sail2_state_monad.lem

open import Pervasives_extra
open import Sail2_instr_kinds
open import Sail2_values

(* 'a is result type *)

type memstate = map nat memory_byte
type tagstate = map nat bitU
(* type regstate = map string (vector bitU) *)

type sequential_state 'regs =
  <| regstate : 'regs;
     memstate : memstate;
     tagstate : tagstate |>

val init_state : forall 'regs. 'regs -> sequential_state 'regs
let init_state regs =
  <| regstate = regs;
     memstate = Map.empty;
     tagstate = Map.empty |>

type ex 'e =
  | Failure of string
  | Throw of 'e

type state_result 'a 'e =
  | Value of 'a
  | Ex of (ex 'e)

(* State, nondeterminism and exception monad with result value type 'a
   and exception type 'e. *)
type monadS 'regs 'a 'e = sequential_state 'regs -> set (state_result 'a 'e * sequential_state 'regs)

val returnS : forall 'regs 'a 'e. 'a -> monadS 'regs 'a 'e
let returnS a s = {(Value a,s)}

val bindS : forall 'regs 'a 'b 'e. monadS 'regs 'a 'e -> ('a -> monadS 'regs 'b 'e) -> monadS 'regs 'b 'e
let bindS m f (s : sequential_state 'regs) =
  Set.bigunion (Set.map (function
                | (Value a, s') -> f a s'
                | (Ex e, s') -> {(Ex e, s')}
                end) (m s))

val seqS: forall 'regs 'b 'e. monadS 'regs unit 'e -> monadS 'regs 'b 'e -> monadS 'regs 'b 'e
let seqS m n = bindS m (fun (_ : unit) -> n)

let inline (>>$=) = bindS
let inline (>>$) = seqS

val readS : forall 'regs 'a 'e. (sequential_state 'regs -> 'a) -> monadS 'regs 'a 'e
let readS f = (fun s -> returnS (f s) s)

val updateS : forall 'regs 'e. (sequential_state 'regs -> sequential_state 'regs) -> monadS 'regs unit 'e
let updateS f = (fun s -> returnS () (f s))

val failS : forall 'regs 'a 'e. string -> monadS 'regs 'a 'e
let failS msg s = {(Ex (Failure msg), s)}

val exitS : forall 'regs 'e 'a. unit -> monadS 'regs 'a 'e
let exitS () = failS "exit"

val throwS : forall 'regs 'a 'e. 'e -> monadS 'regs 'a 'e
let throwS e s = {(Ex (Throw e), s)}

val try_catchS : forall 'regs 'a 'e1 'e2. monadS 'regs 'a 'e1 -> ('e1 -> monadS 'regs 'a 'e2) ->  monadS 'regs 'a 'e2
let try_catchS m h s =
  Set.bigunion (Set.map (function
                | (Value a, s') -> returnS a s'
                | (Ex (Throw e), s') -> h e s'
                | (Ex (Failure msg), s') -> {(Ex (Failure msg), s')}
                end) (m s))

val assert_expS : forall 'regs 'e. bool -> string -> monadS 'regs unit 'e
let assert_expS exp msg = if exp then returnS () else failS msg

(* For early return, we abuse exceptions by throwing and catching
   the return value. The exception type is "either 'r 'e", where "Right e"
   represents a proper exception and "Left r" an early return of value "r". *)
type monadRS 'regs 'a 'r 'e = monadS 'regs 'a (either 'r 'e)

val early_returnS : forall 'regs 'a 'r 'e. 'r -> monadRS 'regs 'a 'r 'e
let early_returnS r = throwS (Left r)

val catch_early_returnS : forall 'regs 'a 'e. monadRS 'regs 'a 'a 'e -> monadS 'regs 'a 'e
let catch_early_returnS m =
  try_catchS m
    (function
      | Left a -> returnS a
      | Right e -> throwS e
     end)

(* Lift to monad with early return by wrapping exceptions *)
val liftRS : forall 'a 'r 'regs 'e. monadS 'regs 'a 'e -> monadRS 'regs 'a 'r 'e
let liftRS m = try_catchS m (fun e -> throwS (Right e))

(* Catch exceptions in the presence of early returns *)
val try_catchRS : forall 'regs 'a 'r 'e1 'e2. monadRS 'regs 'a 'r 'e1 -> ('e1 -> monadRS 'regs 'a 'r 'e2) ->  monadRS 'regs 'a 'r 'e2
let try_catchRS m h =
  try_catchS m
    (function
      | Left r -> throwS (Left r)
      | Right e -> h e
     end)

val maybe_failS : forall 'regs 'a 'e. string -> maybe 'a -> monadS 'regs 'a 'e
let maybe_failS msg = function
  | Just a  -> returnS a
  | Nothing -> failS msg
end

val chooseS : forall 'regs 'a 'e. SetType 'a => set 'a -> monadS 'regs 'a 'e
let chooseS xs s = Set.map (fun x -> (Value x, s)) xs

