This module contains the implementation of the reflection monad, used by all other components of this directory.

instance Lean.Elab.Tactic.BVDecide.Frontend.instToExprBVBinOp : ToExpr Std.Tactic.BVDecide.BVBinOp

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instance Lean.Elab.Tactic.BVDecide.Frontend.instToExprBVUnOp : ToExpr Std.Tactic.BVDecide.BVUnOp

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instance Lean.Elab.Tactic.BVDecide.Frontend.instToExprBVExpr {w : Nat} : ToExpr (Std.Tactic.BVDecide.BVExpr w)

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def Lean.Elab.Tactic.BVDecide.Frontend.instToExprBVExpr.go {w : Nat} : Std.Tactic.BVDecide.BVExpr w → Expr

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• Lean.Elab.Tactic.BVDecide.Frontend.instToExprBVExpr.go (Std.Tactic.BVDecide.BVExpr.var idx) = Lean.mkApp2 (Lean.mkConst `Std.Tactic.BVDecide.BVExpr.var) (Lean.toExpr w) (Lean.toExpr idx)
• Lean.Elab.Tactic.BVDecide.Frontend.instToExprBVExpr.go (Std.Tactic.BVDecide.BVExpr.const val) = Lean.mkApp2 (Lean.mkConst `Std.Tactic.BVDecide.BVExpr.const) (Lean.toExpr w) (Lean.toExpr val)

instance Lean.Elab.Tactic.BVDecide.Frontend.instToExprBVBinPred : ToExpr Std.Tactic.BVDecide.BVBinPred

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instance Lean.Elab.Tactic.BVDecide.Frontend.instToExprGate : ToExpr Std.Tactic.BVDecide.Gate

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instance Lean.Elab.Tactic.BVDecide.Frontend.instToExprBVPred : ToExpr Std.Tactic.BVDecide.BVPred

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def Lean.Elab.Tactic.BVDecide.Frontend.instToExprBVPred.go : Std.Tactic.BVDecide.BVPred → Expr

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instance Lean.Elab.Tactic.BVDecide.Frontend.instToExprBoolExpr {α : Type} [ToExpr α] : ToExpr (Std.Tactic.BVDecide.BoolExpr α)

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def Lean.Elab.Tactic.BVDecide.Frontend.instToExprBoolExpr.go {α : Type} [ToExpr α] : Std.Tactic.BVDecide.BoolExpr α → Expr

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• Lean.Elab.Tactic.BVDecide.Frontend.instToExprBoolExpr.go (Std.Tactic.BVDecide.BoolExpr.const b) = Lean.mkApp2 (Lean.mkConst `Std.Tactic.BVDecide.BoolExpr.const) (Lean.toTypeExpr α) (Lean.toExpr b)

structure Lean.Elab.Tactic.BVDecide.Frontend.Atom : Type

A BitVec atom.

• width : Nat

  The width of the BitVec that is being abstracted.

• atomNumber : Nat

  A unique numeric identifier for the atom.

• synthetic : Bool

  Whether the atom is synthetic. The effect of this is that values for this atom are not considered for the counter example deriviation. This is for example useful when we introduce an atom over an expression, together with additional lemmas that fully describe the behavior of the atom.

structure Lean.Elab.Tactic.BVDecide.Frontend.State : Type

The state of the reflection monad

• atoms : Std.HashMap Expr Atom

  The atoms encountered so far. Saved as a map from BitVec expressions to a (width, atomNumber) pair.

• atomsAssignmentCache : Expr

  A cache for atomsAssignment. We maintain the invariant that this value is only used if atoms is non empty. The reason for not using an Option is that it would pollute a lot of code with error handling that is never hit as this invariant is enforced before all of this code.

@[reducible, inline]

abbrev Lean.Elab.Tactic.BVDecide.Frontend.M (α : Type) : Type

The reflection monad, used to track BitVec variables that we see as we traverse the context.

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• Lean.Elab.Tactic.BVDecide.Frontend.M = StateRefT' IO.RealWorld Lean.Elab.Tactic.BVDecide.Frontend.State Lean.MetaM

structure Lean.Elab.Tactic.BVDecide.Frontend.ReifiedBVExpr : Type

A reified version of an Expr representing a BVExpr.

• width : Nat
• bvExpr : Std.Tactic.BVDecide.BVExpr self.width

  The reified expression.

• evalsAtAtoms : M (Option Expr)

  A proof that bvExpr.eval atomsAssignment = originalBVExpr, none if it holds by rfl.

• expr : Expr

  A cache for toExpr bvExpr.

structure Lean.Elab.Tactic.BVDecide.Frontend.ReifiedBVPred : Type

A reified version of an Expr representing a BVPred.

• bvPred : Std.Tactic.BVDecide.BVPred

  The reified expression.

• evalsAtAtoms : M (Option Expr)

  A proof that bvPred.eval atomsAssignment = originalBVPredExpr, none if it holds by rfl.

• expr : Expr

  A cache for toExpr bvPred

structure Lean.Elab.Tactic.BVDecide.Frontend.ReifiedBVLogical : Type

A reified version of an Expr representing a BVLogicalExpr.

• bvExpr : Std.Tactic.BVDecide.BVLogicalExpr

  The reified expression.

• evalsAtAtoms : M (Option Expr)

  A proof that bvExpr.eval atomsAssignment = originalBVLogicalExpr, none if it holds by rfl.

• expr : Expr

  A cache for toExpr bvExpr

structure Lean.Elab.Tactic.BVDecide.Frontend.SatAtBVLogical : Type

A reified version of an Expr representing a BVLogicalExpr that we know to be true.

