val bind (a:Type) (b:Type)
  (#framed_f:eqtype_as_type bool)
  (#framed_g:eqtype_as_type bool)
  (#[@@@ framing_implicit] pre_f:pre_t)
  (#[@@@ framing_implicit] post_f:post_t a)
  (#[@@@ framing_implicit] req_f:pure_pre)
  (#[@@@ framing_implicit] ens_f:pure_post a)
  (#[@@@ framing_implicit] pre_g:a -> pre_t)
  (#[@@@ framing_implicit] post_g:a -> post_t b)
  (#[@@@ framing_implicit] req_g:a -> pure_pre)
  (#[@@@ framing_implicit] ens_g:(a -> pure_post b))
  (#[@@@ framing_implicit] frame_f:vprop)
  (#[@@@ framing_implicit] frame_g:a -> vprop)
  (#[@@@ framing_implicit] post:post_t b)
  (#[@@@ framing_implicit] _ : squash (maybe_emp framed_f frame_f))
  (#[@@@ framing_implicit] _ : squash (maybe_emp_dep framed_g frame_g))
  (#[@@@ framing_implicit] pr:a -> prop)
  (#[@@@ framing_implicit] p1:squash
    (can_be_split_forall_dep pr
      (fun x -> post_f x `star` frame_f)
      (fun x -> pre_g x `star` frame_g x)))
  (#[@@@ framing_implicit] p2:squash
    (can_be_split_post (fun x y -> post_g x y `star` frame_g x) post))
  (f:repr a framed_f pre_f post_f req_f ens_f)
  (g:(x:a -> repr b framed_g (pre_g x) (post_g x) (req_g x) (ens_g x)))
: repr b
    true
    (pre_f `star` frame_f)
    post
    (bind_req a req_f ens_f pr req_g)
    (bind_ens a b ens_f ens_g)
let bind (a:Type) (b:Type)
         (#framed_f:eqtype_as_type bool)
         (#framed_g:eqtype_as_type bool)
         (#[@@@ framing_implicit] pre_f:pre_t)
         (#[@@@ framing_implicit] post_f:post_t a)
         (#[@@@ framing_implicit] req_f:Type0)
         (#[@@@ framing_implicit] ens_f:a -> Type0)
         (#[@@@ framing_implicit] pre_g:a -> pre_t)
         (#[@@@ framing_implicit] post_g:a -> post_t b)
         (#[@@@ framing_implicit] req_g:(a -> Type0))
         (#[@@@ framing_implicit] ens_g:(a -> b -> Type0))
         (#[@@@ framing_implicit] frame_f:vprop)
         (#[@@@ framing_implicit] frame_g:a -> vprop)
         (#[@@@ framing_implicit] post:post_t b)
         (#[@@@ framing_implicit] _x1: squash (maybe_emp framed_f frame_f))
         (#[@@@ framing_implicit] _x2: squash (maybe_emp_dep framed_g frame_g))
         (#[@@@ framing_implicit] pr:a -> prop)
         (#[@@@ framing_implicit] p1:squash
           (can_be_split_forall_dep pr
             (fun x -> post_f x `star` frame_f)
             (fun x -> pre_g x `star` frame_g x)))
         (#[@@@ framing_implicit] p2:squash
           (can_be_split_post (fun x y -> post_g x y `star` frame_g x) post))
         (f:repr a framed_f pre_f post_f req_f ens_f)
         (g:(x:a -> repr b framed_g (pre_g x) (post_g x) (req_g x) (ens_g x)))
    = let c = Steel.Effect.bind a b #framed_f #framed_g
                                #pre_f
                                #post_f
                                #(fun _ -> req_f)
                                #(fun _ x _ -> ens_f x)
                                #pre_g
                                #post_g
                                #(fun x _ -> req_g x)
                                #(fun x _ y _ -> ens_g x y)
                                #frame_f
                                #frame_g
                                #post
                                #_x1
                                #_x2
                                #pr
                                #p1
                                #p2
