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| 1 | +HB: AddMonoid_of_TYPE is a factory |
| 2 | + (from "./examples/demo1/hierarchy_5.v", line 10) |
| 3 | +HB: AddMonoid_of_TYPE operations and axioms are: |
| 4 | + - zero |
| 5 | + - add |
| 6 | + - addrA |
| 7 | + - add0r |
| 8 | + - addr0 |
| 9 | +HB: AddMonoid_of_TYPE requires the following mixins: |
| 10 | +HB: AddMonoid_of_TYPE provides the following mixins: |
| 11 | + - hierarchy_5.AddMonoid_of_TYPE |
| 12 | + |
| 13 | +HB: AddMonoid_of_TYPE.Build is a factory constructor |
| 14 | + (from "./examples/demo1/hierarchy_5.v", line 10) |
| 15 | +HB: AddMonoid_of_TYPE.Build requires its subject to be already equipped with: |
| 16 | +HB: AddMonoid_of_TYPE.Build provides the following mixins: |
| 17 | + - hierarchy_5.AddMonoid_of_TYPE |
| 18 | +HB: arguments: AddMonoid_of_TYPE.Build S zero add addrA add0r addr0 |
| 19 | + - S : Type |
| 20 | + - zero : AddMonoid.sort S |
| 21 | + - add : S -> S -> S |
| 22 | + - addrA : associative add |
| 23 | + - add0r : left_id 0%G add |
| 24 | + - addr0 : right_id 0%G add |
| 25 | + |
| 26 | +HB: AddAG.type is a structure (from "./examples/demo1/hierarchy_5.v", line 73) |
| 27 | +HB: AddAG.type characterizing operations and axioms are: |
| 28 | + - addNr |
| 29 | + - opp |
| 30 | +HB: hierarchy_5.AddAG is a factory for the following mixins: |
| 31 | + - hierarchy_5.AddMonoid_of_TYPE |
| 32 | + - hierarchy_5.AddComoid_of_AddMonoid |
| 33 | + - hierarchy_5.AddAG_of_AddComoid (* new, not from inheritance *) |
| 34 | +HB: hierarchy_5.AddAG inherits from: |
| 35 | + - hierarchy_5.AddMonoid |
| 36 | + - hierarchy_5.AddComoid |
| 37 | +HB: hierarchy_5.AddAG is inherited by: |
| 38 | + - hierarchy_5.Ring |
| 39 | + |
| 40 | +HB: hierarchy_5.AddMonoid.type is a structure |
| 41 | + (from "./examples/demo1/hierarchy_5.v", line 17) |
| 42 | +HB: hierarchy_5.AddMonoid.type characterizing operations and axioms are: |
| 43 | + - addr0 |
| 44 | + - add0r |
| 45 | + - addrA |
| 46 | + - add |
| 47 | + - zero |
| 48 | +HB: hierarchy_5.AddMonoid is a factory for the following mixins: |
| 49 | + - hierarchy_5.AddMonoid_of_TYPE (* new, not from inheritance *) |
| 50 | +HB: hierarchy_5.AddMonoid inherits from: |
| 51 | +HB: hierarchy_5.AddMonoid is inherited by: |
| 52 | + - hierarchy_5.AddComoid |
| 53 | + - hierarchy_5.AddAG |
| 54 | + - hierarchy_5.BiNearRing |
| 55 | + - hierarchy_5.SemiRing |
| 56 | + - hierarchy_5.Ring |
| 57 | + |
| 58 | +HB: Ring_of_AddAG is a factory |
| 59 | + (from "./examples/demo1/hierarchy_5.v", line 108) |
| 60 | +HB: Ring_of_AddAG operations and axioms are: |
| 61 | + - one |
| 62 | + - mul |
| 63 | + - mulrA |
| 64 | + - mulr1 |
| 65 | + - mul1r |
| 66 | + - mulrDl |
| 67 | + - mulrDr |
| 68 | +HB: Ring_of_AddAG requires the following mixins: |
| 69 | + - hierarchy_5.AddMonoid_of_TYPE |
| 70 | + - hierarchy_5.AddComoid_of_AddMonoid |
| 71 | + - hierarchy_5.AddAG_of_AddComoid |
| 72 | +HB: Ring_of_AddAG provides the following mixins: |
| 73 | + - hierarchy_5.BiNearRing_of_AddMonoid |
| 74 | +Doc: Builds a Ring from an Abelian Group: the absorbing properties mul0r and |
| 75 | + mul0r are derived from addrC and the other ring axioms, following a proof |
| 76 | + of Hankel (Gerhard Betsch. On the beginnings and development of near-ring |
| 77 | + theory. In Near-rings and near-fields. Proceedings of the conference held |
