arithcc
⟷
Archive.Arithcc
The following section lists changes to this file in mathlib3 and mathlib4 that occured after the initial port. Most recent changes are shown first. Hovering over a commit will show all commits associated with the same mathlib3 commit.
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mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83
@@ -296,7 +296,7 @@ theorem write_eq_implies_stateEq {t : Register} {v : Word} {ζ₁ ζ₂ : State}
intro r hr
cases' h with _ h
specialize h r (lt_trans hr (register.lt_succ_self _))
- rwa [if_neg (ne_of_lt hr)] at h
+ rwa [if_neg (ne_of_lt hr)] at h
#align arithcc.write_eq_implies_state_eq Arithcc.write_eq_implies_stateEq
/-- The main **compiler correctness theorem**.
@@ -352,7 +352,7 @@ theorem compiler_correctness :
intros
calc
read (loc x map) ζ₂ = read (loc x map) (write t ν₁ η) := hζ₂ _ (ht' _)
- _ = read (loc x map) η := by simp only [loc] at ht ; simp [(ht _).Ne]
+ _ = read (loc x map) η := by simp only [loc] at ht; simp [(ht _).Ne]
_ = ξ x := hmap x
have hζ₃ : ζ₃ ≃[t + 1] { write t ν₁ η with ac := ν₂ }
calc
mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451
@@ -3,8 +3,8 @@ Copyright (c) 2020 Xi Wang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Xi Wang
-/
-import Mathbin.Order.Basic
-import Mathbin.Tactic.Basic
+import Order.Basic
+import Tactic.Basic
#align_import arithcc from "leanprover-community/mathlib"@"08b081ea92d80e3a41f899eea36ef6d56e0f1db0"
mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345
@@ -2,15 +2,12 @@
Copyright (c) 2020 Xi Wang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Xi Wang
-
-! This file was ported from Lean 3 source module arithcc
-! leanprover-community/mathlib commit 08b081ea92d80e3a41f899eea36ef6d56e0f1db0
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathbin.Order.Basic
import Mathbin.Tactic.Basic
+#align_import arithcc from "leanprover-community/mathlib"@"08b081ea92d80e3a41f899eea36ef6d56e0f1db0"
+
/-!
# A compiler for arithmetic expressions
mathlib commit https://github.com/leanprover-community/mathlib/commit/bf2428c9486c407ca38b5b3fb10b87dad0bc99fa
@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Xi Wang
! This file was ported from Lean 3 source module arithcc
-! leanprover-community/mathlib commit eb3595ed8610db8107b75b75ab64ab6390684155
+! leanprover-community/mathlib commit 08b081ea92d80e3a41f899eea36ef6d56e0f1db0
! Please do not edit these lines, except to modify the commit id
! if you have ported upstream changes.
-/
@@ -14,6 +14,9 @@ import Mathbin.Tactic.Basic
/-!
# A compiler for arithmetic expressions
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
A formalization of the correctness of a compiler from arithmetic expressions to machine language
described by McCarthy and Painter, which is considered the first proof of compiler correctness.
mathlib commit https://github.com/leanprover-community/mathlib/commit/9fb8964792b4237dac6200193a0d533f1b3f7423
@@ -208,7 +208,6 @@ def StateEqRs (t : Register) (ζ₁ ζ₂ : State) : Prop :=
∀ r : Register, r < t → ζ₁.rs r = ζ₂.rs r
#align arithcc.state_eq_rs Arithcc.StateEqRs
