val loop_range_nospec:
    #h0:mem
  -> #a:Type0
  -> #len:size_t
  -> start:size_t
  -> n:size_t{v start + v n <= max_size_t}
  -> buf:lbuffer a len
  -> impl: (i:size_t{v start <= v i /\ v i < v start + v n} -> Stack unit
      (requires fun h -> modifies1 buf h0 h)
      (ensures  fun _ _ h1 -> modifies1 buf h0 h1)) ->
  Stack unit
    (requires fun h -> h0 == h /\ live h0 buf)
    (ensures  fun _ _ h1 -> modifies1 buf h0 h1)
let loop_range_nospec #h0 #a #len start n buf impl =
  let inv h1 j = modifies (loc buf) h0 h1 in
  Lib.Loops.for start (start +. n) inv impl
val loop_range_nospec:
    #h0:mem
  -> #a:Type0
  -> #len:size_t
  -> start:size_t
  -> n:size_t{v start + v n <= max_size_t}
  -> buf:lbuffer a len
  -> impl: (i:size_t{v start <= v i /\ v i < v start + v n} -> Stack unit
      (requires fun h -> modifies1 buf h0 h)
      (ensures  fun _ _ h1 -> modifies1 buf h0 h1)) ->
  Stack unit
    (requires fun h -> h0 == h /\ live h0 buf)
    (ensures  fun _ _ h1 -> modifies1 buf h0 h1)
let loop_range_nospec #h0 #a #len start n buf impl =
let inv h1 j = modifies (loc buf) h0 h1 in
Lib.Loops.for start (start +. n) inv impl
Lib.Buffer.fst.checked
prims.fst.checked LowStar.ImmutableBuffer.fst.checked LowStar.BufferOps.fst.checked LowStar.Buffer.fst.checked Lib.Sequence.fst.checked Lib.RawIntTypes.fsti.checked Lib.Memzero0.fsti.checked Lib.Loops.fsti.checked Lib.LoopCombinators.fst.checked Lib.IntTypes.fsti.checked Lib.ByteSequence.fsti.checked FStar.UInt32.fsti.checked FStar.Seq.fst.checked FStar.Pervasives.Native.fst.checked FStar.Pervasives.fsti.checked FStar.Mul.fst.checked FStar.Monotonic.HyperHeap.fsti.checked FStar.Math.Lemmas.fst.checked FStar.HyperStack.ST.fsti.checked FStar.HyperStack.fst.checked
Lib.Buffer.fst
FStar.Monotonic.HyperStack.mem Lib.IntTypes.size_t Prims.b2t Prims.op_LessThanOrEqual Prims.op_Addition Lib.IntTypes.v Lib.IntTypes.U32 Lib.IntTypes.PUB Lib.IntTypes.max_size_t Lib.Buffer.lbuffer Prims.l_and Prims.op_LessThan Prims.unit Lib.Buffer.modifies1 Lib.Loops.for Lib.IntTypes.op_Plus_Dot Prims.nat Lib.IntTypes.add_mod Lib.Buffer.modifies Lib.Buffer.loc Lib.Buffer.MUT
module Lib.Buffer

open FStar.Mul

open Lib.IntTypes
open Lib.RawIntTypes

friend Lib.Sequence
friend Lib.LoopCombinators

module B = LowStar.Buffer
module IB = LowStar.ImmutableBuffer
module U32 = FStar.UInt32
module ST = FStar.HyperStack.ST
module HS = FStar.HyperStack
module Seq = Lib.Sequence
module ByteSeq = Lib.ByteSequence