val choose_boolS : forall 'regs 'e. unit -> monadS 'regs bool 'e
let choose_boolS () = chooseS {false; true}

val headS : forall 'rv 'a 'e. list 'a -> monadS 'rv 'a 'e
let headS = function
  | x :: _ -> returnS x
  | [] -> failS "headM"
end

val tailS : forall 'rv 'a 'e. list 'a -> monadS 'rv (list 'a) 'e
let tailS = function
  | _ :: xs -> returnS xs
  | [] -> failS "tailM"
end

val read_tagS : forall 'regs 'a 'e. Bitvector 'a => 'a -> monadS 'regs bitU 'e
let read_tagS addr =
  maybe_failS "nat_of_bv" (nat_of_bv addr) >>$= (fun addr ->
  readS (fun s -> fromMaybe B0 (Map.lookup addr s.tagstate)))

(* Read bytes from memory and return in little endian order *)
val get_mem_bytes : forall 'regs. nat -> nat -> sequential_state 'regs -> maybe (list memory_byte * bitU)
let get_mem_bytes addr sz s =
  let addrs = genlist (fun n -> addr + n) sz in
  let read_byte s addr = Map.lookup addr s.memstate in
  let read_tag s addr = Map.findWithDefault addr B0 s.tagstate in
  Maybe.map
    (fun mem_val -> (mem_val, List.foldl and_bit B1 (List.map (read_tag s) addrs)))
    (just_list (List.map (read_byte s) addrs))

val read_memt_bytesS : forall 'regs 'e. read_kind -> nat -> nat -> monadS 'regs (list memory_byte * bitU) 'e
let read_memt_bytesS _ addr sz =
  readS (get_mem_bytes addr sz) >>$=
  maybe_failS "read_memS"

val read_mem_bytesS : forall 'regs 'e. read_kind -> nat -> nat -> monadS 'regs (list memory_byte) 'e
let read_mem_bytesS rk addr sz =
  read_memt_bytesS rk addr sz >>$= (fun (bytes, _) ->
  returnS bytes)

val read_memtS : forall 'regs 'e 'a 'b. Bitvector 'a, Bitvector 'b => read_kind -> 'a -> integer -> monadS 'regs ('b * bitU) 'e
let read_memtS rk a sz =
  maybe_failS "nat_of_bv" (nat_of_bv a) >>$= (fun a ->
  read_memt_bytesS rk a (nat_of_int sz) >>$= (fun (bytes, tag) ->
  maybe_failS "bits_of_mem_bytes" (of_bits (bits_of_mem_bytes bytes)) >>$= (fun mem_val ->
  returnS (mem_val, tag))))

val read_memS : forall 'regs 'e 'a 'b 'addrsize. Bitvector 'a, Bitvector 'b => read_kind -> 'addrsize -> 'a -> integer -> monadS 'regs 'b 'e
let read_memS rk addr_size a sz =
  read_memtS rk a sz >>$= (fun (bytes, _) ->
  returnS bytes)

val excl_resultS : forall 'regs 'e. unit -> monadS 'regs bool 'e
let excl_resultS =
  (* TODO: This used to be more deterministic, checking a flag in the state
     whether an exclusive load has occurred before.  However, this does not
     seem very precise; it might be safer to overapproximate the possible
     behaviours by always making a nondeterministic choice. *)
  choose_boolS

(* Write little-endian list of bytes to given address *)
val put_mem_bytes : forall 'regs. nat -> nat -> list memory_byte -> bitU -> sequential_state 'regs -> sequential_state 'regs
let put_mem_bytes addr sz v tag s =
  let addrs = genlist (fun n -> addr + n) sz in
  let a_v = List.zip addrs v in
  let write_byte mem (addr, v) = Map.insert addr v mem in
  let write_tag mem addr = Map.insert addr tag mem in
  <| s with memstate = List.foldl write_byte s.memstate a_v;
            tagstate = List.foldl write_tag s.tagstate addrs |>

val write_memt_bytesS : forall 'regs 'e. write_kind -> nat -> nat -> list memory_byte -> bitU -> monadS 'regs bool 'e
let write_memt_bytesS _ addr sz v t =
  updateS (put_mem_bytes addr sz v t) >>$
  returnS true

val write_mem_bytesS : forall 'regs 'e. write_kind -> nat -> nat -> list memory_byte -> monadS 'regs bool 'e
let write_mem_bytesS wk addr sz v = write_memt_bytesS wk addr sz v B0

val write_memtS : forall 'regs 'e 'a 'b. Bitvector 'a, Bitvector 'b =>
  write_kind -> 'a -> integer -> 'b -> bitU -> monadS 'regs bool 'e
let write_memtS wk addr sz v t =
  match (nat_of_bv addr, mem_bytes_of_bits v) with
    | (Just addr, Just v) -> write_memt_bytesS wk addr (nat_of_int sz) v t
    | _ -> failS "write_mem"
  end

val write_memS : forall 'regs 'e 'a 'b 'addrsize. Bitvector 'a, Bitvector 'b =>
  write_kind -> 'addrsize -> 'a -> integer -> 'b -> monadS 'regs bool 'e
let write_memS wk addr_size addr sz v = write_memtS wk addr sz v B0

val read_regS : forall 'regs 'rv 'a 'e. register_ref 'regs 'rv 'a -> monadS 'regs 'a 'e
let read_regS reg = readS (fun s -> reg.read_from s.regstate)

