5a5e83c26c
This PR refactors the AIG datastructures that underly bv_decide in order to allow a better tracking of negations in the circuit. This refactor has two effects, for one adding full constant folding to the AIG framework and secondly enabling us to add further simplifications from the Brummayer Biere paper in the future which was previously architecturally impossible.
118 lines
3 KiB
Text
118 lines
3 KiB
Text
import Std.Tactic.BVDecide
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open BitVec
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/--
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error: The prover found a counterexample, consider the following assignment:
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x = 18446744073709551615#64
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-/
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#guard_msgs in
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example (x : BitVec 64) : x < x + 1 := by
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bv_decide
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/--
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error: The prover found a counterexample, consider the following assignment:
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x = 0#64
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-/
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#guard_msgs in
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example (x : BitVec 64) (h : x < 512) : x ^^^ x ≠ 0 := by
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bv_decide
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/-
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This is a modified version of Eval.Popcount with a mistake
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-/
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def pop_spec' (x : BitVec 32) : BitVec 32 :=
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go x 0 32
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where
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go (x : BitVec 32) (pop : BitVec 32) (i : Nat) : BitVec 32 :=
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match i with
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| 0 => pop
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| i + 1 =>
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let pop := pop + (x &&& 1)
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go (x >>> 1) pop i
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def optimized (x : BitVec 32) : BitVec 32 :=
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let x := x - ((x >>> 1) &&& 0x55555555);
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let x := (x &&& 0x33333333) + ((x >>> 2) &&& 0x33333333);
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let x := (x + (x >>> 4)) &&& 0x0F0F0F0F;
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let x := x + (x >>> 8);
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let x := x + (x >>> 16);
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-- MISTAKE HERE: the 4 should be a 3
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x &&& 0x0000004F
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/--
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error: The prover found a counterexample, consider the following assignment:
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x = 4294967295#32
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-/
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#guard_msgs in
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example (x : BitVec 32) : pop_spec' x = optimized x := by
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dsimp [pop_spec', pop_spec'.go, optimized]
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bv_decide
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-- limit the search domain
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/--
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error: The prover found a counterexample, consider the following assignment:
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x = 524287#32
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-/
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#guard_msgs in
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example (x : BitVec 32) (h1 : x < 0xfffff) : pop_spec' x = optimized x := by
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dsimp [pop_spec', pop_spec'.go, optimized]
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bv_decide
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/--
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error: The prover found a counterexample, consider the following assignment:
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x = 0#32
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y = 2147483648#32
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a = true
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-/
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#guard_msgs in
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example (x y : BitVec 32) (a : Bool) (h : x < y) : (x = y) ↔ a := by
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bv_decide
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-- False counter examples but correctly detected as such.
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/--
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error: The prover found a potentially spurious counterexample:
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- The following potentially relevant hypotheses could not be used: [h]
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Consider the following assignment:
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x = 4294967295#32
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y = 2147483647#32
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-/
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#guard_msgs in
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example (x y : BitVec 32) (h : x.toNat = y.toNat) : x = y := by
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bv_decide
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def zeros (w : Nat) : BitVec w := 0#w
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/--
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error: The prover found a potentially spurious counterexample:
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- It abstracted the following unsupported expressions as opaque variables: [zeros 32]
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Consider the following assignment:
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x = 4294967295#32
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zeros 32 = 4294967295#32
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-/
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#guard_msgs in
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example (x : BitVec 32) (h : x = zeros 32) : x = 0 := by
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bv_decide
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/--
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error: The prover found a potentially spurious counterexample:
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- It abstracted the following unsupported expressions as opaque variables: [zeros 32]
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- The following potentially relevant hypotheses could not be used: [h1]
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Consider the following assignment:
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x = 4294967295#32
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zeros 32 = 4294967295#32
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y = 4294967295#32
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-/
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#guard_msgs in
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example (x y : BitVec 32) (h1 : x.toNat = y.toNat) (h2 : x = zeros 32) : y = 0 := by
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bv_decide
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/--
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error: The prover found a counterexample, consider the following assignment:
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x = 3#2
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-/
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#guard_msgs in
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example (x : BitVec 2) : (bif x.ult 1#2 then 1#2 else 2#2) == 3#2 := by
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bv_decide
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