val valid_perm (len offset slice_len: nat) (p: P.perm) : Tot prop
let valid_perm
  (len: nat)
  (offset: nat)
  (slice_len: nat)
  (p: P.perm) : Tot prop =
  let open FStar.Real in
  ((offset + slice_len <= len /\ slice_len > 0) ==> (p.P.v <=. one))
val valid_perm (len offset slice_len: nat) (p: P.perm) : Tot prop
let valid_perm (len offset slice_len: nat) (p: P.perm) : Tot prop =
let open FStar.Real in ((offset + slice_len <= len /\ slice_len > 0) ==> (p.P.v <=. one))
Steel.ST.HigherArray.fst.checked
Steel.ST.PCMReference.fsti.checked Steel.ST.Loops.fsti.checked Steel.PCMMap.fst.checked Steel.PCMFrac.fst.checked Steel.Memory.fsti.checked prims.fst.checked FStar.SizeT.fsti.checked FStar.Seq.fst.checked FStar.Real.fsti.checked FStar.Pervasives.Native.fst.checked FStar.Pervasives.fsti.checked FStar.Map.fsti.checked FStar.Ghost.fsti.checked FStar.Classical.fsti.checked
Steel.ST.HigherArray.fst
Prims.nat Steel.FractionalPermission.perm Prims.l_imp Prims.l_and Prims.b2t Prims.op_LessThanOrEqual Prims.op_Addition Prims.op_GreaterThan FStar.Real.op_Less_Equals_Dot Steel.FractionalPermission.__proj__MkPerm__item__v FStar.Real.one Prims.prop
(*
   Copyright 2022 Microsoft Research

   Licensed under the Apache License, Version 2.0 (the "License");
   you may not use this file except in compliance with the License.
   You may obtain a copy of the License at

       http://www.apache.org/licenses/LICENSE-2.0

   Unless required by applicable law or agreed to in writing, software
   distributed under the License is distributed on an "AS IS" BASIS,
   WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
   See the License for the specific language governing permissions and
   limitations under the License.
*)

module Steel.ST.HigherArray

module P = Steel.PCMFrac
module R = Steel.ST.PCMReference
module M = FStar.Map
module PM = Steel.PCMMap

[@@noextract_to "krml"]
let index_t (len: Ghost.erased nat) : Tot Type0 =
  (i: nat { i < len })

[@@noextract_to "krml"]
let carrier (elt: Type u#a) (len: Ghost.erased nat) : Tot Type =
  PM.map (index_t len) (P.fractional elt)

[@@noextract_to "krml"]
let pcm (elt: Type u#a) (len: Ghost.erased nat) : Tot (P.pcm (carrier elt len)) =
  PM.pointwise (index_t len) (P.pcm_frac #elt)

[@@noextract_to "krml"]
let one (#elt: Type) (#len: Ghost.erased nat) = (pcm elt len).P.p.P.one
let composable (#elt: Type) (#len: Ghost.erased nat) = (pcm elt len).P.p.P.composable
[@@noextract_to "krml"]
let compose (#elt: Type) (#len: Ghost.erased nat) = (pcm elt len).P.p.P.op

[@@noextract_to "krml"]
let mk_carrier
  (#elt: Type)
  (len: nat)
  (offset: nat)
  (s: Seq.seq elt)
  (p: P.perm)
: Tot (carrier elt len)
= let f (i: nat) : Tot (P.fractional elt) =
    if offset + Seq.length s > len || i < offset || i >= offset + Seq.length s
    then None
    else Some (Seq.index s (i - offset), p)
  in
  M.map_literal f

let mk_carrier_inj
  (#elt: Type)
  (len: nat)
  (offset: nat)
  (s1 s2: Seq.seq elt)
  (p1 p2: P.perm)
: Lemma
  (requires (
    mk_carrier len offset s1 p1 == mk_carrier len offset s2 p2 /\
    offset + Seq.length s1 <= len /\
    offset + Seq.length s2 <= len
  ))
  (ensures (
    s1 `Seq.equal` s2 /\
    (Seq.length s1 > 0 ==> p1 == p2)
  ))
= assert (forall (i: nat) . i < Seq.length s1 ==>
    (M.sel (mk_carrier len offset s1 p1) (offset + i) == Some (Seq.index s1 i, p1)));
  assert (forall (i: nat) . i < Seq.length s2 ==>
     M.sel (mk_carrier len offset s2 p2) (offset + i) == Some (Seq.index s2 i, p2))

[@@erasable]
let base_t (elt: Type u#a) : Tot Type0 = Ghost.erased (base_len: US.t & ref _ (pcm elt (US.v base_len)))
let base_len (#elt: Type) (b: base_t elt) : GTot nat = US.v (dfst b)

[@@noextract_to "krml"]
noeq
type ptr (elt: Type u#a) : Type0 = {
  base_len: Ghost.erased US.t;
                   // U32.t to prove that A.read, A.write offset computation does not overflow. TODO: replace U32.t with size_t
  base: (r: ref _ (pcm elt (US.v base_len)) { core_ref_is_null r ==> US.v base_len == 0 });
  offset: (offset: nat { offset <= US.v base_len });
}
let null_ptr a = { base_len = 0sz; base = null #_ #(pcm a 0) ; offset = 0 }
let is_null_ptr p = is_null p.base
let base (#elt: Type) (p: ptr elt) : Tot (base_t elt) = (| Ghost.reveal p.base_len, p.base |)
let offset (#elt: Type) (p: ptr elt) : Ghost nat (requires True) (ensures (fun offset -> offset <= base_len (base p))) = p.offset

let ptr_base_offset_inj (#elt: Type) (p1 p2: ptr elt) : Lemma
  (requires (
    base p1 == base p2 /\
    offset p1 == offset p2
  ))
  (ensures (
    p1 == p2
  ))
= ()

let base_len_null_ptr _ = ()

let length_fits #elt a = ()

let valid_perm
  (len: nat)
  (offset: nat)
  (slice_len: nat)
val valid_perm (len offset slice_len: nat) (p: P.perm) : Tot prop
len: Prims.nat -> offset: Prims.nat -> slice_len: Prims.nat -> p: Steel.FractionalPermission.perm
  -> Prims.prop