do
diff --git a/backends/lean/Base/Utils.lean b/backends/lean/Base/Utils.lean
index 7ae5a832..4be46400 100644
--- a/backends/lean/Base/Utils.lean
+++ b/backends/lean/Base/Utils.lean
@@ -664,7 +664,7 @@ example (h : ∃ x y z, x + y + z ≥ 0) : ∃ x, x ≥ 0 := by
    Something very annoying is that there is no function which allows to
    initialize a simp context without doing an elaboration - as a consequence
    we write our own here. -/
-def mkSimpCtx (simpOnly : Bool) (declsToUnfold : List Name) (thms : List Name) (hypsToUse : List FVarId) :
+def mkSimpCtx (simpOnly : Bool) (config : Simp.Config) (declsToUnfold : List Name) (thms : List Name) (hypsToUse : List FVarId) :
   Tactic.TacticM Simp.Context := do
   -- Initialize either with the builtin simp theorems or with all the simp theorems
   let simpThms ←
@@ -693,7 +693,7 @@ def mkSimpCtx (simpOnly : Bool) (declsToUnfold : List Name) (thms : List Name) (
         throwError "Not a proposition: {thmName}"
       ) simpThms
   let congrTheorems ← getSimpCongrTheorems
-  pure { simpTheorems := #[simpThms], congrTheorems }
+  pure { config, simpTheorems := #[simpThms], congrTheorems }
 
 inductive Location where
   /-- Apply the tactic everywhere. Same as `Tactic.Location.wildcard` -/
@@ -731,29 +731,90 @@ where
     return usedSimps
 
 /- Call the simp tactic. -/
-def simpAt (simpOnly : Bool) (declsToUnfold : List Name) (thms : List Name) (hypsToUse : List FVarId)
+def simpAt (simpOnly : Bool) (config : Simp.Config) (declsToUnfold : List Name) (thms : List Name) (hypsToUse : List FVarId)
   (loc : Location) :
   Tactic.TacticM Unit := do
   -- Initialize the simp context
-  let ctx ← mkSimpCtx simpOnly declsToUnfold thms hypsToUse
+  let ctx ← mkSimpCtx simpOnly config declsToUnfold thms hypsToUse
   -- Apply the simplifier
   let _ ← customSimpLocation ctx (discharge? := .none) loc
 
 /- Call the dsimp tactic. -/
-def dsimpAt (simpOnly : Bool) (declsToUnfold : List Name) (thms : List Name) (hypsToUse : List FVarId)
+def dsimpAt (simpOnly : Bool) (config : Simp.Config) (declsToUnfold : List Name) (thms : List Name) (hypsToUse : List FVarId)
   (loc : Tactic.Location) :
   Tactic.TacticM Unit := do
   -- Initialize the simp context
-  let ctx ← mkSimpCtx simpOnly declsToUnfold thms hypsToUse
+  let ctx ← mkSimpCtx simpOnly config declsToUnfold thms hypsToUse
   -- Apply the simplifier
   dsimpLocation ctx loc
 
 -- Call the simpAll tactic
-def simpAll (declsToUnfold : List Name) (thms : List Name) (hypsToUse : List FVarId) :
+def simpAll (config : Simp.Config) (declsToUnfold : List Name) (thms : List Name) (hypsToUse : List FVarId) :
   Tactic.TacticM Unit := do
   -- Initialize the simp context
-  let ctx ← mkSimpCtx false declsToUnfold thms hypsToUse
+  let ctx ← mkSimpCtx false config declsToUnfold thms hypsToUse
   -- Apply the simplifier
   let _ ← Lean.Meta.simpAll (← getMainGoal) ctx
 
+/- Adapted from Elab.Tactic.Rewrite -/
+def rewriteTarget (eqThm : Expr) (symm : Bool) (config : Rewrite.Config := {}) : TacticM Unit := do
+  Term.withSynthesize <| withMainContext do
+    let r ← (← getMainGoal).rewrite (← getMainTarget) eqThm symm (config := config)
+    let mvarId' ← (← getMainGoal).replaceTargetEq r.eNew r.eqProof
+    replaceMainGoal (mvarId' :: r.mvarIds)
+
+/- Adapted from Elab.Tactic.Rewrite -/
+def rewriteLocalDecl (eqThm : Expr) (symm : Bool) (fvarId : FVarId) (config : Rewrite.Config := {}) :
+    TacticM Unit := withMainContext do
+  -- Note: we cannot execute `replaceLocalDecl` inside `Term.withSynthesize`.
+  -- See issues #2711 and #2727.
+  let rwResult ← Term.withSynthesize <| withMainContext do
+    let localDecl ← fvarId.getDecl
+    (← getMainGoal).rewrite localDecl.type eqThm symm (config := config)
+  let replaceResult ← (← getMainGoal).replaceLocalDecl fvarId rwResult.eNew rwResult.eqProof
+  replaceMainGoal (replaceResult.mvarId :: rwResult.mvarIds)
+
+/- Adapted from Elab.Tactic.Rewrite -/
+def rewriteWithThms
+  (thms : List (Bool × Expr))
+  (rewrite : (symm : Bool) → (thm : Expr) → TacticM Unit)
+  : TacticM Unit := do
+  let rec go thms :=
+    match thms with
+    | [] => throwError "Failed to rewrite with any theorem"
+    | (symm, eqThm)::thms =>
+      rewrite symm eqThm <|> go thms
+  go thms
+
+/- Adapted from Elab.Tactic.Rewrite -/
+def evalRewriteSeqAux (cfg : Rewrite.Config) (thms : List (Bool × Expr)) (loc : Tactic.Location) : TacticM Unit :=
+  rewriteWithThms thms fun symm term => do
+    withLocation loc
+      (rewriteLocalDecl term symm · cfg)
+      (rewriteTarget term symm cfg)
+      (throwTacticEx `rewrite · "did not find instance of the pattern in the current goal")
+
+/-- `rpt`: if `true`, repeatedly rewrite -/
+def rewriteAt (cfg : Rewrite.Config) (rpt : Bool)
+  (thms : List (Bool × Name)) (loc : Tactic.Location) : TacticM Unit := do
+  -- Lookup the theorems
+  let lookupThm (x : Bool × Name) : TacticM (List (Bool × Expr)) := do
+    let thName := x.snd
+    let lookupOne (thName : Name) : TacticM (Bool × Expr) := do
+      -- Lookup the theorem and introduce fresh meta-variables for the universes
+      let th ← mkConstWithFreshMVarLevels thName
+      pure (x.fst, th)
+    match ← getEqnsFor? thName (nonRec := true) with
+    | some eqThms => do
+      eqThms.data.mapM lookupOne
+    | none => do
+      pure [← lookupOne thName]
+  let thms ← List.mapM lookupThm thms
+  let thms := thms.flatten
+  -- Rewrite
+  if rpt then
+    Utils.repeatTac (evalRewriteSeqAux cfg thms loc)
+  else
+    evalRewriteSeqAux cfg thms loc
+
 end Utils