refactor: incorporate an AxEffects field in SymContext, introduce `Sy…

…mM` monad for `SymContext` state (#180)

### Description:

This turned into a rather big tech-debt removal PR. The primary focus is
the removal of the duplication we had between `SymContext` tracking
names of hypotheses, and `AxEffects` tracking `Expr`s for those same
hypotheses.

- Added an `effects : AxEffects` field to `SymContext`, which stores the
`AxEffects` for a single (non-aggregated!) step
- To make live easier, we introduce a `SymM` monad, so that we don't
have to project out to the effect field every single every time
(credits/blame go to @bollu for showing me the `MonadStateOf` trick).
- This allowed us to remove a bunch of fields of `SymContext` which had
duplicates in `AxEffects`
- Also, it allowed us to move reflection of the PC out of `explodeSteps`
and into `prepareForNextStep` (which was previously called
`SymContext.next`),
- Finally, we extract `ensureAtMostRunSteps` and
`assertStepTheoremsGenerated` functions out of the main body of `sym_n`

### Testing:

What tests have been run? Did `make all` succeed for your changes? Was
conformance testing successful on an Aarch64 machine? yes

### License:

By submitting this pull request, I confirm that my contribution is
made under the terms of the Apache 2.0 license.

---------

Co-authored-by: Shilpi Goel <[email protected]>

Tactics/Common.lean

@@ -223,9 +223,9 @@ def findLocalDeclOfType? (expectedType : Expr) : MetaM (Option LocalDecl) := do
     --    the local context, so we can safely pass it to `get!`
 
 def findLocalDeclOfTypeOrError (expectedType : Expr) : MetaM LocalDecl := do
-    let some name ← findLocalDeclOfType? expectedType
+    let some decl ← findLocalDeclOfType? expectedType
       | throwError "Failed to find a local hypothesis of type {expectedType}"
-    return name
+    return decl
 
 /-- `findProgramHyp` searches the local context for an hypothesis of type
   `state.program = ?concreteProgram`,
@@ -269,3 +269,12 @@ def traceHeartbeats (cls : Name) (header : Option String := none) :
   let percent ← heartbeatsPercent
   trace cls fun _ =>
     m!"{header}used {heartbeats} heartbeats ({percent}% of maximum)"
+
+/-! ## `withMainContext'` -/
+
+variable {m} [Monad m] [MonadLiftT TacticM m] [MonadControlT MetaM m] in
+/-- Execute `x` using the main goal local context and instances.
+
+Unlike the standard `withMainContext`, `x` may live in a generic monad `m`. -/
+def withMainContext' (x : m α) : m α := do
+  (← getMainGoal).withContext x

Tactics/Reflect/AxEffects.lean

@@ -82,6 +82,37 @@ structure AxEffects where
 
 namespace AxEffects
 
+/-! ## Monad getters -/
+
+section Monad
+variable {m} [Monad m] [MonadReaderOf AxEffects m]
+
+def getCurrentState       : m Expr := do return (← read).currentState
+def getInitialState       : m Expr := do return (← read).initialState
+def getNonEffectProof     : m Expr := do return (← read).nonEffectProof
+def getMemoryEffect       : m Expr := do return (← read).memoryEffect
+def getMemoryEffectProof  : m Expr := do return (← read).memoryEffectProof
+def getProgramProof       : m Expr := do return (← read).programProof
+
+def getStackAlignmentProof? : m (Option Expr) := do
+  return (← read).stackAlignmentProof?
+
+variable [MonadLiftT MetaM m] in
+/-- Retrieve the user-facing name of the current state, assuming that
+the current state is a free variable in the ambient local context -/
+def getCurrentStateName : m Name := do
+  let state ← getCurrentState
+  @id (MetaM _) <| do
+    let state ← instantiateMVars state
+    let Expr.fvar id := state.consumeMData
+      | throwError "error: expected a free variable, found:\n  {state} WHHOPS"
+    let lctx ← getLCtx
+    let some decl := lctx.find? id
+      | throwError "error: unknown fvar: {state}"
+    return decl.userName
+
+end Monad
+
 /-! ## Initial Reflected State -/
 
 /-- An initial `AxEffects` state which has no writes.
@@ -185,7 +216,7 @@ partial def mkAppNonEffect (eff : AxEffects) (field : Expr) : MetaM Expr := do
       return nonEffectProof
 
 /-- Get the value for a field, if one is stored in `eff.fields`,
-or assemble an instantiation of the non-effects proof -/
+or assemble an instantiation of the non-effects proof otherwise -/
 def getField (eff : AxEffects) (fld : StateField) : MetaM FieldEffect :=
   let msg := m!"getField {fld}"
   withTraceNode `Tactic.sym (fun _ => pure msg) <| do
@@ -200,6 +231,11 @@ def getField (eff : AxEffects) (fld : StateField) : MetaM FieldEffect :=
       let proof  ← eff.mkAppNonEffect (toExpr fld)
       pure { value, proof }
 
+variable {m} [Monad m] [MonadReaderOf AxEffects m] [MonadLiftT MetaM m] in
+@[inherit_doc getField]
+def getFieldM (field : StateField) : m FieldEffect := do
+  (← read).getField field
+
 /-! ## Update a Reflected State -/
 
 /-- Execute `write_mem <n> <addr> <val>` against the state stored in `eff`
@@ -359,6 +395,24 @@ private def assertIsDefEq (e expected : Expr) : MetaM Unit := do
   if !(←isDefEq e expected) then
     throwError "expected:\n  {expected}\nbut found:\n  {e}"
 
+/-- Given an expression `e : ArmState`,
+which is a sequence of `w`/`write_mem`s to `eff.currentState`,
+return an `AxEffects` where `e` is the new `currentState`. -/
+partial def updateWithExpr (eff : AxEffects) (e : Expr) : MetaM AxEffects := do
+  let msg := m!"Updating effects with writes from: {e}"
+  withTraceNode `Tactic.sym (fun _ => pure msg) <| do match_expr e with
+    | write_mem_bytes n addr val e =>
+        let eff ← eff.updateWithExpr e
+        eff.update_write_mem n addr val
+
+    | w field value e =>
+        let eff ← eff.updateWithExpr e
+        eff.update_w field value
+
+    | _ =>
+        assertIsDefEq e eff.currentState
+        return eff
+
 /-- Given an expression `e : ArmState`,
 which is a sequence of `w`/`write_mem`s to the some state `s`,
 return an `AxEffects` where `s` is the intial state, and `e` is `currentState`.
@@ -466,7 +520,10 @@ def withField (eff : AxEffects) (eq : Expr) : MetaM AxEffects := do
     trace[Tactic.sym] "current field effect: {fieldEff}"
 
     if field ∉ eff.fields then
-      let proof ← mkEqTrans fieldEff.proof eq
+      let proof ← if eff.currentState == eff.initialState then
+          pure eq
+        else
+          mkEqTrans fieldEff.proof eq
       let fields := eff.fields.insert field { value, proof }
       return { eff with fields }
     else