Std.Tactic.BVDecide.Bitblast.BVExpr.Circuit.Impl.Operations.ShiftRight

This module contains the implementation of a bitblaster for BitVec.shiftRight. It distinguishes two cases:

Shifting by a constant distance (trivial)
Shifting by a symbolic BitVec distance (requires symbolic branches over the distance).

def Std.Tactic.BVDecide.BVExpr.bitblast.blastShiftRightConst {α : Type} [Hashable α] [DecidableEq α] {w : Nat} (aig : Std.Sat.AIG α) (target : aig.ShiftTarget w) :

Std.Sat.AIG.RefVecEntry α w

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@[irreducible]

def Std.Tactic.BVDecide.BVExpr.bitblast.blastShiftRightConst.go {α : Type} [Hashable α] [DecidableEq α] {w : Nat} (aig : Std.Sat.AIG α) (input : aig.RefVec w) (distance : Nat) (curr : Nat) (hcurr : curr ≤ w) (s : aig.RefVec curr) :

Std.Sat.AIG.RefVecEntry α w

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@[irreducible]

theorem Std.Tactic.BVDecide.BVExpr.bitblast.blastShiftRightConst.go_le_size {α : Type} [Hashable α] [DecidableEq α] {w : Nat} (aig : Std.Sat.AIG α) (distance : Nat) (input : aig.RefVec w) (curr : Nat) (hcurr : curr ≤ w) (s : aig.RefVec curr) :

aig.decls.size ≤ (Std.Tactic.BVDecide.BVExpr.bitblast.blastShiftRightConst.go aig input distance curr hcurr s).aig.decls.size

source

@[irreducible]

theorem Std.Tactic.BVDecide.BVExpr.bitblast.blastShiftRightConst.go_decl_eq {α : Type} [Hashable α] [DecidableEq α] {w : Nat} (aig : Std.Sat.AIG α) (distance : Nat) (input : aig.RefVec w) (curr : Nat) (hcurr : curr ≤ w) (s : aig.RefVec curr) (idx : Nat) (h1 : idx < aig.decls.size) (h2 : idx < (Std.Tactic.BVDecide.BVExpr.bitblast.blastShiftRightConst.go aig input distance curr hcurr s).aig.decls.size) :

(Std.Tactic.BVDecide.BVExpr.bitblast.blastShiftRightConst.go aig input distance curr hcurr s).aig.decls[idx] = aig.decls[idx]

source

instance Std.Tactic.BVDecide.BVExpr.bitblast.instLawfulVecOperatorShiftTargetBlastShiftRightConst {α : Type} [Hashable α] [DecidableEq α] :

Std.Sat.AIG.LawfulVecOperator α Std.Sat.AIG.ShiftTarget fun {len : Nat} => Std.Tactic.BVDecide.BVExpr.bitblast.blastShiftRightConst

Equations

Std.Tactic.BVDecide.BVExpr.bitblast.instLawfulVecOperatorShiftTargetBlastShiftRightConst = { le_size := ⋯, decl_eq := ⋯ }

source

def Std.Tactic.BVDecide.BVExpr.bitblast.blastArithShiftRightConst {α : Type} [Hashable α] [DecidableEq α] {w : Nat} (aig : Std.Sat.AIG α) (target : aig.ShiftTarget w) :

Std.Sat.AIG.RefVecEntry α w

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@[irreducible]

def Std.Tactic.BVDecide.BVExpr.bitblast.blastArithShiftRightConst.go {α : Type} [Hashable α] [DecidableEq α] {w : Nat} {aig : Std.Sat.AIG α} (input : aig.RefVec w) (distance : Nat) (curr : Nat) (hcurr : curr ≤ w) (s : aig.RefVec curr) :

aig.RefVec w

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instance Std.Tactic.BVDecide.BVExpr.bitblast.instLawfulVecOperatorShiftTargetBlastArithShiftRightConst {α : Type} [Hashable α] [DecidableEq α] :

Std.Sat.AIG.LawfulVecOperator α Std.Sat.AIG.ShiftTarget fun {len : Nat} => Std.Tactic.BVDecide.BVExpr.bitblast.blastArithShiftRightConst

