From fb2e5e5555503a29728ca42c0553b0bf8230fa5f Mon Sep 17 00:00:00 2001 From: Leonardo de Moura Date: Tue, 11 Feb 2025 18:14:00 -0800 Subject: [PATCH] chore: remove dead code from `Nat/Linear.lean` (#7042) --- src/Init/Data/Nat/Linear.lean | 169 ------------------------------- tests/lean/run/linearByRefl.lean | 7 -- 2 files changed, 176 deletions(-) diff --git a/src/Init/Data/Nat/Linear.lean b/src/Init/Data/Nat/Linear.lean index 3100e065e7..195b6c6ed9 100644 --- a/src/Init/Data/Nat/Linear.lean +++ b/src/Init/Data/Nat/Linear.lean @@ -66,18 +66,6 @@ where | [] => r | (k, v) :: p => go p (r.insert k v) -def Poly.mul (k : Nat) (p : Poly) : Poly := - bif k == 0 then - [] - else bif k == 1 then - p - else - go p -where - go : Poly → Poly - | [] => [] - | (k', v) :: p => (Nat.mul k k', v) :: go p - def Poly.cancelAux (fuel : Nat) (m₁ m₂ r₁ r₂ : Poly) : Poly × Poly := match fuel with | 0 => (r₁.reverse ++ m₁, r₂.reverse ++ m₂) @@ -122,24 +110,6 @@ def Poly.denote_eq (ctx : Context) (mp : Poly × Poly) : Prop := mp.1.denote ctx def Poly.denote_le (ctx : Context) (mp : Poly × Poly) : Prop := mp.1.denote ctx ≤ mp.2.denote ctx -def Poly.combineAux (fuel : Nat) (p₁ p₂ : Poly) : Poly := - match fuel with - | 0 => p₁ ++ p₂ - | fuel + 1 => - match p₁, p₂ with - | p₁, [] => p₁ - | [], p₂ => p₂ - | (k₁, v₁) :: p₁, (k₂, v₂) :: p₂ => - bif Nat.blt v₁ v₂ then - (k₁, v₁) :: combineAux fuel p₁ ((k₂, v₂) :: p₂) - else bif Nat.blt v₂ v₁ then - (k₂, v₂) :: combineAux fuel ((k₁, v₁) :: p₁) p₂ - else - (Nat.add k₁ k₂, v₁) :: combineAux fuel p₁ p₂ - -def Poly.combine (p₁ p₂ : Poly) : Poly := - combineAux hugeFuel p₁ p₂ - def Expr.toPoly (e : Expr) := go 1 e [] where @@ -178,13 +148,6 @@ instance : LawfulBEq PolyCnstr where show (eq == eq && (lhs == lhs && rhs == rhs)) = true simp [LawfulBEq.rfl] -def PolyCnstr.mul (k : Nat) (c : PolyCnstr) : PolyCnstr := - { c with lhs := c.lhs.mul k, rhs := c.rhs.mul k } - -def PolyCnstr.combine (c₁ c₂ : PolyCnstr) : PolyCnstr := - let (lhs, rhs) := Poly.cancel (c₁.lhs.combine c₂.lhs) (c₁.rhs.combine c₂.rhs) - { eq := c₁.eq && c₂.eq, lhs, rhs } - structure ExprCnstr where eq : Bool lhs : Expr @@ -225,23 +188,6 @@ def ExprCnstr.toNormPoly (c : ExprCnstr) : PolyCnstr := let (lhs, rhs) := Poly.cancel c.lhs.toNormPoly c.rhs.toNormPoly { c with lhs, rhs } -abbrev Certificate := List (Nat × ExprCnstr) - -def Certificate.combineHyps (c : PolyCnstr) (hs : Certificate) : PolyCnstr := - match hs with - | [] => c - | (k, c') :: hs => combineHyps (PolyCnstr.combine c (c'.toNormPoly.mul (Nat.add k 1))) hs - -def Certificate.combine (hs : Certificate) : PolyCnstr := - match hs with - | [] => { eq := true, lhs := [], rhs := [] } - | (k, c) :: hs => combineHyps (c.toNormPoly.mul (Nat.add k 1)) hs - -def Certificate.denote (ctx : Context) (c : Certificate) : Prop := - match c with - | [] => False - | (_, c)::hs => c.denote