#reset-options "--z3rlimit 350 --max_fuel 0 --max_ifuel 0"

let modifies_includes l1 l2 h0 h1 = ()
let modifies_trans l1 l2 h0 h1 h2 = ()
let live_sub #t #a #len b start n h = ()
let modifies_sub #t #a #len b start n h0 h1 = ()

let as_seq_gsub #t #a #len h b start n = ()

let sub #t #a #len b start n =
  match t with
  | MUT -> B.sub (b <: buffer a) start n
  | IMMUT -> IB.isub (b <: ibuffer a) start n
  | CONST -> CB.sub (b <: cbuffer a) start n

let index #t #a #len b i =
  match t with
  | MUT -> B.index (b <: buffer a) i
  | IMMUT -> IB.index (b <: ibuffer a) i
  | CONST -> CB.index (b <: cbuffer a) i

let upd #a #len b i v =
  let h0 = ST.get() in
  B.upd (b <: buffer a) i v;
  let h1 = ST.get() in
  assert (B.modifies (loc b) h0 h1);
  assert (modifies (loc b) h0 h1)

let bget_as_seq #t #a #len h b i = ()

let recall #t #a #len b =
  match t with
  | IMMUT -> B.recall (b <: ibuffer a)
  | MUT -> B.recall (b <: buffer a)
  | CONST -> B.recall (CB.cast (b <: cbuffer a))

let create #a clen init =
  B.alloca init (normalize_term clen)

#set-options "--max_fuel 1"

let createL #a init =
  B.alloca_of_list init

let createL_global #a init =
  CB.of_ibuffer (IB.igcmalloc_of_list #a root init)

let createL_mglobal #a init =
  B.mgcmalloc_of_list #a FStar.Monotonic.HyperHeap.root init

let recall_contents #a #len b s =
  B.recall_p (CB.to_ibuffer b) (cpred s)

(* JP: why triplicate the code? would it not extract if we just cast i to a monotonic buffer?! *)
let copy #t #a #len o i =
  match t with
  | MUT ->
    let h0 = ST.get () in
    LowStar.BufferOps.blit (i <: buffer a) 0ul (o <: buffer a) 0ul len;
    let h1 = ST.get () in
    assert (Seq.slice (as_seq h1 o) 0 (v len) == Seq.slice (as_seq h0 i) 0 (v len))
  | IMMUT ->
    let h0 = ST.get () in
    LowStar.BufferOps.blit (i <: ibuffer a) 0ul (o <: buffer a) 0ul len;
    let h1 = ST.get () in
    assert (Seq.slice (as_seq h1 o) 0 (v len) == Seq.slice (as_seq h0 i) 0 (v len))
  | CONST ->
    let h0 = ST.get () in
    LowStar.BufferOps.blit (CB.cast (i <: cbuffer a)) 0ul (o <: buffer a) 0ul len;
    let h1 = ST.get () in
    assert (Seq.slice (as_seq h1 o) 0 (v len) == Seq.slice (as_seq h0 i) 0 (v len))

let memset #a #blen b init len =
  B.fill #a #(fun _ _ -> True) #(fun _ _ -> True) b init len

#set-options "--max_fuel 0"

let update_sub #t #a #len dst start n src =
  match t with
  | MUT ->
      let h0 = ST.get () in
      LowStar.BufferOps.blit (src <: buffer a)
        0ul (dst <: buffer a) (size_to_UInt32 start) (size_to_UInt32 n);
      let h1 = ST.get () in
      assert (forall (k:nat{k < v n}). bget h1 dst (v start + k) == bget h0 src k);
      FStar.Seq.lemma_eq_intro
        (as_seq h1 dst)
        (Seq.update_sub #a #(v len) (as_seq h0 dst) (v start) (v n) (as_seq h0 src))
  | IMMUT ->
      let h0 = ST.get () in
      LowStar.BufferOps.blit (src <: ibuffer a)
        0ul (dst <: buffer a) (size_to_UInt32 start) (size_to_UInt32 n);
      let h1 = ST.get () in
      assert (forall (k:nat{k < v n}). bget h1 dst (v start + k) == bget h0 src k);
      FStar.Seq.lemma_eq_intro
        (as_seq h1 dst)
        (Seq.update_sub #a #(v len) (as_seq h0 dst) (v start) (v n) (as_seq h0 src))
  | CONST ->
      let h0 = ST.get () in
      LowStar.BufferOps.blit (CB.cast (src <: cbuffer a))
        0ul (dst <: buffer a) (size_to_UInt32 start) (size_to_UInt32 n);
      let h1 = ST.get () in
      assert (forall (k:nat{k < v n}). bget h1 dst (v start + k) == bget h0 src k);
      FStar.Seq.lemma_eq_intro
        (as_seq h1 dst)
        (Seq.update_sub #a #(v len) (as_seq h0 dst) (v start) (v n) (as_seq h0 src))