Equations

Std.Tactic.BVDecide.BVExpr.bitblast.instLawfulVecOperatorShiftTargetBlastArithShiftRightConst = { le_size := ⋯, decl_eq := ⋯ }

source

structure Std.Tactic.BVDecide.BVExpr.bitblast.blastShiftRight.TwoPowShiftTarget {α : Type} [Hashable α] [DecidableEq α] (aig : Std.Sat.AIG α) (w : Nat) :

Type

n : Nat
lhs : aig.RefVec w
rhs : aig.RefVec self.n
pow : Nat

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def Std.Tactic.BVDecide.BVExpr.bitblast.blastShiftRight.twoPowShift {α : Type} [Hashable α] [DecidableEq α] {w : Nat} (aig : Std.Sat.AIG α) (target : Std.Tactic.BVDecide.BVExpr.bitblast.blastShiftRight.TwoPowShiftTarget aig w) :

Std.Sat.AIG.RefVecEntry α w

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instance Std.Tactic.BVDecide.BVExpr.bitblast.blastShiftRight.instLawfulVecOperatorTwoPowShiftTargetTwoPowShift {α : Type} [Hashable α] [DecidableEq α] :

Std.Sat.AIG.LawfulVecOperator α Std.Tactic.BVDecide.BVExpr.bitblast.blastShiftRight.TwoPowShiftTarget fun {len : Nat} => Std.Tactic.BVDecide.BVExpr.bitblast.blastShiftRight.twoPowShift

Equations

Std.Tactic.BVDecide.BVExpr.bitblast.blastShiftRight.instLawfulVecOperatorTwoPowShiftTargetTwoPowShift = { le_size := ⋯, decl_eq := ⋯ }

source

def Std.Tactic.BVDecide.BVExpr.bitblast.blastShiftRight {α : Type} [Hashable α] [DecidableEq α] {w : Nat} (aig : Std.Sat.AIG α) (target : aig.ArbitraryShiftTarget w) :

Std.Sat.AIG.RefVecEntry α w

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@[irreducible]

def Std.Tactic.BVDecide.BVExpr.bitblast.blastShiftRight.go {α : Type} [Hashable α] [DecidableEq α] {w : Nat} {n : Nat} (aig : Std.Sat.AIG α) (distance : aig.RefVec n) (curr : Nat) (hcurr : curr ≤ n - 1) (acc : aig.RefVec w) :

Std.Sat.AIG.RefVecEntry α w

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@[irreducible]

theorem Std.Tactic.BVDecide.BVExpr.bitblast.blastShiftRight.go_le_size {α : Type} [Hashable α] [DecidableEq α] {n : Nat} {w : Nat} (aig : Std.Sat.AIG α) (distance : aig.RefVec n) (curr : Nat) (hcurr : curr ≤ n - 1) (acc : aig.RefVec w) :

aig.decls.size ≤ (Std.Tactic.BVDecide.BVExpr.bitblast.blastShiftRight.go aig distance curr hcurr acc).aig.decls.size

source

@[irreducible]

theorem Std.Tactic.BVDecide.BVExpr.bitblast.blastShiftRight.go_decl_eq {α : Type} [Hashable α] [DecidableEq α] {n : Nat} {w : Nat} (aig : Std.Sat.AIG α) (distance : aig.RefVec n) (curr : Nat) (hcurr : curr ≤ n - 1) (acc : aig.RefVec w) (idx : Nat) (h1 : idx < aig.decls.size) (h2 : idx < (Std.Tactic.BVDecide.BVExpr.bitblast.blastShiftRight.go aig distance curr hcurr acc).aig.decls.size) :

(Std.Tactic.BVDecide.BVExpr.bitblast.blastShiftRight.go aig distance curr hcurr acc).aig.decls[idx] = aig.decls[idx]

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instance Std.Tactic.BVDecide.BVExpr.bitblast.instLawfulVecOperatorArbitraryShiftTargetBlastShiftRight {α : Type} [Hashable α] [DecidableEq α] :

Std.Sat.AIG.LawfulVecOperator α Std.Sat.AIG.ArbitraryShiftTarget fun {len : Nat} => Std.Tactic.BVDecide.BVExpr.bitblast.blastShiftRight

Equations

Std.Tactic.BVDecide.BVExpr.bitblast.instLawfulVecOperatorArbitraryShiftTargetBlastShiftRight = { le_size := ⋯, decl_eq := ⋯ }