(* TODO
let read_reg_range reg i j state =
  let v = slice (get_reg state (name_of_reg reg)) i j in
  [(Value (vec_to_bvec v),state)]
let read_reg_bit reg i state =
  let v = access (get_reg state (name_of_reg reg)) i in
  [(Value v,state)]
let read_reg_field reg regfield =
  let (i,j) = register_field_indices reg regfield in
  read_reg_range reg i j
let read_reg_bitfield reg regfield =
  let (i,_) = register_field_indices reg regfield in
  read_reg_bit reg i *)

val read_regvalS : forall 'regs 'rv 'e.
  register_accessors 'regs 'rv -> string -> monadS 'regs 'rv 'e
let read_regvalS (read, _) reg =
  readS (fun s -> read reg s.regstate) >>$= (function
      | Just v ->  returnS v
      | Nothing -> failS ("read_regvalS " ^ reg)
    end)

val write_regvalS : forall 'regs 'rv 'e.
  register_accessors 'regs 'rv -> string -> 'rv -> monadS 'regs unit 'e
let write_regvalS (_, write) reg v =
  readS (fun s -> write reg v s.regstate) >>$= (function
      | Just rs' -> updateS (fun s -> <| s with regstate = rs' |>)
      | Nothing ->  failS ("write_regvalS " ^ reg)
    end)

val write_regS : forall 'regs 'rv 'a 'e. register_ref 'regs 'rv 'a -> 'a -> monadS 'regs unit 'e
let write_regS reg v =
  updateS (fun s -> <| s with regstate = reg.write_to v s.regstate |>)

(* TODO
val update_reg : forall 'regs 'rv 'a 'b 'e. register_ref 'regs 'rv 'a -> ('a -> 'b -> 'a) -> 'b -> monadS 'regs unit 'e
let update_reg reg f v state =
  let current_value = get_reg state reg in
  let new_value = f current_value v in
  [(Value (), set_reg state reg new_value)]

let write_reg_field reg regfield = update_reg reg regfield.set_field

val update_reg_range : forall 'regs 'rv 'a 'b. Bitvector 'a, Bitvector 'b => register_ref 'regs 'rv 'a -> integer -> integer -> 'a -> 'b -> 'a
let update_reg_range reg i j reg_val new_val = set_bits (reg.is_inc) reg_val i j (bits_of new_val)
let write_reg_range reg i j = update_reg reg (update_reg_range reg i j)

let update_reg_pos reg i reg_val x = update_list reg.is_inc reg_val i x
let write_reg_pos reg i = update_reg reg (update_reg_pos reg i)

let update_reg_bit reg i reg_val bit = set_bit (reg.is_inc) reg_val i (to_bitU bit)
let write_reg_bit reg i = update_reg reg (update_reg_bit reg i)

let update_reg_field_range regfield i j reg_val new_val =
  let current_field_value = regfield.get_field reg_val in
  let new_field_value = set_bits (regfield.field_is_inc) current_field_value i j (bits_of new_val) in
  regfield.set_field reg_val new_field_value
let write_reg_field_range reg regfield i j = update_reg reg (update_reg_field_range regfield i j)

let update_reg_field_pos regfield i reg_val x =
  let current_field_value = regfield.get_field reg_val in
  let new_field_value = update_list regfield.field_is_inc current_field_value i x in
  regfield.set_field reg_val new_field_value
let write_reg_field_pos reg regfield i = update_reg reg (update_reg_field_pos regfield i)

let update_reg_field_bit regfield i reg_val bit =
  let current_field_value = regfield.get_field reg_val in
  let new_field_value = set_bit (regfield.field_is_inc) current_field_value i (to_bitU bit) in
  regfield.set_field reg_val new_field_value
let write_reg_field_bit reg regfield i = update_reg reg (update_reg_field_bit regfield i)*)

(* TODO Add Show typeclass for value and exception type *)
val show_result : forall 'a 'e. state_result 'a 'e -> string
let show_result = function
  | Value _ -> "Value ()"
  | Ex (Failure msg) -> "Failure " ^ msg
  | Ex (Throw _) -> "Throw"
end

val prerr_results : forall 'a 'e 's. SetType 's => set (state_result 'a 'e * 's) -> unit
let prerr_results rs =
  let _ = Set.map (fun (r, _) -> let _ = prerr_endline (show_result r) in ()) rs in
  ()