1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
|
$ifndef _FLOW
$define _FLOW
/*
This file contains the basic definitions for equality and comparison
that is required for flow typing to work correctly. It should
therefore be included in just about every Sail specification.
*/
val eq_unit : (unit, unit) -> bool
val eq_bit = { lem : "eq", _ : "eq_bit" } : (bit, bit) -> bool
function eq_unit(_, _) = true
val not_bool = {coq: "negb", _: "not"} : bool -> bool
/* NB: There are special cases in Sail for effectful uses of and_bool and
or_bool that are not shown here. */
val and_bool = {coq: "andb", _: "and_bool"} : (bool, bool) -> bool
val or_bool = {coq: "orb", _: "or_bool"} : (bool, bool) -> bool
val eq_atom = {ocaml: "eq_int", lem: "eq", c: "eq_int", coq: "Z.eqb"} : forall 'n 'm. (atom('n), atom('m)) -> bool
val neq_atom = {lem: "neq", coq: "neq_atom"} : forall 'n 'm. (atom('n), atom('m)) -> bool
function neq_atom (x, y) = not_bool(eq_atom(x, y))
val lteq_atom = {coq: "Z.leb", _: "lteq"} : forall 'n 'm. (atom('n), atom('m)) -> bool
val gteq_atom = {coq: "Z.geb", _: "gteq"} : forall 'n 'm. (atom('n), atom('m)) -> bool
val lt_atom = {coq: "Z.ltb", _: "lt"} : forall 'n 'm. (atom('n), atom('m)) -> bool
val gt_atom = {coq: "Z.gtb", _: "gt"} : forall 'n 'm. (atom('n), atom('m)) -> bool
val lt_range_atom = {coq: "ltb_range_l", _: "lt"} : forall 'n 'm 'o. (range('n, 'm), atom('o)) -> bool
val lteq_range_atom = {coq: "leb_range_l", _: "lteq"} : forall 'n 'm 'o. (range('n, 'm), atom('o)) -> bool
val gt_range_atom = {coq: "gtb_range_l", _: "gt"} : forall 'n 'm 'o. (range('n, 'm), atom('o)) -> bool
val gteq_range_atom = {coq: "geb_range_l", _: "gteq"} : forall 'n 'm 'o. (range('n, 'm), atom('o)) -> bool
val lt_atom_range = {coq: "ltb_range_r", _: "lt"} : forall 'n 'm 'o. (atom('n), range('m, 'o)) -> bool
val lteq_atom_range = {coq: "leb_range_r", _: "lteq"} : forall 'n 'm 'o. (atom('n), range('m, 'o)) -> bool
val gt_atom_range = {coq: "gtb_range_r", _: "gt"} : forall 'n 'm 'o. (atom('n), range('m, 'o)) -> bool
val gteq_atom_range = {coq: "geb_range_r", _: "gteq"} : forall 'n 'm 'o. (atom('n), range('m, 'o)) -> bool
val eq_range = {ocaml: "eq_int", lem: "eq", c: "eq_int", coq: "eq_range"} : forall 'n 'm 'o 'p. (range('n, 'm), range('o, 'p)) -> bool
val eq_int = {ocaml: "eq_int", lem: "eq", c: "eq_int", coq: "Z.eqb"} : (int, int) -> bool
val eq_bool = {ocaml: "eq_bool", lem: "eq", c: "eq_bool", coq: "Bool.eqb"} : (bool, bool) -> bool
val neq_range = {lem: "neq"} : forall 'n 'm 'o 'p. (range('n, 'm), range('o, 'p)) -> bool
function neq_range (x, y) = not_bool(eq_range(x, y))
val neq_int = {lem: "neq"} : (int, int) -> bool
function neq_int (x, y) = not_bool(eq_int(x, y))
val neq_bool : (bool, bool) -> bool
function neq_bool (x, y) = not_bool(eq_bool(x, y))
val lteq_int = {coq: "Z.leb", _:"lteq"} : (int, int) -> bool
val gteq_int = {coq: "Z.geb", _:"gteq"} : (int, int) -> bool
val lt_int = {coq: "Z.ltb", _:"lt"} : (int, int) -> bool
val gt_int = {coq: "Z.gtb", _:"gt"} : (int, int) -> bool
overload operator == = {eq_atom, eq_range, eq_int, eq_bit, eq_bool, eq_unit}
overload operator != = {neq_atom, neq_range, neq_int, neq_bool}
overload operator | = {or_bool}
overload operator & = {and_bool}
overload operator <= = {lteq_atom, lteq_range_atom, lteq_atom_range, lteq_int}
overload operator < = {lt_atom, lt_range_atom, lt_atom_range, lt_int}
overload operator >= = {gteq_atom, gteq_range_atom, gteq_atom_range, gteq_int}
overload operator > = {gt_atom, gt_range_atom, gt_atom_range, gt_int}
$ifdef TEST
val __flow_test : forall 'n 'm. (atom('n), atom('m)) -> unit
function __flow_test (x, y) = {
if lteq_atom(x, y) then {
_prove(constraint('n <= 'm))
} else {
_prove(constraint('n > 'm))
}
}
$endif
$endif
|
