default Order dec

$include <smt.sail>
$include <arith.sail>

type bits ('n : Int) = bitvector('n, dec)

val eq_vec = {ocaml: "eq_list", interpreter: "eq_list", lem: "eq_vec", c: "eq_bits", coq: "eq_vec"} : forall 'n. (bits('n), bits('n)) -> bool

val eq_string = {ocaml: "eq_string", interpreter: "eq_string", lem: "eq", c: "eq_string", coq: "generic_eq"} : (string, string) -> bool

val eq_real = {ocaml: "eq_real", interpreter: "eq_real", lem: "eq", c: "eq_real", coq: "Reqb"} : (real, real) -> bool

val eq_anything = {
  ocaml: "(fun (x, y) -> x = y)",
  interpreter: "eq_anything",
  lem: "eq",
  c: "eq_anything",
  coq: "generic_eq"
} : forall ('a : Type). ('a, 'a) -> bool

val bitvector_length = "length" : forall 'n. bits('n) -> atom('n)
val vector_length = {ocaml: "length", interpreter: "length", lem: "length_list", c: "length", coq: "vec_length"} : forall 'n ('a : Type). vector('n, dec, 'a) -> atom('n)
val list_length = {ocaml: "length", interpreter: "length", lem: "length_list", c: "length", coq: "length_list"} : forall ('a : Type). list('a) -> int

overload length = {bitvector_length, vector_length, list_length}

overload operator == = {eq_vec, eq_string, eq_real, eq_anything}

val vector_subrange_A = {
  ocaml: "subrange",
  interpreter: "subrange",
  lem: "subrange_vec_dec",
  c: "vector_subrange",
  coq: "subrange_vec_dec"
} : forall ('n : Int) ('m : Int) ('o : Int), 'o <= 'm <= 'n.
  (bits('n), atom('m), atom('o)) -> bits('m - ('o - 1))

val vector_subrange_B = {
  ocaml: "subrange",
  interpreter: "subrange",
  lem: "subrange_vec_dec",
  c: "vector_subrange"
} : forall ('n : Int) ('m : Int) ('o : Int).
  (bits('n), atom('m), atom('o)) -> bits('m - ('o - 1))

overload vector_subrange = {vector_subrange_A, vector_subrange_B}

val bitvector_access_A = {
  ocaml: "access",
  interpreter: "access",
  lem: "access_vec_dec",
  c: "vector_access",
  coq: "access_vec_dec"
} : forall ('n : Int) ('m : Int), 0 <= 'm < 'n. (bits('n), atom('m)) -> bit

val bitvector_access_B = {
  ocaml: "access",
  interpreter: "access",
  lem: "access_vec_dec",
  c: "vector_access",
  coq: "access_vec_dec"
} : forall ('n : Int). (bits('n), int) -> bit

val vector_access_A = {
  ocaml: "access",
  interpreter: "access",
  lem: "access_list_dec",
  c: "vector_access",
  coq: "vec_access_dec"
} : forall ('n : Int) ('m : Int) ('a : Type), 0 <= 'm < 'n. (vector('n, dec, 'a), atom('m)) -> 'a

val vector_access_B = {
  ocaml: "access",
  interpreter: "access",
  lem: "access_list_dec",
  c: "vector_access"
} : forall ('n : Int) ('a : Type). (vector('n, dec, 'a), int) -> 'a

overload vector_access = {bitvector_access_A, bitvector_access_B, vector_access_A, vector_access_B}

val bitvector_update_B = {ocaml: "update", interpreter: "update", lem: "update_vec_dec", c: "vector_update", coq: "update_vec_dec"} : forall 'n.
  (bits('n), int, bit) -> bits('n)

val vector_update_B = {ocaml: "update", interpreter: "update", lem: "update_list_dec", c: "vector_update", coq: "vec_update_dec"} : forall 'n ('a : Type).
  (vector('n, dec, 'a), int, 'a) -> vector('n, dec, 'a)

overload vector_update = {bitvector_update_B, vector_update_B}

val vector_update_subrange = {
  ocaml: "update_subrange",
  interpreter: "update_subrange",
  lem: "update_subrange_vec_dec",
  c: "vector_update_subrange",
  coq: "update_subrange_vec_dec"
} : forall 'n 'm 'o. (bits('n), atom('m), atom('o), bits('m - ('o - 1))) -> bits('n)

