Skip to content
New issue

Have a question about this project? Sign up for a free GitHub account to open an issue and contact its maintainers and the community.

Sign up for GitHub

By clicking “Sign up for GitHub”, you agree to our terms of service and privacy statement. We’ll occasionally send you account related emails.

Already on GitHub? Sign in to your account

Add a proof #26

Open
wants to merge 2 commits into
base: main
Choose a base branch
from
Open

Add a proof #26

Changes from all commits
Commits
Show all changes
2 commits
Select commit Hold shift + click to select a range
0af0e68
Add proof for theorem add_x1_x1_1_sym
casavaca Mar 19, 2024
5f0ed8a
simp --> simp only
casavaca Mar 20, 2024
File filter

Filter by extension

Filter by extension
Conversations
Failed to load comments.
Loading
Jump to
Jump to file
Failed to load files.
Loading
Diff view
Diff view
53 changes: 36 additions & 17 deletions Proofs/Test.lean
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -56,7 +56,7 @@ theorem zeroExtend_irrelevant (x : BitVec 64) :

theorem add_x1_x1_1_sym_helper (x1_var : BitVec 64) :
(BitVec.toNat x1_var + 1)#64 = x1_var + 1#64 := by
sorry
rfl

theorem add_x1_x1_1_sym
(h_pc : read_pc s = 0#64)
Expand All @@ -66,22 +66,41 @@ theorem add_x1_x1_1_sym
(h_s' : s' = run 1 s)
(h_x1': x1' = read_gpr 64 1#5 s') :
x1' = x1 + 1#64 ∧ read_err s' = StateError.None := by
sorry
-- simp [*] at *
-- unfold run stepi; simp [h_pc, h_inst, h_s_ok]
-- unfold exec_inst
-- simp (config := { ground := true }) only [h_inst]
-- -- This proof is still broken in `simp (config := { ground := true })`
-- sorry
-- unfold DPI.exec_add_sub_imm; simp (config := { ground := true })
-- unfold AddWithCarry
-- simp (config := { ground := true }) only [zeroExtend_twice, zeroExtend_of_Nat_64]
-- generalize (r (StateField.GPR 1#5) s) = x1_var
-- unfold state_value at x1_var;
-- simp at x1_var
-- simp [zeroExtend_irrelevant]
-- rw [add_x1_x1_1_sym_helper]
-- trivial
-- the following can be removed once we add builtin_simproc for HShift for Nat.
have tmp1 : (2432697377 >>> 25)#4 = 8#4 := by decide
have tmp2 : (2432697377 >>> 23)#6 = 34#6 := by decide
have tmp3 : (2432697377 >>> 31)#1 = 1#1 := by decide
have tmp4 : (2432697377 >>> 30)#1 = 0#1 := by decide
have tmp5 : (2432697377 >>> 29)#1 = 0#1 := by decide
have tmp6 : (2432697377 >>> 22)#1 = 0#1 := by decide
have tmp7 : (2432697377 >>> 10)#12 = 1#12 := by decide
have tmp8 : (2432697377 >>> 5)#5 = 1#5 := by decide
conv at h_s' => {
rhs
unfold run run stepi
simp only [h_s_ok, h_pc, h_inst]
unfold decode_raw_inst
-- apply hints provided by `simp? [decode_data_proc_imm]`
simp only [decode_data_proc_imm, BitVec.extractLsb_ofNat, Nat.reduceAdd, Nat.reduceSub, Nat.reducePow,
Nat.reduceMod, Bool.true_and, beq_iff_eq, Nat.sub_zero, Nat.shiftRight_zero, reduceOfNat]
-- guide lean to do the calculation. In the future, this should be done automatically by Lean,
-- by adding builtin_simproc for HShift for Nat.
-- https://github.com/leanprover/lean4/blob/master/src/Lean/Meta/Tactic/Simp/BuiltinSimprocs/Nat.lean
simp only [tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7, tmp8]
-- apply hints provided by `simp? [exec_inst, DPI.exec_add_sub_imm]`
simp only [exec_inst, DPI.exec_add_sub_imm, Nat.reduceAdd, beq_self_eq_true, ↓reduceIte, reduceAppend,
reduceNot, beq_iff_eq]
-- guide lean to do the calculation.
-- similarly, the following can be removed once we add builtin_simproc for BEq for BitVec.
-- https://github.com/leanprover/lean4/blob/master/src/Lean/Meta/Tactic/Simp/BuiltinSimprocs/BitVec.lean
rw [if_pos ((by decide) : 1#1 == 1#1), if_neg ((by decide) : 0#1 ≠ 1#1)]
rw [←h_x1, h_pc, ofNat_add_ofNat, Nat.zero_add]
rw [instDecidableEqBool, Bool.decEq, AddWithCarry]
rw [((by decide) : (0#1 == 1#1) = false)]
dsimp only
}
rw [h_x1', h_s', ←h_s_ok]
simp [state_simp_rules, ←ofNat_add_ofNat]

-- This version of the theorem opens up run only once. See the
-- revert...intro block below.
Expand Down