| 78 | + in Fredericton, New Brunswick, July 18-24, 1993, pages 1–11. Mathematics |
| 79 | + and its Applications, 336. Kluwer Academic Publishers Group, Dordrecht, |
| 80 | + 1995). |
| 81 | + |
| 82 | +HB: Ring_of_AddAG.Build is a factory constructor |
| 83 | + (from "./examples/demo1/hierarchy_5.v", line 108) |
| 84 | +HB: Ring_of_AddAG.Build requires its subject to be already equipped with: |
| 85 | + - hierarchy_5.AddMonoid_of_TYPE |
| 86 | + - hierarchy_5.AddComoid_of_AddMonoid |
| 87 | + - hierarchy_5.AddAG_of_AddComoid |
| 88 | +HB: Ring_of_AddAG.Build provides the following mixins: |
| 89 | + - hierarchy_5.BiNearRing_of_AddMonoid |
| 90 | +HB: arguments: Ring_of_AddAG.Build A [one] [mul] mulrA mulr1 mul1r mulrDl mulrDr |
| 91 | + - A : Type |
| 92 | + - one : A |
| 93 | + - mul : A -> A -> A |
| 94 | + - mulrA : associative mul |
| 95 | + - mulr1 : left_id one mul |
| 96 | + - mul1r : right_id one mul |
| 97 | + - mulrDl : left_distributive mul add |
| 98 | + - mulrDr : right_distributive mul add |
| 99 | +Doc: Builds a Ring from an Abelian Group: the absorbing properties mul0r and |
| 100 | + mul0r are derived from addrC and the other ring axioms, following a proof |
| 101 | + of Hankel (Gerhard Betsch. On the beginnings and development of near-ring |
| 102 | + theory. In Near-rings and near-fields. Proceedings of the conference held |
| 103 | + in Fredericton, New Brunswick, July 18-24, 1993, pages 1–11. Mathematics |
| 104 | + and its Applications, 336. Kluwer Academic Publishers Group, Dordrecht, |
| 105 | + 1995). |
| 106 | + |
| 107 | +HB: add is an operation of structure hierarchy_5.AddMonoid |
| 108 | + (from "./examples/demo1/hierarchy_5.v", line 17) |
| 109 | +HB: add comes from mixin hierarchy_5.AddMonoid_of_TYPE |
| 110 | + (from "./examples/demo1/hierarchy_5.v", line 10) |
| 111 | + |
| 112 | +HB: AddAG.sort is a canonical projection |
| 113 | + (from "./examples/demo1/hierarchy_5.v", line 73) |
| 114 | +HB: AddAG.sort has the following canonical values: |
| 115 | + - @eta |
| 116 | + - Ring.sort (from "./examples/demo1/hierarchy_5.v", line 196) |
| 117 | + - Z |
| 118 | + |
| 119 | +HB: AddAG.sort is a coercion from hierarchy_5.AddAG to Sortclass |
| 120 | + (from "./examples/demo1/hierarchy_5.v", line 73) |
| 121 | + |
| 122 | +HB: Z is canonically equipped with mixins: |
| 123 | + - hierarchy_5.AddMonoid |
| 124 | + hierarchy_5.AddComoid |
| 125 | + hierarchy_5.AddAG |
| 126 | + (from "(stdin)", line 5) |
| 127 | + - hierarchy_5.BiNearRing |
| 128 | + hierarchy_5.SemiRing |
| 129 | + hierarchy_5.Ring |
| 130 | + (from "(stdin)", line 10) |
| 131 | + |
| 132 | +HB: hierarchy_5_Ring_class__to__hierarchy_5_SemiRing_class is a coercion from |
| 133 | + hierarchy_5.Ring to hierarchy_5.SemiRing |
| 134 | + (from "./examples/demo1/hierarchy_5.v", line 196) |
| 135 | + |
| 136 | +HB: hierarchy_5_Ring__to__hierarchy_5_SemiRing is a coercion from |
| 137 | + hierarchy_5.Ring to hierarchy_5.SemiRing |
| 138 | + (from "./examples/demo1/hierarchy_5.v", line 196) |
| 139 | + |
| 140 | +HB: todo HB.about for builder from hierarchy_5.Ring_of_AddAG to |
| 141 | +hierarchy_5.BiNearRing_of_AddMonoid |
| 142 | +HB: synthesized in file File "(stdin)", line 5, column 122, character 127: |
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