val vcons : forall ('n : Int) ('a : Type).
  ('a, vector('n, dec, 'a)) -> vector('n + 1, dec, 'a)

val bitvector_concat = {ocaml: "append", interpreter: "append", lem: "concat_vec", c: "append", coq: "concat_vec"} : forall ('n : Int) ('m : Int).
  (bits('n), bits('m)) -> bits('n + 'm)

val vector_concat = {ocaml: "append", interpreter: "append", lem: "append_list", coq: "append_list"} : forall ('n : Int) ('m : Int) ('a : Type).
  (vector('n, dec, 'a), vector('m, dec, 'a)) -> vector('n + 'm, dec, 'a)

overload append = {bitvector_concat, vector_concat}

val not_vec = {
  ocaml: "not_vec",
  interpreter: "not_vec",
  lem: "not_vec",
  c: "not_bits",
  coq: "not_vec"
} : forall 'n. bits('n) -> bits('n)

overload ~ = {not_bool, not_vec}

val neq_vec = {lem: "neq_vec"} : forall 'n. (bits('n), bits('n)) -> bool

function neq_vec (x, y) = not_bool(eq_vec(x, y))

val neq_anything = {lem: "neq", coq: "generic_neq"} : forall ('a : Type). ('a, 'a) -> bool

function neq_anything (x, y) = not_bool(x == y)

overload operator != = {neq_vec, neq_anything}

val builtin_and_vec = {ocaml: "and_vec", interpreter: "and_vec", c: "and_bits"} : forall 'n. (bits('n), bits('n)) -> bits('n)

val and_vec = {lem: "and_vec", c: "and_bits", coq: "and_vec"} : forall 'n. (bits('n), bits('n)) -> bits('n)

function and_vec (xs, ys) = builtin_and_vec(xs, ys)

overload operator & = {and_vec}

val builtin_or_vec = {ocaml: "or_vec", interpreter: "or_vec", c: "or_bits"} : forall 'n. (bits('n), bits('n)) -> bits('n)

val or_vec = {lem: "or_vec", c: "or_bits", coq: "or_vec"}: forall 'n. (bits('n), bits('n)) -> bits('n)

function or_vec (xs, ys) = builtin_or_vec(xs, ys)

overload operator | = {or_vec}

val UInt = {
  ocaml: "uint",
  lem: "uint",
  interpreter: "uint",
  c: "sail_unsigned",
  coq: "uint"
} : forall 'n. bits('n) -> {'m, 0 <= 'm <= 2 ^ 'n - 1. int('m)}

val SInt = {
  c: "sail_signed",
  _: "sint"
} : forall 'n. bits('n) -> {'m, (- (2 ^ ('n - 1))) <= 'm <= 2 ^ ('n - 1) - 1. int('m)}

val hex_slice = "hex_slice" : forall 'n 'm. (string, atom('n), atom('m)) -> bits('n - 'm) effect {escape}

val __SetSlice_bits = "set_slice" : forall 'n 'm.
  (atom('n), atom('m), bits('n), int, bits('m)) -> bits('n)

val __SetSlice_int = "set_slice_int" : forall 'w. (atom('w), int, int, bits('w)) -> int

val __raw_SetSlice_int : forall 'w. (atom('w), int, int, bits('w)) -> int

val __raw_GetSlice_int = "get_slice_int" : forall 'w /*, 'w >= 0*/. (atom('w), int, int) -> bits('w)

val __GetSlice_int : forall 'n /*, 'n >= 0*/. (atom('n), int, int) -> bits('n)

function __GetSlice_int (n, m, o) = __raw_GetSlice_int(n, m, o)

val __raw_SetSlice_bits : forall 'n 'w.
  (atom('n), atom('w), bits('n), int, bits('w)) -> bits('n)

val __raw_GetSlice_bits : forall 'n 'w.
  (atom('n), atom('w), bits('n), int) -> bits('w)

val __ShiftLeft = "shiftl" : forall 'm. (bits('m), int) -> bits('m)

