|
| 1 | +path: type. |
| 2 | +mkpath: (Modules: list string) (Data: list string) -> path. |
| 3 | + |
| 4 | +endinanness: type. |
| 5 | +big_endian: endinanness. |
| 6 | +little_endian: endinanness. |
| 7 | + |
| 8 | +rel_expr: type. |
| 9 | +rel_hole: rel_expr. |
| 10 | +rel_sizeof: rel_expr. |
| 11 | +rel_int: int -> rel_expr. |
| 12 | +rel_ref: path -> rel_expr. |
| 13 | + |
| 14 | +rel: type. |
| 15 | +rel_lt: rel_expr -> rel_expr -> rel. |
| 16 | +rel_le: rel_expr -> rel_expr -> rel. |
| 17 | +rel_eq: rel_expr -> rel_expr -> rel. |
| 18 | +rel_ge: rel_expr -> rel_expr -> rel. |
| 19 | +rel_gt: rel_expr -> rel_expr -> rel. |
| 20 | + |
| 21 | +value: type. |
| 22 | +value_bool: bool -> value. |
| 23 | +value_int: int -> value. |
| 24 | + |
| 25 | +ty: type. |
| 26 | +top: ty. |
| 27 | +bottom: ty. |
| 28 | + |
| 29 | +boolean: ty. |
| 30 | +integer: ty. |
| 31 | + |
| 32 | +u: int -> endinanness -> ty. |
| 33 | +s: int -> endinanness -> ty. |
| 34 | + |
| 35 | +arr: ty -> list rel -> ty. |
| 36 | +str: list rel -> ty. |
| 37 | + |
| 38 | +meet: list ty -> ty. |
| 39 | +join: list ty -> ty. |
| 40 | + |
| 41 | +ref: path -> ty. |
| 42 | + |
| 43 | +liq: ty -> list rel -> ty. |
| 44 | +size: list rel -> ty. |
| 45 | +val: value -> ty -> ty. |
| 46 | + |
| 47 | +prod: list path -> ty. |
| 48 | + |
| 49 | +reduced: ty -> ty. |
| 50 | + |
| 51 | +typeof: (Path: path) (Type: ty) -> prop. |
| 52 | +ctypeof: (Path: path) (Type: ty) -> prop. |
| 53 | + |
| 54 | +simpl: (Complex: ty) (Simple: ty) -> prop. |
| 55 | +subst: ty -> ty -> prop. |
| 56 | +reduce_meet: ty -> ty -> ty -> prop. |
| 57 | + |
| 58 | +ctypeof P T :- |
| 59 | + typeof P Tx, |
| 60 | + subst Tx Ty, |
| 61 | + simpl Ty T. |
| 62 | + |
| 63 | +is_simple: ty -> prop. |
| 64 | +is_simple (join X::Xs) :- |
| 65 | + failure. |
| 66 | +is_simple (prod X::Xs) :- |
| 67 | + failure. |
| 68 | +is_simple _ :- |
| 69 | + success. |
| 70 | + |
| 71 | +subst (arr Tx Nx) (arr Ty Ny) :- |
| 72 | + subst Tx Ty, |
| 73 | + subst Nx Ny. |
| 74 | +subst (str X) (str Y) :- |
| 75 | + subst X Y. |
| 76 | +subst (meet X::Xs) (meet Y::Ys) :- |
| 77 | + subst X Y, |
| 78 | + subst (meet Xs) (meet Ys). |
| 79 | +subst (liq Tx P) (liq Ty P) :- |
| 80 | + subst Tx Ty. |
| 81 | +subst (size X) (size Y) :- |
| 82 | + subst X Y. |
| 83 | +subst (val V Tx) (val V Ty) :- |
| 84 | + subst Tx Ty. |
| 85 | +subst (ref P) T :- |
| 86 | + ctypeof P Tx, |
| 87 | + if is_simple Tx |
| 88 | + then eq T Tx |
| 89 | + else eq T (ref P). |
| 90 | +subst T T. |
| 91 | + |
| 92 | +simpl (arr Tx Nx) (arr Ty Ny) :- |
| 93 | + simpl Tx Ty, |
| 94 | + simpl Nx Ny. |
| 95 | +simpl (str Tx) (str Ty) :- |
| 96 | + simpl Tx Ty. |
| 97 | +simpl (liq Tx P) (liq Ty P) :- |
| 98 | + simpl Tx Ty. |
| 99 | +simpl (size Tx) (size Ty) :- |
| 100 | + simpl Tx Ty. |
| 101 | +simpl (val V Tx) (val V Ty) :- |
| 102 | + simpl Tx Ty. |
| 103 | +simpl (meet []) top. |
