| 1 | // (c) 2020 Aaron Taylor <ataylor at subgeniuskitty dot com> |
| 2 | // See LICENSE.txt file for copyright and license details. |
| 3 | |
| 4 | package main |
| 5 | |
| 6 | import ( |
| 7 | "flag" |
| 8 | "fmt" |
| 9 | "log" |
| 10 | ) |
| 11 | |
| 12 | // ============================================================================= |
| 13 | |
| 14 | type surrealUniverse struct { |
| 15 | // TODO: Note that the elements of this array are maintained in order |
| 16 | // w.r.t. Axiom 2. |
| 17 | numbers []surrealNumber |
| 18 | nextUniqueID int |
| 19 | } |
| 20 | |
| 21 | func (u *surrealUniverse) exists(num surrealNumber) bool { |
| 22 | // TODO: After I implement a LEQ comparison function, the fact that |
| 23 | // u.numbers[] is ordered by that comparison will allow me to greatly |
| 24 | // shorten the search. |
| 25 | for i := 0; i < len(u.numbers); i++ { |
| 26 | if num.number == u.numbers[i].number { |
| 27 | return true |
| 28 | } |
| 29 | } |
| 30 | return false |
| 31 | } |
| 32 | |
| 33 | func (u *surrealUniverse) cardinality() int { |
| 34 | return len(u.numbers) |
| 35 | } |
| 36 | |
| 37 | func (u *surrealUniverse) insert(num surrealNumber) { |
| 38 | if !u.exists(num) { |
| 39 | num.metadata.identifier = u.nextUniqueID |
| 40 | u.nextUniqueID++ |
| 41 | // TODO: Need a LEQ function before I can insert in the correct order. |
| 42 | // For now, just append to the end. |
| 43 | u.numbers = append(u.numbers, num) |
| 44 | } |
| 45 | } |
| 46 | |
| 47 | func (u *surrealUniverse) remove(num surrealNumber) { |
| 48 | for i := 0; i < len(u.numbers); i++ { |
| 49 | if num.number == u.numbers[i].number { |
| 50 | u.numbers = append(u.numbers[:i], u.numbers[i+1:]...) |
| 51 | } |
| 52 | } |
| 53 | } |
| 54 | |
| 55 | // ============================================================================= |
| 56 | |
| 57 | type surrealNumber struct { |
| 58 | number surrealValue |
| 59 | metadata surrealMetadata |
| 60 | } |
| 61 | |
| 62 | // TODO: Note that this is split from the metadata so we can do direct |
| 63 | // comparisons when numbers are in reduced form. |
| 64 | type surrealValue struct { |
| 65 | leftSet *surrealSet |
| 66 | rightSet *surrealSet |
| 67 | } |
| 68 | |
| 69 | type surrealMetadata struct { |
| 70 | identifier int |
| 71 | generation int |
| 72 | } |
| 73 | |
| 74 | // ============================================================================= |
| 75 | |
| 76 | type surrealSet struct { |
| 77 | members []surrealNumber |
| 78 | } |
| 79 | |
| 80 | func (s *surrealSet) isMember(num surrealNumber) bool { |
| 81 | for i := 0; i < len(s.members); i++ { |
| 82 | if num.number == s.members[i].number { |
| 83 | return true |
| 84 | } |
| 85 | } |
| 86 | return false |
| 87 | } |
| 88 | |
| 89 | func (s *surrealSet) cardinality() int { |
| 90 | return len(s.members) |
| 91 | } |
| 92 | |
| 93 | func (s *surrealSet) insert(num surrealNumber) { |
| 94 | if !s.isMember(num) { |
| 95 | s.members = append(s.members, num) |
| 96 | } |
| 97 | } |
| 98 | |
| 99 | func (s *surrealSet) remove(num surrealNumber) { |
| 100 | for i := 0; i < len(s.members); i++ { |
| 101 | if num.number == s.members[i].number { |
| 102 | s.members[i] = s.members[len(s.members)-1] |
| 103 | s.members = s.members[:len(s.members)-1] |
| 104 | } |
| 105 | } |
| 106 | } |
| 107 | |
| 108 | // ============================================================================= |
| 109 | |
| 110 | func main() { |
| 111 | // Obtain termination conditions from user. |
| 112 | remainingGenerations := flag.Int("generations", 2, "Number of generations of surreal numbers to breed.") |
| 113 | flag.Parse() |
| 114 | if *remainingGenerations < 1 { |
| 115 | log.Fatal("ERROR: The argument to '-generations' must be greater than zero.") |
| 116 | } |
| 117 | |
| 118 | // Build a universe to contain all the surreal numbers we breed. |
| 119 | // Seed it by hand with the number zero as generation-0. |
| 120 | var universe surrealUniverse |
| 121 | universe.insert(surrealNumber{surrealValue{nil, nil}, surrealMetadata{0, 0}}) |
| 122 | |
| 123 | // TODO: Describe the basic algorithm. |
| 124 | for generation := 1; generation <= *remainingGenerations; generation++ { |
| 125 | // TODO: Continue here next time. |
| 126 | // Rough Plan: |
| 127 | // allSymbols := buildAllSymbolCombinations(generation) |
| 128 | // validNumbers := pruneInvalidSymbolCombinations(allSymbols) |
| 129 | // addNumbersToUniverse(validNumbers) |
| 130 | } |
| 131 | |
| 132 | // TODO: These are just for checking progress. How do I want to render the |
| 133 | // final generations vs magnitude chart? |
| 134 | fmt.Println("Total Numbers:", len(universe.numbers)) |
| 135 | fmt.Println(universe.numbers) |
| 136 | } |
| 137 | |
| 138 | // ============================================================================= |