val __SignExtendSlice = {lem: "exts_slice"} : forall 'm. (bits('m), int, int) -> bits('m)

val __ZeroExtendSlice = {lem: "extz_slice"} : forall 'm. (bits('m), int, int) -> bits('m)

val cast cast_unit_vec : bit -> bits(1)

function cast_unit_vec b =
  match b {
    bitzero => 0b0,
    bitone  => 0b1
  }

val print = "prerr" : string -> unit
val prerr = "prerr" : string -> unit

val putchar = {
  ocaml: "putchar",
  lem: "putchar",
  interpreter: "putchar",
  c: "sail_putchar",
  coq: "putchar"
} : int -> unit

val concat_str = {ocaml: "concat_str", interpreter: "concat_str", lem: "stringAppend", c: "concat_str", coq: "String.append"} : (string, string) -> string

val DecStr = "dec_str" : int -> string

val HexStr = "hex_str" : int -> string

val BoolStr : bool -> string

function BoolStr(b) = if b then "true" else "false"

val BitStr = "string_of_bits" : forall 'n. bits('n) -> string

val xor_vec = {
  ocaml: "xor_vec",
  interpreter: "xor_vec",
  lem: "xor_vec",
  c: "xor_bits",
  coq: "xor_vec"
} : forall 'n. (bits('n), bits('n)) -> bits('n)

val int_power = {lem: "pow"} : (int, int) -> int

val real_power = {ocaml: "real_power", interpreter: "real_power", lem: "realPowInteger", c: "real_power", coq: "powerRZ"} : (real, int) -> real

overload operator ^ = {xor_vec, int_power, real_power}

val add_vec = {
  ocaml: "add_vec",
  interpreter: "add_vec",
  lem: "add_vec",
  c: "add_bits",
  coq: "add_vec"
} : forall 'n. (bits('n), bits('n)) -> bits('n)

val add_vec_int = {
  ocaml: "add_vec_int",
  interpreter: "add_vec_int",
  lem: "add_vec_int",
  c: "add_bits_int",
  coq: "add_vec_int"
} : forall 'n. (bits('n), int) -> bits('n)

val add_real = {ocaml: "add_real", interpreter: "add_real", lem: "realAdd", c: "add_real", coq: "Rplus"} : (real, real) -> real

overload operator + = {add_vec, add_vec_int, add_real}

val sub_vec = {c: "sub_bits", _: "sub_vec"} : forall 'n. (bits('n), bits('n)) -> bits('n)

val sub_vec_int = {
  ocaml: "sub_vec_int",
  interpreter: "sub_vec_int",
  lem: "sub_vec_int",
  c: "sub_bits_int",
  coq: "sub_vec_int"
} : forall 'n. (bits('n), int) -> bits('n)

val sub_real = {ocaml: "sub_real", interpreter: "sub_real", lem: "realMinus", c: "sub_real", coq: "Rminus"} : (real, real) -> real

val negate_real = {ocaml: "negate_real", interpreter: "negate_real", lem: "realNegate", c: "neg_real", coq: "Ropp"} : real -> real

overload operator - = {sub_vec, sub_vec_int, sub_real}

overload negate = {negate_real}

val mult_real = {ocaml: "mult_real", interpreter: "mult_real", lem: "realMult", c: "mult_real", coq: "Rmult"} : (real, real) -> real

overload operator * = {mult_real}

val Sqrt = {ocaml: "sqrt_real", interpreter: "sqrt_real", lem: "realSqrt", c: "sqrt_real", coq: "sqrt"} : real -> real

val gteq_real = {ocaml: "gteq_real", interpreter: "gteq_real", lem: "gteq", c: "gteq_real", coq: "gteq_real"} : (real, real) -> bool

overload operator >= = {gteq_real}

val lteq_real = {ocaml: "lteq_real", interpreter: "lteq_real", lem: "lteq", c: "lteq_real", coq: "lteq_real"} : (real, real) -> bool

overload operator <= = {lteq_real}

val gt_real = {ocaml: "gt_real", interpreter: "gt_real", lem: "gt", c: "gt_real", coq: "gt_real"} : (real, real) -> bool