| 104 | +simpl (join []) bottom. |
| 105 | +simpl (meet X::Xs) T :- |
| 106 | + reduce_meet X (meet Xs) T. |
| 107 | +simpl (join X::[]) Y :- |
| 108 | + simpl X Y. |
| 109 | +simpl (join X::Xs) (join Z) :- |
| 110 | + simpl X Y, |
| 111 | + simpl (join Xs) (join Ys), |
| 112 | + reduce_join Y::Ys Z. |
| 113 | +simpl T T. |
| 114 | + |
| 115 | +reduce_join (join X)::Xs Y :- |
| 116 | + append X Xs Z, |
| 117 | + reduce_join Z Y. |
| 118 | +reduce_join X::Ys X::Zs :- |
| 119 | + reduce_join Ys Zs. |
| 120 | +reduce_join [] []. |
| 121 | + |
| 122 | +reduce_meet X X X. |
| 123 | +reduce_meet top X X. |
| 124 | +reduce_meet X top X. |
| 125 | +reduce_meet bottom X bottom. |
| 126 | +reduce_meet X bottom bottom. |
| 127 | +reduce_meet integer (u S E) (u S E). |
| 128 | +reduce_meet integer (s S E) (s S E). |
| 129 | +reduce_meet (arr Tx Sx) (arr Ty Sy) (arr T S) :- |
| 130 | + reduce_meet Tx Ty T, |
| 131 | + reduce_meet Sx Sy S. |
| 132 | +reduce_meet (str Sx) (str Sy) (str S) :- |
| 133 | + reduce_meet Sx Sy S. |
| 134 | + |
| 135 | +reduce_meet (liq Tx Px) (liq Ty Py) (liq T P) :- |
| 136 | + reduce_meet Tx Ty T, |
| 137 | + append Px Py P. |
| 138 | +reduce_meet (liq Tx P) (val V Ty) (val V (liq T P)) :- |
| 139 | + reduce_meet Tx Ty T. |
| 140 | +reduce_meet (val V Tx) (liq Ty P) (val V (liq T P)) :- |
| 141 | + reduce_meet Tx Ty T. |
| 142 | +reduce_meet (val Vx Tx) (val Vy Ty) (val V T) :- |
| 143 | + reduce_meet Vx Vy V, |
| 144 | + reduce_meet Tx Ty T. |
| 145 | +reduce_meet (val V Tx) Ty (val V T) :- |
| 146 | + reduce_meet Tx Ty T. |
| 147 | +reduce_meet Tx (val V Ty) (val V T) :- |
| 148 | + reduce_meet Tx Ty T. |
| 149 | + |
| 150 | +(* TODO: support non-reducible terms *) |
| 151 | +reduce_meet (meet X::Xs) (meet Y) Z :- |
| 152 | + append Xs Y Ts, |
| 153 | + reduce_meet X (meet Ts) Z. |
| 154 | +reduce_meet (meet []) Y Y. |
| 155 | +reduce_meet (meet X::Xs) Y Z :- |
| 156 | + append Xs [Y] Ts, |
| 157 | + reduce_meet X (meet Ts) Z. |
| 158 | +reduce_meet X (meet []) X. |
| 159 | +reduce_meet X (meet Y::Ys) Z :- |
| 160 | + reduce_meet X Y T, |
| 161 | + reduce_meet T (meet Ys) Z. |
| 162 | + |
| 163 | +reduce_meet X (join [Y]) Z :- |
| 164 | + reduce_meet X Y Z. |
| 165 | +reduce_meet X (join Y::Ys) (join Z::Zs) :- |
| 166 | + reduce_meet X Y Z, |
| 167 | + reduce_meet X (join Ys) (join Zs). |
| 168 | + |
| 169 | +reduce_meet (join [X]) Y Z :- |
| 170 | + reduce_meet X Y Z. |
| 171 | +reduce_meet (join X::Xs) Y (join Z::Zs) :- |
| 172 | + reduce_meet X Y Z, |
| 173 | + reduce_meet (join Xs) Y (join Zs). |
| 174 | + |
| 175 | +reduce_meet (ref X) Y (reduced (meet [X, Y])). |
| 176 | +reduce_meet X (ref Y) Z (reduced (meet [X, Y])). |
| 177 | + |
| 178 | +reduce_meet (prod X) Y Z :- failure. |
| 179 | +reduce_meet X (prod Y) Z :- failure. |
| 180 | + |
| 181 | +(* TODO: everything else *) |
| 182 | +reduce_meet _ _ bottom. |
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