--- mathport name: «expr ≃[ ]/ac »
notation:50 ζ₁ " ≃[" t "]/ac " ζ₂:50 => StateEqRs t ζ₁ ζ₂
@[refl]
@@ -230,7 +229,6 @@ def StateEq (t : Register) (ζ₁ ζ₂ : State) : Prop :=
ζ₁.ac = ζ₂.ac ∧ StateEqRs t ζ₁ ζ₂
#align arithcc.state_eq Arithcc.StateEq
--- mathport name: «expr ≃[ ] »
notation:50 ζ₁ " ≃[" t "] " ζ₂:50 => StateEq t ζ₁ ζ₂
@[refl]
mathlib commit https://github.com/leanprover-community/mathlib/commit/7e5137f579de09a059a5ce98f364a04e221aabf0
@@ -331,7 +331,6 @@ theorem compiler_correctness :
calc
ζ₁ = outcome (compile map e_s₁ t) η := by cc
_ ≃[t] { η with ac := ν₁ } := by apply e_ih_s₁ <;> assumption
-
have hζ₁_ν₁ : ζ₁.ac = ν₁ := by finish [state_eq]
have hζ₂ : ζ₂ ≃[t + 1]/ac write t ν₁ η
calc
@@ -343,7 +342,6 @@ theorem compiler_correctness :
by
apply state_eq_rs_implies_write_eq_rs
simp [state_eq_rs]
-
have hζ₂_ν₂ : read t ζ₂ = ν₁ := by
simp [state_eq_rs] at hζ₂ ⊢
specialize hζ₂ t (register.lt_succ_self _)
@@ -358,13 +356,11 @@ theorem compiler_correctness :
read (loc x map) ζ₂ = read (loc x map) (write t ν₁ η) := hζ₂ _ (ht' _)
_ = read (loc x map) η := by simp only [loc] at ht ; simp [(ht _).Ne]
_ = ξ x := hmap x
-
have hζ₃ : ζ₃ ≃[t + 1] { write t ν₁ η with ac := ν₂ }
calc
ζ₃ = outcome (compile map e_s₂ (t + 1)) ζ₂ := by cc
_ ≃[t + 1] { ζ₂ with ac := ν₂ } := by apply e_ih_s₂ <;> assumption
_ ≃[t + 1] { write t ν₁ η with ac := ν₂ } := by simp [state_eq]; apply hζ₂
-
have hζ₃_ν₂ : ζ₃.ac = ν₂ := by finish [state_eq]
have hζ₃_ν₁ : read t ζ₃ = ν₁ :=
by
@@ -380,7 +376,6 @@ theorem compiler_correctness :
_ ≃[t + 1] { { write t ν₁ η with ac := ν₂ } with ac := ν } := by simp [state_eq] at hζ₃ ⊢;
cases hζ₃; assumption
_ ≃[t + 1] { write t ν₁ η with ac := ν } := by simp
-
apply write_eq_implies_state_eq <;> assumption
#align arithcc.compiler_correctness Arithcc.compiler_correctness
mathlib commit https://github.com/leanprover-community/mathlib/commit/a3209ddf94136d36e5e5c624b10b2a347cc9d090
@@ -319,7 +319,8 @@ theorem compiler_correctness
-- 5.III
| sum =>
rename_i e_s₁ e_s₂ e_ih_s₁ e_ih_s₂
- simp
+ simp only [compile, List.append_assoc, List.singleton_append, List.cons_append, outcome_append,
+ outcome, value]
generalize value e_s₁ ξ = ν₁ at e_ih_s₁ ⊢
generalize value e_s₂ ξ = ν₂ at e_ih_s₂ ⊢
generalize dν : ν₁ + ν₂ = ν
@@ -249,7 +249,7 @@ protected theorem StateEq.trans {t : Register} (ζ₁ ζ₂ ζ₃ : State) :
· trans ζ₂ <;> assumption
#align arithcc.state_eq.trans Arithcc.StateEq.trans
--- Porting note: added
+-- Porting note (#10754): added instance
instance (t : Register) : Trans (StateEq (t + 1)) (StateEq (t + 1)) (StateEq (t + 1)) :=
⟨@StateEq.trans _⟩
@@ -261,7 +261,7 @@ protected theorem StateEqStateEqRs.trans (t : Register) (ζ₁ ζ₂ ζ₃ : Sta
trans ζ₂ <;> assumption
#align arithcc.state_eq_state_eq_rs.trans Arithcc.StateEqStateEqRs.trans
--- Porting note: added
+-- Porting note (#10754): added instance
instance (t : Register) : Trans (StateEq (t + 1)) (StateEqRs (t + 1)) (StateEqRs (t + 1)) :=
⟨@StateEqStateEqRs.trans _⟩
have
, replace
and suffices
(#10640)
No changes to tactic file, it's just boring fixes throughout the library.
This follows on from #6964.