let update_sub_f #a #len h0 buf start n spec f =
  let tmp = sub buf start n in
  let h0 = ST.get () in
  f ();
  let h1 = ST.get () in
  assert (v (len -! (start +! n)) == v len - v (start +! n));
  B.modifies_buffer_elim (B.gsub #a buf 0ul start) (loc tmp) h0 h1;
  B.modifies_buffer_elim (B.gsub #a buf (start +! n) (len -! (start +! n))) (loc tmp) h0 h1;
  Sequence.lemma_update_sub (as_seq h0 buf) (v start) (v n) (spec h0) (as_seq h1 buf)

let concat2 #a #t0 #t1 len0 s0 len1 s1 s =
  let h0 = ST.get () in
  update_sub s (size 0) len0 s0;
  update_sub s len0 len1 s1;
  let h1 = ST.get () in
  Seq.eq_intro (Seq.sub (as_seq h1 s) 0 (v len0)) (as_seq h0 s0);
  Seq.lemma_concat2 (v len0) (as_seq h0 s0) (v len1) (as_seq h0 s1) (as_seq h1 s)

let concat3 #a #t0 #t1 #t2 len0 s0 len1 s1 len2 s2 s =
  let h0 = ST.get () in
  update_sub s (size 0) len0 s0;
  update_sub s len0 len1 s1;
  let h1 = ST.get () in
  Seq.eq_intro (Seq.sub (as_seq h1 s) 0 (v len0)) (as_seq h0 s0);
  update_sub s (len0 +! len1) len2 s2;
  let h2 = ST.get () in
  Seq.eq_intro (Seq.sub (as_seq h2 s) 0 (v len0)) (as_seq h0 s0);
  Seq.eq_intro (Seq.sub (as_seq h2 s) (v len0) (v len1)) (as_seq h0 s1);
  Seq.lemma_concat3 (v len0) (as_seq h0 s0) (v len1) (as_seq h0 s1) (v len2) (as_seq h0 s2) (as_seq h2 s)

let loop_nospec #h0 #a #len n buf impl =
  let inv h1 j = modifies (loc buf) h0 h1 in
  Lib.Loops.for (size 0) n inv impl

let loop_nospec2 #h0 #a1 #a2 #len1 #len2 n buf1 buf2 impl =
  let inv h1 j = modifies (union (loc buf1) (loc buf2)) h0 h1 in
  Lib.Loops.for (size 0) n inv impl

let loop_nospec3 #h0 #a1 #a2 #a3 #len1 #len2 #len3 n buf1 buf2 buf3 impl =
  let inv h1 j = modifies (union (loc buf3) (union (loc buf1) (loc buf2))) h0 h1 in
  Lib.Loops.for (size 0) n inv impl
val loop_range_nospec:
    #h0:mem
  -> #a:Type0
  -> #len:size_t
  -> start:size_t
  -> n:size_t{v start + v n <= max_size_t}
  -> buf:lbuffer a len
  -> impl: (i:size_t{v start <= v i /\ v i < v start + v n} -> Stack unit
      (requires fun h -> modifies1 buf h0 h)
      (ensures  fun _ _ h1 -> modifies1 buf h0 h1)) ->
  Stack unit
    (requires fun h -> h0 == h /\ live h0 buf)
    (ensures  fun _ _ h1 -> modifies1 buf h0 h1)

    start: Lib.IntTypes.size_t ->
    n: Lib.IntTypes.size_t{Lib.IntTypes.v start + Lib.IntTypes.v n <= Lib.IntTypes.max_size_t} ->
    buf: Lib.Buffer.lbuffer a len ->
    impl:
      (
            i:
              Lib.IntTypes.size_t
                { Lib.IntTypes.v start <= Lib.IntTypes.v i /\
                  Lib.IntTypes.v i < Lib.IntTypes.v start + Lib.IntTypes.v n }
          -> FStar.HyperStack.ST.Stack Prims.unit)
  -> FStar.HyperStack.ST.Stack Prims.unit