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 derivation. 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 : Option Expr

  A cache for atomsAssignment. If it is none the cache is currently invalidated as new atoms have been added since it was last updated, if it is some it must be consistent with the atoms contained in atoms.

• evalsAtCache : Std.HashMap Expr (Option Expr)

  Cached calls to evalsAtAtoms of various reflection structures. Whenever atoms is modified this cache is invalidated as evalsAtAtoms relies on atoms.

@[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.

• originalExpr : Expr

  The expression that was reflected, used for caching of evalsAtAtoms.

• evalsAtAtoms' : M (Option Expr)

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

• expr : Expr

  A cache for toExpr bvExpr.

def Lean.Elab.Tactic.BVDecide.Frontend.ReifiedBVExpr.evalsAtAtoms (reified : ReifiedBVExpr) : M (Option Expr)

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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.

• originalExpr : Expr

  The expression that was reflected, usef for caching of evalsAtAtoms.

• evalsAtAtoms' : M (Option Expr)

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

• expr : Expr

  A cache for toExpr bvPred

def Lean.Elab.Tactic.BVDecide.Frontend.ReifiedBVPred.evalsAtAtoms (reified : ReifiedBVPred) : M (Option Expr)

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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.

• originalExpr : Expr

  The expression that was reflected, usef for caching of evalsAtAtoms.

• evalsAtAtoms' : M (Option Expr)

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

• expr : Expr

  A cache for toExpr bvExpr

def Lean.Elab.Tactic.BVDecide.Frontend.ReifiedBVLogical.evalsAtAtoms (reified : ReifiedBVLogical) : M (Option Expr)

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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 { }

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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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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@[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.

• bvExprCache : Std.HashMap Expr (Option ReifiedBVExpr)

  Cache for reification of BVExpr.

• bvPredCache : Std.HashMap Expr (Option ReifiedBVPred)

  Cache for reification of BVPred.

• bvLogicalCache : Std.HashMap Expr (Option ReifiedBVLogical)

  Cache for reification of BVLogicalExpr.

@[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 := { }) : 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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@[specialize #[]]

def Lean.Elab.Tactic.BVDecide.Frontend.LemmaM.withBVExprCache (e : Expr) (f : Expr → LemmaM (Option ReifiedBVExpr)) : LemmaM (Option ReifiedBVExpr)

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@[specialize #[]]

def Lean.Elab.Tactic.BVDecide.Frontend.LemmaM.withBVPredCache (e : Expr) (f : Expr → LemmaM (Option ReifiedBVPred)) : LemmaM (Option ReifiedBVPred)

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@[specialize #[]]

def Lean.Elab.Tactic.BVDecide.Frontend.LemmaM.withBVLogicalCache (e : Expr) (f : Expr → LemmaM (Option ReifiedBVLogical)) : LemmaM (Option ReifiedBVLogical)

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