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/- Vectors -/
import Lean
import Lean.Meta.Tactic.Simp
import Init.Data.List.Basic
import Mathlib.Tactic.RunCmd
import Mathlib.Tactic.Linarith
import Base.IList
import Base.Primitives.Scalar
import Base.Primitives.ArraySlice
import Base.Arith
import Base.Progress.Base
namespace Primitives
open Result Error
namespace alloc.vec
def Vec (α : Type u) := { l : List α // l.length ≤ Usize.max }
instance (a : Type u) : Arith.HasIntProp (Vec a) where
prop_ty := λ v => 0 ≤ v.val.len ∧ v.val.len ≤ Scalar.max ScalarTy.Usize
prop := λ ⟨ _, l ⟩ => by simp[Scalar.max, List.len_eq_length, *]
instance {α : Type u} (p : Vec α → Prop) : Arith.HasIntProp (Subtype p) where
prop_ty := λ x => p x
prop := λ x => x.property
@[simp]
abbrev Vec.length {α : Type u} (v : Vec α) : Int := v.val.len
@[simp]
abbrev Vec.v {α : Type u} (v : Vec α) : List α := v.val
example {a: Type u} (v : Vec a) : v.length ≤ Scalar.max ScalarTy.Usize := by
scalar_tac
def Vec.new (α : Type u): Vec α := ⟨ [], by apply Scalar.cMax_suffices .Usize; simp ⟩
instance (α : Type u) : Inhabited (Vec α) := by
constructor
apply Vec.new
-- TODO: very annoying that the α is an explicit parameter
def Vec.len (α : Type u) (v : Vec α) : Usize :=
Usize.ofIntCore v.val.len (by scalar_tac) (by scalar_tac)
@[simp]
theorem Vec.len_val {α : Type u} (v : Vec α) : (Vec.len α v).val = v.length :=
by rfl
-- This shouldn't be used
def Vec.push_fwd (α : Type u) (_ : Vec α) (_ : α) : Unit := ()
-- This is actually the backward function
def Vec.push (α : Type u) (v : Vec α) (x : α) : Result (Vec α)
:=
let nlen := List.length v.val + 1
if h : nlen ≤ U32.max || nlen ≤ Usize.max then
have h : nlen ≤ Usize.max := by
simp [Usize.max] at *
have hm := Usize.refined_max.property
cases h <;> cases hm <;> simp [U32.max, U64.max] at * <;> try linarith
return ⟨ List.concat v.val x, by simp at *; assumption ⟩
else
fail maximumSizeExceeded
-- This shouldn't be used
def Vec.insert_fwd (α : Type u) (v: Vec α) (i: Usize) (_: α) : Result Unit :=
if i.val < v.length then
.ret ()
else
.fail arrayOutOfBounds
-- This is actually the backward function
def Vec.insert (α : Type u) (v: Vec α) (i: Usize) (x: α) : Result (Vec α) :=
if i.val < v.length then
.ret ⟨ v.val.update i.val x, by have := v.property; simp [*] ⟩
else
.fail arrayOutOfBounds
@[pspec]
theorem Vec.insert_spec {α : Type u} (v: Vec α) (i: Usize) (x: α)
(hbound : i.val < v.length) :
∃ nv, v.insert α i x = ret nv ∧ nv.val = v.val.update i.val x := by
simp [insert, *]
def Vec.index_usize {α : Type u} (v: Vec α) (i: Usize) : Result α :=
match v.val.indexOpt i.val with
| none => fail .arrayOutOfBounds
| some x => ret x
/- In the theorems below: we don't always need the `∃ ..`, but we use one
so that `progress` introduces an opaque variable and an equality. This
helps control the context.
-/
@[pspec]
theorem Vec.index_usize_spec {α : Type u} [Inhabited α] (v: Vec α) (i: Usize)
(hbound : i.val < v.length) :
∃ x, v.index_usize i = ret x ∧ x = v.val.index i.val := by
simp only [index_usize]
-- TODO: dependent rewrite
have h := List.indexOpt_eq_index v.val i.val (by scalar_tac) (by simp [*])
simp [*]
def Vec.update_usize {α : Type u} (v: Vec α) (i: Usize) (x: α) : Result (Vec α) :=
match v.val.indexOpt i.val with
| none => fail .arrayOutOfBounds
| some _ =>
.ret ⟨ v.val.update i.val x, by have := v.property; simp [*] ⟩
@[pspec]
theorem Vec.update_usize_spec {α : Type u} (v: Vec α) (i: Usize) (x : α)
(hbound : i.val < v.length) :
∃ nv, v.update_usize i x = ret nv ∧
nv.val = v.val.update i.val x
:= by
simp only [update_usize]
have h := List.indexOpt_bounds v.val i.val
split
. simp_all [length]; cases h <;> scalar_tac
. simp_all
def Vec.index_mut_usize {α : Type u} (v: Vec α) (i: Usize) :
Result (α × (α → Result (Vec α))) :=
match Vec.index_usize v i with
| ret x =>
ret (x, Vec.update_usize v i)
| fail e => fail e
| div => div
@[pspec]
theorem Vec.index_mut_usize_spec {α : Type u} [Inhabited α] (v: Vec α) (i: Usize)
(hbound : i.val < v.length) :
∃ x back, v.index_mut_usize i = ret (x, back) ∧
x = v.val.index i.val ∧
-- Backward function
back = v.update_usize i
:= by
simp only [index_mut_usize]
have ⟨ x, h ⟩ := index_usize_spec v i hbound
simp [h]
/- [alloc::vec::Vec::index]: forward function -/
def Vec.index (T I : Type) (inst : core.slice.index.SliceIndex I (Slice T))
(self : Vec T) (i : I) : Result inst.Output :=
sorry -- TODO
/- [alloc::vec::Vec::index_mut]: forward function -/
def Vec.index_mut (T I : Type) (inst : core.slice.index.SliceIndex I (Slice T))
(self : Vec T) (i : I) :
Result (inst.Output × (inst.Output → Result (Vec T))) :=
sorry -- TODO
/- Trait implementation: [alloc::vec::Vec] -/
def Vec.coreopsindexIndexInst (T I : Type)
(inst : core.slice.index.SliceIndex I (Slice T)) :
core.ops.index.Index (alloc.vec.Vec T) I := {
Output := inst.Output
index := Vec.index T I inst
}
/- Trait implementation: [alloc::vec::Vec] -/
def Vec.coreopsindexIndexMutInst (T I : Type)
(inst : core.slice.index.SliceIndex I (Slice T)) :
core.ops.index.IndexMut (alloc.vec.Vec T) I := {
indexInst := Vec.coreopsindexIndexInst T I inst
index_mut := Vec.index_mut T I inst
}
@[simp]
theorem Vec.index_slice_index {α : Type} (v : Vec α) (i : Usize) :
Vec.index α Usize (core.slice.index.SliceIndexUsizeSliceTInst α) v i =
Vec.index_usize v i :=
sorry
@[simp]
theorem Vec.index_mut_slice_index {α : Type} (v : Vec α) (i : Usize) :
Vec.index_mut α Usize (core.slice.index.SliceIndexUsizeSliceTInst α) v i =
index_mut_usize v i :=
sorry
end alloc.vec
end Primitives
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