Co-authored-by: sgouezel <sebastien.gouezel@univ-rennes1.fr> Co-authored-by: Eric Wieser <wieser.eric@gmail.com>
@@ -327,13 +327,11 @@ theorem compiler_correctness
generalize dζ₂ : step (Instruction.sto t) ζ₁ = ζ₂
generalize dζ₃ : outcome (compile _ e_s₂ (t + 1)) ζ₂ = ζ₃
generalize dζ₄ : step (Instruction.add t) ζ₃ = ζ₄
- have hζ₁ : ζ₁ ≃[t] { η with ac := ν₁ }
- calc
+ have hζ₁ : ζ₁ ≃[t] { η with ac := ν₁ } := calc
ζ₁ = outcome (compile map e_s₁ t) η := by simp_all
_ ≃[t] { η with ac := ν₁ } := by apply e_ih_s₁ <;> assumption
have hζ₁_ν₁ : ζ₁.ac = ν₁ := by simp_all [StateEq]
- have hζ₂ : ζ₂ ≃[t + 1]/ac write t ν₁ η
- calc
+ have hζ₂ : ζ₂ ≃[t + 1]/ac write t ν₁ η := calc
ζ₂ = step (Instruction.sto t) ζ₁ := by simp_all
_ = write t ζ₁.ac ζ₁ := by simp [step]
_ = write t ν₁ ζ₁ := by simp_all
@@ -350,8 +348,7 @@ theorem compiler_correctness
read (loc x map) ζ₂ = read (loc x map) (write t ν₁ η) := hζ₂ _ (ht' _)
_ = read (loc x map) η := by simp only [loc] at ht; simp [(ht _).ne]
_ = ξ x := hmap x
- have hζ₃ : ζ₃ ≃[t + 1] { write t ν₁ η with ac := ν₂ }
- calc
+ have hζ₃ : ζ₃ ≃[t + 1] { write t ν₁ η with ac := ν₂ } := calc
ζ₃ = outcome (compile map e_s₂ (t + 1)) ζ₂ := by simp_all
_ ≃[t + 1] { ζ₂ with ac := ν₂ } := by apply e_ih_s₂ <;> assumption
_ ≃[t + 1] { write t ν₁ η with ac := ν₂ } := by simp [StateEq]; apply hζ₂
@@ -361,14 +358,13 @@ theorem compiler_correctness
cases' hζ₃ with _ hζ₃
specialize hζ₃ t (Register.lt_succ_self _)
simp_all
- have hζ₄ : ζ₄ ≃[t + 1] { write t ν₁ η with ac := ν }
- calc
+ have hζ₄ : ζ₄ ≃[t + 1] { write t ν₁ η with ac := ν } := calc
ζ₄ = step (Instruction.add t) ζ₃ := by simp_all
- _ = { ζ₃ with ac := read t ζ₃ + ζ₃.ac } := by simp [step]
- _ = { ζ₃ with ac := ν } := by simp_all
- _ ≃[t + 1] { { write t ν₁ η with ac := ν₂ } with ac := ν } := by
+ _ = { ζ₃ with ac := read t ζ₃ + ζ₃.ac } := by simp [step]
+ _ = { ζ₃ with ac := ν } := by simp_all
+ _ ≃[t + 1] { { write t ν₁ η with ac := ν₂ } with ac := ν } := by
simp [StateEq] at hζ₃ ⊢; cases hζ₃; assumption
- _ ≃[t + 1] { write t ν₁ η with ac := ν } := by simp_all; rfl
+ _ ≃[t + 1] { write t ν₁ η with ac := ν } := by simp_all; rfl
apply write_eq_implies_stateEq <;> assumption
#align arithcc.compiler_correctness Arithcc.compiler_correctness
Nat
file (#9551)
Data.Nat.Basic
is currently made of two things:
I need the first ones earlier in the algebraic order hierarchy, hence the split.
@@ -3,8 +3,8 @@ Copyright (c) 2020 Xi Wang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Xi Wang
-/
+import Mathlib.Init.Data.Nat.Lemmas
import Mathlib.Order.Basic
-import Mathlib.Data.Nat.Basic
import Mathlib.Tactic.Common
#align_import arithcc from "leanprover-community/mathlib"@"eb3595ed8610db8107b75b75ab64ab6390684155"
cases x with | ...
instead of cases x; case => ...
(#9321)
This converts usages of the pattern
cases h
case inl h' => ...
case inr h' => ...
which derive from mathported code, to the "structured cases
" syntax:
cases h with
| inl h' => ...
| inr h' => ...