overload operator > = {gt_real}

val lt_real = {ocaml: "lt_real", interpreter: "lt_real", lem: "lt", c: "lt_real", coq: "lt_real"} : (real, real) -> bool

overload operator < = {lt_real}

val RoundDown = {ocaml: "round_down", interpreter: "round_down", lem: "realFloor", c: "round_down", coq: "Zfloor"} : real -> int

val RoundUp = {ocaml: "round_up", interpreter: "round_up", lem: "realCeiling", c: "round_up", coq: "Zceil"} : real -> int

val abs_real = {coq: "Rabs", _: "abs_real"} : real -> real

overload abs = {abs_atom, abs_real}

val quotient_real = {ocaml: "quotient_real", interpreter: "quotient_real", lem: "realDiv", c: "div_real", coq: "Rdiv"} : (real, real) -> real

overload operator / = {ediv_int, quotient_real}
overload div = {ediv_int}
overload operator % = {emod_int}

val Real = {ocaml: "to_real", interpreter: "to_real", lem: "realFromInteger", c: "to_real", coq: "IZR"} : int -> real

val min_nat = {ocaml: "min_int", interpreter: "min_int", lem: "min", c: "min_int"} : (nat, nat) -> nat

val min_int = {ocaml: "min_int", interpreter: "min_int", lem: "min", c: "min_int", coq: "Z.min"} : (int, int) -> int

val max_nat = {ocaml: "max_int", interpreter: "max_int", lem: "max", c: "max_int"} : (nat, nat) -> nat

val max_int = {ocaml: "max_int", interpreter: "max_int", lem: "max", c: "max_int", coq: "Z.max"} : (int, int) -> int

overload min = {min_nat, min_int}

overload max = {max_nat, max_int}

val print_bits = "print_bits" : forall 'n. (string, bits('n)) -> unit

val prerr_bits = "prerr_bits" : forall 'n. (string, bits('n)) -> unit

val replicate_bits = "replicate_bits" : forall 'n 'm. (bits('n), atom('m)) -> bits('n * 'm)

val cast ex_nat : nat -> {'n, 'n >= 0. atom('n)}

function ex_nat 'n = n

val cast ex_int : int -> {'n, true. atom('n)}

function ex_int 'n = n

val ex_range : forall 'n 'm.
  range('n, 'm) -> {'o, 'n <= 'o & 'o <= 'm. atom('o)}

val coerce_int_nat : int -> nat effect {escape}

function coerce_int_nat 'x = {
  assert(constraint('x >= 0), "Cannot coerce int to nat");
  x
}

val slice = "slice" : forall ('n : Int) ('m : Int), 'm >= 0 & 'n >= 0.
  (bits('m), int, atom('n)) -> bits('n)

val pow2_atom = "pow2" : forall 'n. atom('n) -> atom(2 ^ 'n)
val pow2_int = "pow2" : int -> int

overload pow2 = {pow2_atom, pow2_int}

val break : unit -> unit

function break () = ()

union exception = {
  Error_Undefined : unit,
  Error_See : string,
  Error_Implementation_Defined : string,
  Error_ReservedEncoding : unit,
  Error_ExceptionTaken : unit
}

/*
union option ('a : Type) = {
  None,
  Some : 'a
}
*/

val __SleepRequest = {ocaml: "sleep_request", interpreter: "sleep_request", lem: "sleep_request", smt: "sleep_request", interpreter: "sleep_request", c: "sleep_request"}: unit -> unit effect {rreg, undef}

val __WakeupRequest = {ocaml: "wakeup_request", interpreter: "wakeup_request", lem: "wakeup_request", smt: "wakeup_request", interpreter: "wakeup_request", c: "wakeup_request"}: unit -> unit effect {rreg, undef}

val __Sleeping = {ocaml: "sleeping", interpreter: "sleeping", lem: "sleeping", smt: "sleeping", interpreter: "sleeping", c: "sleeping"}: unit -> bool effect {rreg, undef}

val __GetVerbosity = {c: "sail_get_verbosity"}: unit -> bits(64) effect {rreg, undef}

val get_cycle_count = { c: "get_cycle_count" } : unit -> int effect {undef, wreg, rreg, rmem, wmem}

overload __size = {length}