                                f g
      in
      weaken_repr _ _ _ _ _ _ _ _ c () ()
val bind (a:Type) (b:Type)
  (#framed_f:eqtype_as_type bool)
  (#framed_g:eqtype_as_type bool)
  (#[@@@ framing_implicit] pre_f:pre_t)
  (#[@@@ framing_implicit] post_f:post_t a)
  (#[@@@ framing_implicit] req_f:pure_pre)
  (#[@@@ framing_implicit] ens_f:pure_post a)
  (#[@@@ framing_implicit] pre_g:a -> pre_t)
  (#[@@@ framing_implicit] post_g:a -> post_t b)
  (#[@@@ framing_implicit] req_g:a -> pure_pre)
  (#[@@@ framing_implicit] ens_g:(a -> pure_post b))
  (#[@@@ framing_implicit] frame_f:vprop)
  (#[@@@ framing_implicit] frame_g:a -> vprop)
  (#[@@@ framing_implicit] post:post_t b)
  (#[@@@ framing_implicit] _ : squash (maybe_emp framed_f frame_f))
  (#[@@@ framing_implicit] _ : squash (maybe_emp_dep framed_g frame_g))
  (#[@@@ framing_implicit] pr:a -> prop)
  (#[@@@ framing_implicit] p1:squash
    (can_be_split_forall_dep pr
      (fun x -> post_f x `star` frame_f)
      (fun x -> pre_g x `star` frame_g x)))
  (#[@@@ framing_implicit] p2:squash
    (can_be_split_post (fun x y -> post_g x y `star` frame_g x) post))
  (f:repr a framed_f pre_f post_f req_f ens_f)
  (g:(x:a -> repr b framed_g (pre_g x) (post_g x) (req_g x) (ens_g x)))
: repr b
    true
    (pre_f `star` frame_f)
    post
    (bind_req a req_f ens_f pr req_g)
    (bind_ens a b ens_f ens_g)
let bind
      (a b: Type)
      (#framed_f #framed_g: eqtype_as_type bool)
      (#[@@@ framing_implicit]pre_f: pre_t)
      (#[@@@ framing_implicit]post_f: post_t a)
      (#[@@@ framing_implicit]req_f: Type0)
      (#[@@@ framing_implicit]ens_f: (a -> Type0))
      (#[@@@ framing_implicit]pre_g: (a -> pre_t))
      (#[@@@ framing_implicit]post_g: (a -> post_t b))
      (#[@@@ framing_implicit]req_g: (a -> Type0))
      (#[@@@ framing_implicit]ens_g: (a -> b -> Type0))
      (#[@@@ framing_implicit]frame_f: vprop)
      (#[@@@ framing_implicit]frame_g: (a -> vprop))
      (#[@@@ framing_implicit]post: post_t b)
      (#[@@@ framing_implicit]_x1: squash (maybe_emp framed_f frame_f))
      (#[@@@ framing_implicit]_x2: squash (maybe_emp_dep framed_g frame_g))
      (#[@@@ framing_implicit]pr: (a -> prop))
      (#[@@@ framing_implicit]p1:
          squash (can_be_split_forall_dep pr
                (fun x -> (post_f x) `star` frame_f)
                (fun x -> (pre_g x) `star` (frame_g x))))
      (#[@@@ framing_implicit]p2:
          squash (can_be_split_post (fun x y -> (post_g x y) `star` (frame_g x)) post))
      (f: repr a framed_f pre_f post_f req_f ens_f)
      (g: (x: a -> repr b framed_g (pre_g x) (post_g x) (req_g x) (ens_g x)))
     =
let c =
  Steel.Effect.bind a b #framed_f #framed_g #pre_f #post_f #(fun _ -> req_f) #(fun _ x _ -> ens_f x)
    #pre_g #post_g #(fun x _ -> req_g x) #(fun x _ y _ -> ens_g x y) #frame_f #frame_g #post #_x1
    #_x2 #pr #p1 #p2 f g
in
weaken_repr _ _ _ _ _ _ _ _ c () ()
Steel.ST.Effect.fst.checked
Steel.Memory.fsti.checked Steel.Effect.Common.fsti.checked Steel.Effect.fst.checked prims.fst.checked FStar.Tactics.fst.checked FStar.Pervasives.fsti.checked FStar.Monotonic.Pure.fst.checked FStar.Ghost.fsti.checked FStar.Classical.Sugar.fsti.checked
Steel.ST.Effect.fst