The case where the subgoals are handled with ·
instead of case
is more contentious (and much more numerous) so I left those alone. This pattern also appears with cases'
, induction
, induction'
, and rcases
. Furthermore, there is a similar transformation for by_cases
:
by_cases h : cond
case pos => ...
case neg => ...
is replaced by:
if h : cond then
...
else
...
Co-authored-by: Mario Carneiro <di.gama@gmail.com>
@@ -303,23 +303,21 @@ theorem write_eq_implies_stateEq {t : Register} {v : Word} {ζ₁ ζ₂ : State}
Unlike Theorem 1 in the paper, both `map` and the assumption on `t` are explicit.
-/
-theorem compiler_correctness :
- ∀ (map : Identifier → Register) (e : Expr) (ξ : Identifier → Word) (η : State) (t : Register),
- (∀ x, read (loc x map) η = ξ x) →
- (∀ x, loc x map < t) → outcome (compile map e t) η ≃[t] { η with ac := value e ξ } := by
- intro map e ξ η t hmap ht
- revert η t
- induction e <;> intro η t hmap ht
+theorem compiler_correctness
+ (map : Identifier → Register) (e : Expr) (ξ : Identifier → Word) (η : State) (t : Register)
+ (hmap : ∀ x, read (loc x map) η = ξ x) (ht : ∀ x, loc x map < t) :
+ outcome (compile map e t) η ≃[t] { η with ac := value e ξ } := by
+ induction e generalizing η t with
-- 5.I
- case const => simp [StateEq, step]; rfl
+ | const => simp [StateEq, step]; rfl
-- 5.II
- case var =>
+ | var =>
simp [hmap, StateEq, step] -- Porting note: was `finish [hmap, StateEq, step]`
constructor
· simp_all only [read, loc]
· rfl
-- 5.III
- case sum =>
+ | sum =>
rename_i e_s₁ e_s₂ e_ih_s₁ e_ih_s₂
simp
generalize value e_s₁ ξ = ν₁ at e_ih_s₁ ⊢
cases'
(#9171)
I literally went through and regex'd some uses of cases'
, replacing them with rcases
; this is meant to be a low effort PR as I hope that tools can do this in the future.
rcases
is an easier replacement than cases
, though with better tools we could in future do a second pass converting simple rcases
added here (and existing ones) to cases
.
@@ -272,7 +272,7 @@ theorem stateEq_implies_write_eq {t : Register} {ζ₁ ζ₂ : State} (h : ζ₁
constructor; · exact h.1
intro r hr
have hr : r ≤ t := Register.le_of_lt_succ hr
- cases' lt_or_eq_of_le hr with hr hr
+ rcases lt_or_eq_of_le hr with hr | hr
· cases' h with _ h
specialize h r hr
simp_all
@@ -4,7 +4,8 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Xi Wang
-/
import Mathlib.Order.Basic
-import Mathlib.Tactic.Basic
+import Mathlib.Data.Nat.Basic
+import Mathlib.Tactic.Common
#align_import arithcc from "leanprover-community/mathlib"@"eb3595ed8610db8107b75b75ab64ab6390684155"
@@ -2,15 +2,12 @@
Copyright (c) 2020 Xi Wang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Xi Wang
-
-! This file was ported from Lean 3 source module arithcc
-! leanprover-community/mathlib commit eb3595ed8610db8107b75b75ab64ab6390684155
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathlib.Order.Basic
import Mathlib.Tactic.Basic
+#align_import arithcc from "leanprover-community/mathlib"@"eb3595ed8610db8107b75b75ab64ab6390684155"
+
/-!
# A compiler for arithmetic expressions
This is the second half of the changes originally in #5699, removing all occurrences of ;
after a space and implementing a linter rule to enforce it.
In most cases this 2-character substring has a space after it, so the following command was run first:
find . -type f -name "*.lean" -exec sed -i -E 's/ ; /; /g' {} \;
The remaining cases were few enough in number that they were done manually.
@@ -352,7 +352,7 @@ theorem compiler_correctness :
intro x
calc
read (loc x map) ζ₂ = read (loc x map) (write t ν₁ η) := hζ₂ _ (ht' _)
- _ = read (loc x map) η := by simp only [loc] at ht ; simp [(ht _).ne]
+ _ = read (loc x map) η := by simp only [loc] at ht; simp [(ht _).ne]
_ = ξ x := hmap x
have hζ₃ : ζ₃ ≃[t + 1] { write t ν₁ η with ac := ν₂ }
calc
All dependencies are ported!