c7939cfb03
This PR implements support for offset constraints in the `grind` tactic. Several features are still missing, such as constraint propagation and support for offset equalities, but `grind` can already solve examples like the following: ```lean example (a b c : Nat) : a ≤ b → b + 2 ≤ c → a + 1 ≤ c := by grind example (a b c : Nat) : a ≤ b → b ≤ c → a ≤ c := by grind example (a b c : Nat) : a + 1 ≤ b → b + 1 ≤ c → a + 2 ≤ c := by grind example (a b c : Nat) : a + 1 ≤ b → b + 1 ≤ c → a + 1 ≤ c := by grind example (a b c : Nat) : a + 1 ≤ b → b ≤ c + 2 → a ≤ c + 1 := by grind example (a b c : Nat) : a + 2 ≤ b → b ≤ c + 2 → a ≤ c := by grind ``` --------- Co-authored-by: Kim Morrison <scott.morrison@gmail.com>
117 lines
3.6 KiB
Text
117 lines
3.6 KiB
Text
/-
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Copyright (c) 2019 Microsoft Corporation. All rights reserved.
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Released under Apache 2.0 license as described in the file LICENSE.
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Author: Leonardo de Moura
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-/
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prelude
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import Init.Control.Id
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import Init.Data.List.Impl
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universe u v w w'
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namespace Lean
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/-- List-like type to avoid extra level of indirection -/
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inductive AssocList (α : Type u) (β : Type v) where
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| nil : AssocList α β
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| cons (key : α) (value : β) (tail : AssocList α β) : AssocList α β
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deriving Inhabited
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namespace AssocList
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variable {α : Type u} {β : Type v} {δ : Type w} {m : Type w → Type w} [Monad m]
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abbrev empty : AssocList α β :=
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nil
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instance : EmptyCollection (AssocList α β) := ⟨empty⟩
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abbrev insertNew (m : AssocList α β) (k : α) (v : β) : AssocList α β :=
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m.cons k v
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def isEmpty : AssocList α β → Bool
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| nil => true
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| _ => false
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@[specialize] def foldlM (f : δ → α → β → m δ) : (init : δ) → AssocList α β → m δ
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| d, nil => pure d
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| d, cons a b es => do
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let d ← f d a b
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foldlM f d es
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@[inline] def foldl (f : δ → α → β → δ) (init : δ) (as : AssocList α β) : δ :=
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Id.run (foldlM f init as)
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def toList (as : AssocList α β) : List (α × β) :=
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as.foldl (init := []) (fun r a b => (a, b)::r) |>.reverse
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@[specialize] def forM (f : α → β → m PUnit) : AssocList α β → m PUnit
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| nil => pure ⟨⟩
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| cons a b es => do f a b; forM f es
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def mapKey (f : α → δ) : AssocList α β → AssocList δ β
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| nil => nil
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| cons k v t => cons (f k) v (mapKey f t)
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def mapVal (f : β → δ) : AssocList α β → AssocList α δ
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| nil => nil
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| cons k v t => cons k (f v) (mapVal f t)
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def findEntry? [BEq α] (a : α) : AssocList α β → Option (α × β)
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| nil => none
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| cons k v es => match k == a with
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| true => some (k, v)
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| false => findEntry? a es
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def find? [BEq α] (a : α) : AssocList α β → Option β
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| nil => none
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| cons k v es => match k == a with
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| true => some v
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| false => find? a es
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def contains [BEq α] (a : α) : AssocList α β → Bool
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| nil => false
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| cons k _ es => k == a || contains a es
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def replace [BEq α] (a : α) (b : β) : AssocList α β → AssocList α β
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| nil => nil
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| cons k v es => match k == a with
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| true => cons a b es
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| false => cons k v (replace a b es)
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def insert [BEq α] (m : AssocList α β) (k : α) (v : β) : AssocList α β :=
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if m.contains k then
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m.replace k v
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else
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m.insertNew k v
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def erase [BEq α] (a : α) : AssocList α β → AssocList α β
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| nil => nil
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| cons k v es => match k == a with
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| true => es
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| false => cons k v (erase a es)
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def any (p : α → β → Bool) : AssocList α β → Bool
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| nil => false
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| cons k v es => p k v || any p es
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def all (p : α → β → Bool) : AssocList α β → Bool
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| nil => true
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| cons k v es => p k v && all p es
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@[inline] protected def forIn {α : Type u} {β : Type v} {δ : Type w} {m : Type w → Type w'} [Monad m]
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(as : AssocList α β) (init : δ) (f : (α × β) → δ → m (ForInStep δ)) : m δ :=
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let rec @[specialize] loop
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| d, nil => pure d
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| d, cons k v es => do
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match (← f (k, v) d) with
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| ForInStep.done d => pure d
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| ForInStep.yield d => loop d es
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loop init as
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instance : ForIn m (AssocList α β) (α × β) where
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forIn := AssocList.forIn
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end Lean.AssocList
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def List.toAssocList' {α : Type u} {β : Type v} : List (α × β) → Lean.AssocList α β
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| [] => Lean.AssocList.nil
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| (a,b) :: es => Lean.AssocList.cons a b (toAssocList' es)
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