FStar.Pervasives.eqtype_as_type Prims.bool Steel.Effect.Common.pre_t Steel.Effect.Common.post_t Steel.Effect.Common.vprop Prims.squash Steel.Effect.Common.maybe_emp Steel.Effect.Common.maybe_emp_dep Prims.prop Steel.Effect.Common.can_be_split_forall_dep Steel.Effect.Common.star Steel.Effect.Common.can_be_split_post Steel.ST.Effect.repr Steel.ST.Effect.weaken_repr Steel.Effect.bind_req Steel.Effect.Common.rmem Steel.ST.Effect.bind_req Steel.Effect.bind_ens Steel.ST.Effect.bind_ens Steel.Effect.repr Steel.Effect.Common.rmem' Steel.Effect.Common.valid_rmem Prims.l_and Prims.l_Forall Steel.Effect.Common.hmem Prims.l_imp FStar.Tactics.Effect.rewrite_with_tactic Steel.Effect.Common.frame_vc_norm Steel.Effect.Common.frame_equalities' Steel.Effect.Common.focus_rmem Steel.Effect.Common.mk_rmem Prims.l_Exists Steel.Effect.bind
(*
   Copyright 2020 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.Effect
friend Steel.Effect
open Steel.Memory
open FStar.Ghost
module Mem = Steel.Memory
module T = FStar.Tactics
include Steel.Effect.Common
open Steel.Effect
#set-options "--warn_error -330"  //turn off the experimental feature warning
#set-options "--ide_id_info_off"

let repr a framed pre post req ens : Type u#2 =
  Steel.Effect.repr a framed pre post (fun _ -> req) (fun _ v _ -> ens v)

let equiv_star_emp_r (p:vprop)
  : Lemma ((p `star` emp) `equiv` p)
  = cm_identity p;
    assert ((emp `star` p) `equiv` p);
    star_commutative p emp;
    equiv_trans (p `star` emp) (emp `star` p) p

let weaken_repr a framed
                (pre:pre_t)
                (post:post_t a)
                (req req':req_t pre)
                (ens ens':ens_t pre a post)
                (f:Steel.Effect.repr a framed pre post req ens)
                (_:squash (forall (h0:hmem pre).
                            req' (mk_rmem _ h0) ==>
                            req (mk_rmem _ h0)))
                (_:squash (forall (h0:hmem pre) x (h1:hmem (post x)).
                            ens (mk_rmem _ h0)
                                x
                                (mk_rmem _ h1) ==>
                            ens' (mk_rmem _ h0) x (mk_rmem _ h1)))
  : Tot (Steel.Effect.repr a framed pre post req' ens')
  = let focus_rmem_refl (r:vprop) (h:rmem r)
      : Lemma (ensures focus_rmem #r h r == h)
              [SMTPat (focus_rmem #r h r)]
      = focus_rmem_refl r h
    in
    let equiv_trans (x y z:vprop) : Lemma
      (requires equiv x y /\ equiv y z)
      (ensures equiv x z)
      [SMTPat (equiv x z);
       SMTPat (equiv x y)]
     = equiv_trans x y z
    in
    let cbs (p:vprop)
      : Lemma (p `can_be_split` (p `star` emp))
              [SMTPat (p `can_be_split` (p `star` emp))]
      = star_commutative p emp;
        cm_identity p;
        equiv_sym (p `star` emp) p;
        equiv_can_be_split p (p `star` emp)
    in
    let epost ()
      : Lemma (equiv_forall post (fun x -> star (post x) emp))
      = introduce forall x. post x `equiv` (post x `star` emp)
        with (
          equiv_star_emp_r (post x);
          equiv_sym (post x `star` emp) (post x)
        );
        equiv_forall_elim post (fun x -> star (post x) emp)
    in
    epost ();
    Steel.Effect.subcomp_opaque a #framed #framed
                         #pre #post
                         #req #ens
                         #pre #post
                         #req' #ens'
                         #emp
                         #True
                         #()
                         #()