ctx → denote ctx hs - def monomialToExpr (k : Nat) (v : Var) : Expr := bif v == fixedVar then .num k @@ -265,7 +211,6 @@ def PolyCnstr.toExpr (c : PolyCnstr) : ExprCnstr := attribute [local simp] Nat.add_comm Nat.add_assoc Nat.add_left_comm Nat.right_distrib Nat.left_distrib Nat.mul_assoc Nat.mul_comm attribute [local simp] Poly.denote Expr.denote Poly.insert Poly.norm Poly.norm.go Poly.cancelAux -attribute [local simp] Poly.mul Poly.mul.go theorem Poly.denote_insert (ctx : Context) (k : Nat) (v : Var) (p : Poly) : (p.insert k v).denote ctx = p.denote ctx + k * v.denote ctx := by @@ -320,21 +265,11 @@ theorem Poly.denote_reverse (ctx : Context) (p : Poly) : denote ctx (List.revers attribute [local simp] Poly.denote_reverse -theorem Poly.denote_mul (ctx : Context) (k : Nat) (p : Poly) : (p.mul k).denote ctx = k * p.denote ctx := by - simp - by_cases h : k == 0 <;> simp [h]; simp [eq_of_beq h] - by_cases h : k == 1 <;> simp [h]; simp [eq_of_beq h] - induction p with - | nil => simp - | cons kv m ih => cases kv with | _ k' v => simp [ih] - private theorem eq_of_not_blt_eq_true (h₁ : ¬ (Nat.blt x y = true)) (h₂ : ¬ (Nat.blt y x = true)) : x = y := have h₁ : ¬ x < y := fun h => h₁ (Nat.blt_eq.mpr h) have h₂ : ¬ y < x := fun h => h₂ (Nat.blt_eq.mpr h) Nat.le_antisymm (Nat.ge_of_not_lt h₂) (Nat.ge_of_not_lt h₁) -attribute [local simp] Poly.denote_mul - theorem Poly.denote_eq_cancelAux (ctx : Context) (fuel : Nat) (m₁ m₂ r₁ r₂ : Poly) (h : denote_eq ctx (r₁.reverse ++ m₁, r₂.reverse ++ m₂)) : denote_eq ctx (cancelAux fuel m₁ m₂ r₁ r₂) := by induction fuel generalizing m₁ m₂ r₁ r₂ with @@ -493,21 +428,6 @@ theorem Poly.denote_le_cancel_eq (ctx : Context) (m₁ m₂ : Poly) : denote_le attribute [local simp] Poly.denote_le_cancel_eq -theorem Poly.denote_combineAux (ctx : Context) (fuel : Nat) (p₁ p₂ : Poly) : (p₁.combineAux fuel p₂).denote ctx = p₁.denote ctx + p₂.denote ctx := by - induction fuel generalizing p₁ p₂ with simp [combineAux] - | succ fuel ih => - split <;> simp - rename_i k₁ v₁ p₁ k₂ v₂ p₂ - by_cases hltv : Nat.blt v₁ v₂ <;> simp [hltv, ih] - by_cases hgtv : Nat.blt v₂ v₁ <;> simp [hgtv, ih] - have heqv : v₁ = v₂ := eq_of_not_blt_eq_true hltv hgtv - simp [heqv] - -theorem Poly.denote_combine (ctx : Context) (p₁ p₂ : Poly) : (p₁.combine p₂).denote ctx = p₁.denote ctx + p₂.denote ctx := by - simp [combine, denote_combineAux] - -attribute [local simp] Poly.denote_combine - theorem Expr.denote_toPoly_go (ctx : Context) (e : Expr) : (toPoly.go k e p).denote ctx = k * e.denote ctx + p.denote ctx := by induction k, e using Expr.toPoly.go.induct generalizing p with @@ -572,51 +492,6 @@ theorem ExprCnstr.denote_toNormPoly (ctx : Context) (c : ExprCnstr) : c.toNormPo attribute [local simp] ExprCnstr.denote_toNormPoly -theorem Poly.mul.go_denote (ctx : Context) (k : Nat) (p : Poly) : (Poly.mul.go k p).denote ctx = k * p.denote ctx := by - match p with - | [] => rfl - | (k', v) :: p => simp [Poly.mul.go, go_denote] - -attribute [local simp] Poly.mul.go_denote - -section -attribute [-simp] Nat.right_distrib Nat.left_distrib - -theorem PolyCnstr.denote_mul (ctx : Context) (k : Nat) (c : PolyCnstr) : (c.mul (k+1)).denote ctx = c.denote ctx := by - cases c; rename_i eq lhs rhs - have : k ≠ 0 → k + 1 ≠ 1 := by intro h; match k with | 0 => contradiction | k+1 => simp [Nat.succ.injEq] - have : ¬ (k == 0) → (k + 1 == 1) = false := fun h => beq_false_of_ne (this (ne_of_beq_false (Bool.of_not_eq_true h))) - have : ¬ ((k + 1 == 0) = true) := fun h => absurd (eq_of_beq h) (Nat.succ_ne_zero k) - by_cases he : eq = true <;> simp [he, PolyCnstr.mul, PolyCnstr.denote, Poly.denote_le, Poly.denote_eq] - <;> by_cases hk : k == 0 <;> (try simp [eq_of_beq hk]) <;> simp [*] <;> apply Iff.intro <;> intro h - · exact Nat.eq_of_mul_eq_mul_left (Nat.zero_lt_succ _) h - · rw [h] - · exact Nat.le_of_mul_le_mul_left h (Nat.zero_lt_succ _) - · apply Nat.mul_le_mul_left _ h - -end - -attribute [local simp] PolyCnstr.denote_mul - -theorem PolyCnstr.denote_combine {ctx : Context} {c₁ c₂ : PolyCnstr} (h₁ : c₁.denote ctx) (h₂ : c₂.denote ctx) : (c₁.combine c₂).denote ctx := by - cases c₁; cases c₂; rename_i eq₁ lhs₁ rhs₁ eq₂ lhs₂ rhs₂ - simp [denote] at h₁ h₂ - simp [PolyCnstr.combine, denote] - by_cases he₁ : eq₁ = true <;> by_cases he₂ : eq₂ = true <;> simp [he₁, he₂] at h₁ h₂ |- - · rw [Poly.denote_eq_cancel_eq]; simp [Poly.denote_eq] at h₁ h₂ |-; simp [h₁, h₂] - · rw [Poly.denote_le_cancel_eq]; simp [Poly.denote_eq, Poly.denote_le] at h₁ h₂ |-; rw [h₁]; apply Nat.add_le_add_left h₂ - · rw [Poly.denote_le_cancel_eq]; simp [Poly.denote_eq, Poly.denote_le] at h₁ h₂ |-; rw [h₂]; apply Nat.add_le_add_right h₁ - · rw [Poly.denote_le_cancel_eq]; simp [Poly.denote_eq, Poly.denote_le] at h₁ h₂ |-; apply Nat.add_le_add h₁ h₂ - -attribute [local simp] PolyCnstr.denote_combine - -theorem Poly.isNum?_eq_some (ctx : Context) {p : Poly} {k : Nat} : p.isNum? = some k → p.denote ctx = k := by - simp [isNum?] - split - next => intro h; injection h - next k v => by_cases h : v == fixedVar <;> simp [h]; intros; simp [Var.denote, eq_of_beq h]; assumption - next => intros; contradiction - theorem Poly.of_isZero (ctx : Context) {p : Poly} (h : isZero p = true) : p.denote ctx = 0 := by simp [isZero] at h split at h @@ -662,50 +537,6 @@ theorem ExprCnstr.eq_true_of_isValid (ctx : Context) (c : ExprCnstr) (h : c.toNo simp [-eq_iff_iff] at this assumption -theorem Certificate.of_combineHyps (ctx : Context) (c : PolyCnstr) (cs : Certificate) (h : (combineHyps c cs).denote ctx → False) : c.denote ctx → cs.denote ctx := by - match cs with - | [] => simp [combineHyps, denote] at *; exact h - | (k, c')::cs => - intro h₁ h₂ - have := PolyCnstr.denote_combine (ctx := ctx) (c₂ := PolyCnstr.mul (k + 1) (ExprCnstr.toNormPoly c')) h₁ - simp at this - have := this h₂ - have ih := of_combineHyps ctx (PolyCnstr.combine c (PolyCnstr.mul (k + 1) (ExprCnstr.toNormPoly c'))) cs - exact ih h this - -theorem Certificate.of_combine (ctx : Context) (cs : Certificate) (h : cs.combine.denote ctx → False) : cs.denote ctx := by - match cs with - | [] => simp [combine, PolyCnstr.denote, Poly.denote_eq] at h - | (k, c)::cs => - simp [denote, combine] at * - intro h' - apply of_combineHyps (h := h) - simp [h'] - -theorem Certificate.of_combine_isUnsat (ctx : Context) (cs : Certificate) (h : cs.combine.isUnsat) : cs.denote ctx := - have h := PolyCnstr.eq_false_of_isUnsat ctx h - of_combine ctx cs (fun h' => Eq.mp h h') - -theorem denote_monomialToExpr (ctx : Context) (k : Nat) (v : Var) : (monomialToExpr k v).denote ctx = k * v.denote ctx := by - simp [monomialToExpr] - by_cases h : v == fixedVar <;> simp [h, Expr.denote] - · simp [eq_of_beq h, Var.denote] - · by_cases h : k == 1 <;> simp [h, Expr.denote]; simp [eq_of_beq h] - -attribute [local simp] denote_monomialToExpr - -theorem Poly.denote_toExpr_go (ctx : Context) (e : Expr) (p : Poly) : (toExpr.go e p).denote ctx = e.denote ctx + p.denote ctx := by - induction p generalizing e with - | nil => simp [toExpr.go, Poly.denote] - | cons kv p ih => cases kv; simp [toExpr.go, ih, Expr.denote, Poly.denote] - -attribute [local simp] Poly.denote_toExpr_go - -theorem Poly.denote_toExpr (ctx : Context) (p : Poly) : p.toExpr.denote ctx = p.denote ctx := by - match p with - | [] => simp [toExpr, Expr.denote, Poly.denote] - | (k, v) :: p => simp [toExpr, Expr.denote, Poly.denote] - theorem ExprCnstr.eq_of_toNormPoly_eq (ctx : Context) (c d : ExprCnstr) (h : c.toNormPoly == d.toPoly) : c.denote ctx = d.denote ctx := by have h := congrArg (PolyCnstr.denote ctx) (eq_of_beq h) simp [-eq_iff_iff] at h diff --git a/tests/lean/run/linearByRefl.lean b/tests/lean/run/linearByRefl.lean index 2d95e03992..14fed4bea7 100644 --- a/tests/lean/run/linearByRefl.lean +++ b/tests/lean/run/linearByRefl.lean @@ -42,13 +42,6 @@ example (x₁ x₂ x₃ : Nat) : ((x₁ + x₂) + (x₂ + x₃) < x₃ + x₂) = (Expr.num 0) rfl -example (x₁ x₂ : Nat) : x₁ + 2 ≤ 3*x₂ → 4*x₂ ≤ 3 + x₁ → 3 ≤ 2*x₂ → False := - Certificate.of_combine_isUnsat #R[x₁, x₂] - [ (1, { eq := false, lhs := Expr.add (Expr.var 0) (Expr.num 2), rhs := Expr.mulL 3 (Expr.var 1) }), - (1, { eq := false, lhs := Expr.mulL 4 (Expr.var 1), rhs := Expr.add (Expr.num 3) (Expr.var 0) }), - (0, { eq := false, lhs := Expr.num 3, rhs := Expr.mulL 2 (Expr.var 1) }) ] - rfl - example (x : Nat) (xs : List Nat) : (sizeOf x < 1 + (1 + sizeOf x + sizeOf xs)) = True := ExprCnstr.eq_true_of_isValid #R[sizeOf x, sizeOf xs] { eq := false, lhs := Expr.inc (Expr.var 0), rhs := Expr.add (Expr.num 1) (Expr.add (Expr.add (Expr.num 1) (Expr.var 0)) (Expr.var 1)) }