• bvExpr : Std.Tactic.BVDecide.BVLogicalExpr

  The reified expression.

• satAtAtoms : M Expr

  A proof that bvExpr.eval atomsAssignment = true.

• expr : Expr

  A cache for toExpr bvExpr

def Lean.Elab.Tactic.BVDecide.Frontend.M.run {α : Type} (m : M α) : MetaM α

Run a reflection computation as a MetaM one.

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• m.run = StateRefT'.run' m { atoms := ∅, atomsAssignmentCache := Lean.mkConst `illegal }

def Lean.Elab.Tactic.BVDecide.Frontend.M.atoms : M (Array (Nat × Expr))

Retrieve the atoms as pairs of their width and expression.

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def Lean.Elab.Tactic.BVDecide.Frontend.M.atomsAssignment : M Expr

Retrieve a BitVec.Assignment representing the atoms we found so far.

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• Lean.Elab.Tactic.BVDecide.Frontend.M.atomsAssignment = do let __do_lift ← getThe Lean.Elab.Tactic.BVDecide.Frontend.State pure __do_lift.atomsAssignmentCache

def Lean.Elab.Tactic.BVDecide.Frontend.M.lookup (e : Expr) (width : Nat) (synthetic : Bool) : M Nat

Look up an expression in the atoms, recording it if it has not previously appeared.

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def Lean.Elab.Tactic.BVDecide.Frontend.M.lookup.updateAtomsAssignment : M Unit

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@[specialize #[]]

def Lean.Elab.Tactic.BVDecide.Frontend.M.simplifyBinaryProof' (mkFRefl : Expr → Expr) (fst : Expr) (fproof : Option Expr) (mkSRefl : Expr → Expr) (snd : Expr) (sproof : Option Expr) : Option (Expr × Expr)

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• Lean.Elab.Tactic.BVDecide.Frontend.M.simplifyBinaryProof' mkFRefl fst (some fproof_2) mkSRefl snd (some sproof_2) = some (fproof_2, sproof_2)
• Lean.Elab.Tactic.BVDecide.Frontend.M.simplifyBinaryProof' mkFRefl fst (some fproof_2) mkSRefl snd none = some (fproof_2, mkSRefl snd)
• Lean.Elab.Tactic.BVDecide.Frontend.M.simplifyBinaryProof' mkFRefl fst none mkSRefl snd (some sproof_2) = some (mkFRefl fst, sproof_2)
• Lean.Elab.Tactic.BVDecide.Frontend.M.simplifyBinaryProof' mkFRefl fst none mkSRefl snd none = none

@[specialize #[]]

def Lean.Elab.Tactic.BVDecide.Frontend.M.simplifyBinaryProof (mkRefl : Expr → Expr) (fst : Expr) (fproof : Option Expr) (snd : Expr) (sproof : Option Expr) : Option (Expr × Expr)

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• Lean.Elab.Tactic.BVDecide.Frontend.M.simplifyBinaryProof mkRefl fst fproof snd sproof = Lean.Elab.Tactic.BVDecide.Frontend.M.simplifyBinaryProof' mkRefl fst fproof mkRefl snd sproof

@[specialize #[]]

def Lean.Elab.Tactic.BVDecide.Frontend.M.simplifyTernaryProof (mkRefl : Expr → Expr) (fst : Expr) (fproof : Option Expr) (snd : Expr) (sproof : Option Expr) (thd : Expr) (tproof : Option Expr) : Option (Expr × Expr × Expr)

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• Lean.Elab.Tactic.BVDecide.Frontend.M.simplifyTernaryProof mkRefl fst (some fproof_2) snd sproof thd tproof = some (fproof_2, stproof)
• Lean.Elab.Tactic.BVDecide.Frontend.M.simplifyTernaryProof mkRefl fst (some fproof_2) snd sproof thd tproof = some (fproof_2, mkRefl snd, mkRefl thd)
• Lean.Elab.Tactic.BVDecide.Frontend.M.simplifyTernaryProof mkRefl fst none snd sproof thd tproof = some (mkRefl fst, stproof)
• Lean.Elab.Tactic.BVDecide.Frontend.M.simplifyTernaryProof mkRefl fst none snd sproof thd tproof = none

structure Lean.Elab.Tactic.BVDecide.Frontend.LemmaState : Type

The state of the lemma reflection monad.

• lemmas : Array SatAtBVLogical

  The list of top level lemmas that got created on the fly during reflection.

@[reducible, inline]

abbrev Lean.Elab.Tactic.BVDecide.Frontend.LemmaM (α : Type) : Type

The lemma reflection monad. It extends the usual reflection monad M by adding the ability to add additional top level lemmas on the fly.

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• Lean.Elab.Tactic.BVDecide.Frontend.LemmaM = StateRefT' IO.RealWorld Lean.Elab.Tactic.BVDecide.Frontend.LemmaState Lean.Elab.Tactic.BVDecide.Frontend.M

def Lean.Elab.Tactic.BVDecide.Frontend.LemmaM.run {α : Type} (m : LemmaM α) (state : LemmaState := { lemmas := #[] }) : M (α × Array SatAtBVLogical)

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• m.run state = do let __discr ← StateRefT'.run m state match __discr with | (res, state) => pure (res, state.lemmas)

def Lean.Elab.Tactic.BVDecide.Frontend.LemmaM.addLemma (lemma : SatAtBVLogical) : LemmaM Unit

Add another top level lemma.

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• Lean.Elab.Tactic.BVDecide.Frontend.LemmaM.addLemma lemma = modify fun (s : Lean.Elab.Tactic.BVDecide.Frontend.LemmaState) => { lemmas := s.lemmas.push lemma }