                         #()
                         f


let return_ (a:Type)
            (x:a)
            (#[@@@ framing_implicit] p:a -> vprop)
  : Tot (repr a true (return_pre (p x)) p True (fun v -> v == x))
  = let k : Steel.Effect.repr a true
            (p x)
            p
            (fun _ -> True)
            (return_ens a x p)
          = Steel.Effect.return_ a x #p
    in
    weaken_repr _ _ _ _ _ _ _ _ k () ()

let bind (a:Type) (b:Type)
         (#framed_f:eqtype_as_type bool)
         (#framed_g:eqtype_as_type bool)
         (#[@@@ framing_implicit] pre_f:pre_t)
         (#[@@@ framing_implicit] post_f:post_t a)
         (#[@@@ framing_implicit] req_f:Type0)
         (#[@@@ framing_implicit] ens_f:a -> Type0)
         (#[@@@ framing_implicit] pre_g:a -> pre_t)
         (#[@@@ framing_implicit] post_g:a -> post_t b)
         (#[@@@ framing_implicit] req_g:(a -> Type0))
         (#[@@@ framing_implicit] ens_g:(a -> b -> Type0))
         (#[@@@ framing_implicit] frame_f:vprop)
         (#[@@@ framing_implicit] frame_g:a -> vprop)
         (#[@@@ framing_implicit] post:post_t b)
         (#[@@@ framing_implicit] _x1: squash (maybe_emp framed_f frame_f))
         (#[@@@ framing_implicit] _x2: squash (maybe_emp_dep framed_g frame_g))
         (#[@@@ framing_implicit] pr:a -> prop)
         (#[@@@ framing_implicit] p1:squash
           (can_be_split_forall_dep pr
             (fun x -> post_f x `star` frame_f)
             (fun x -> pre_g x `star` frame_g x)))
         (#[@@@ framing_implicit] p2:squash
           (can_be_split_post (fun x y -> post_g x y `star` frame_g x) post))
         (f:repr a framed_f pre_f post_f req_f ens_f)
val bind (a:Type) (b:Type)
  (#framed_f:eqtype_as_type bool)
  (#framed_g:eqtype_as_type bool)
  (#[@@@ framing_implicit] pre_f:pre_t)
  (#[@@@ framing_implicit] post_f:post_t a)
  (#[@@@ framing_implicit] req_f:pure_pre)
  (#[@@@ framing_implicit] ens_f:pure_post a)
  (#[@@@ framing_implicit] pre_g:a -> pre_t)
  (#[@@@ framing_implicit] post_g:a -> post_t b)
  (#[@@@ framing_implicit] req_g:a -> pure_pre)
  (#[@@@ framing_implicit] ens_g:(a -> pure_post b))
  (#[@@@ framing_implicit] frame_f:vprop)
  (#[@@@ framing_implicit] frame_g:a -> vprop)
  (#[@@@ framing_implicit] post:post_t b)
  (#[@@@ framing_implicit] _ : squash (maybe_emp framed_f frame_f))
  (#[@@@ framing_implicit] _ : squash (maybe_emp_dep framed_g frame_g))
  (#[@@@ framing_implicit] pr:a -> prop)
  (#[@@@ framing_implicit] p1:squash
    (can_be_split_forall_dep pr
      (fun x -> post_f x `star` frame_f)
      (fun x -> pre_g x `star` frame_g x)))
  (#[@@@ framing_implicit] p2:squash
    (can_be_split_post (fun x y -> post_g x y `star` frame_g x) post))
  (f:repr a framed_f pre_f post_f req_f ens_f)
  (g:(x:a -> repr b framed_g (pre_g x) (post_g x) (req_g x) (ens_g x)))
: repr b
    true
    (pre_f `star` frame_f)
    post
    (bind_req a req_f ens_f pr req_g)
    (bind_ens a b ens_f ens_g)

    a: Type ->
    b: Type ->
    f: Steel.ST.Effect.repr a framed_f pre_f post_f req_f ens_f ->
    g: (x: a -> Steel.ST.Effect.repr b framed_g (pre_g x) (post_g x) (req_g x) (ens_g x))
  -> Steel.ST.Effect.repr b
      true
      (Steel.Effect.Common.star pre_f frame_f)
      post
      (Steel.ST.Effect.bind_req a req_f ens_f pr req_g)
      (Steel.ST.Effect.bind_ens a b ens_f ens_g)