From 3c02a58e9eaea92e14f5a58096cfa3deed59ddc8 Mon Sep 17 00:00:00 2001
From: Aaron Taylor <ataylor@subgeniuskitty.com>
Date: Tue, 4 May 2021 21:58:52 -0700
Subject: [PATCH] Created basic data structures and methods for dealing with a
 collection of surreal numbers.

---
 chapter-1-experiments/ch1-breeding-numbers.go | 128 +++++++++++++++++-
 1 file changed, 127 insertions(+), 1 deletion(-)

diff --git a/chapter-1-experiments/ch1-breeding-numbers.go b/chapter-1-experiments/ch1-breeding-numbers.go
index 1e53fc3..d063cdd 100644
--- a/chapter-1-experiments/ch1-breeding-numbers.go
+++ b/chapter-1-experiments/ch1-breeding-numbers.go
@@ -4,9 +4,135 @@
 package main
 
 import (
+    "flag"
     "fmt"
+    "log"
 )
 
+// =============================================================================
+
+type surrealUniverse struct {
+    // TODO: Note that the elements of this array are maintained in order
+    // w.r.t. Axiom 2.
+    numbers []surrealNumber
+    nextUniqueID int
+}
+
+func (u *surrealUniverse) exists(num surrealNumber) bool {
+    // TODO: After I implement a LEQ comparison function, the fact that
+    // u.numbers[] is ordered by that comparison will allow me to greatly
+    // shorten the search.
+    for i := 0; i < len(u.numbers); i++ {
+        if num.number == u.numbers[i].number {
+            return true
+        }
+    }
+    return false
+}
+
+func (u *surrealUniverse) cardinality() int {
+    return len(u.numbers)
+}
+
+func (u *surrealUniverse) insert(num surrealNumber) {
+    if !u.exists(num) {
+        num.metadata.identifier = u.nextUniqueID
+        u.nextUniqueID++
+        // TODO: Need a LEQ function before I can insert in the correct order.
+        // For now, just append to the end.
+        u.numbers = append(u.numbers, num)
+    }
+}
+
+func (u *surrealUniverse) remove(num surrealNumber) {
+    for i := 0; i < len(u.numbers); i++ {
+        if num.number == u.numbers[i].number {
+            u.numbers = append(u.numbers[:i], u.numbers[i+1:]...)
+        }
+    }
+}
+
+// =============================================================================
+
+type surrealNumber struct {
+    number surrealValue
+    metadata surrealMetadata
+}
+
+// TODO: Note that this is split from the metadata so we can do direct
+// comparisons when numbers are in reduced form.
+type surrealValue struct {
+    leftSet *surrealSet
+    rightSet *surrealSet
+}
+
+type surrealMetadata struct {
+    identifier int
+    generation int
+}
+
+// =============================================================================
+
+type surrealSet struct {
+    members []surrealNumber
+}
+
+func (s *surrealSet) isMember(num surrealNumber) bool {
+    for i := 0; i < len(s.members); i++ {
+        if num.number == s.members[i].number {
+            return true
+        }
+    }
+    return false
+}
+
+func (s *surrealSet) cardinality() int {
+    return len(s.members)
+}
+
+func (s *surrealSet) insert(num surrealNumber) {
+    if !s.isMember(num) {
+        s.members = append(s.members, num)
+    }
+}
+
+func (s *surrealSet) remove(num surrealNumber) {
+    for i := 0; i < len(s.members); i++ {
+        if num.number == s.members[i].number {
+            s.members[i] = s.members[len(s.members)-1]
+            s.members = s.members[:len(s.members)-1]
+        }
+    }
+}
+
+// =============================================================================
+
 func main() {
-    fmt.Println("Hello, World!")
+    // Obtain termination conditions from user.
+    remainingGenerations := flag.Int("generations", 2, "Number of generations of surreal numbers to breed.")
+    flag.Parse()
+    if *remainingGenerations < 1 {
+        log.Fatal("ERROR: The argument to '-generations' must be greater than zero.")
+    }
+
+    // Build a universe to contain all the surreal numbers we breed.
+    // Seed it by hand with the number zero as generation-0.
+    var universe surrealUniverse
+    universe.insert(surrealNumber{surrealValue{nil, nil}, surrealMetadata{0, 0}})
+
+    // TODO: Describe the basic algorithm.
+    for generation := 1; generation <= *remainingGenerations; generation++ {
+// TODO: Continue here next time.
+// Rough Plan:
+//        allSymbols := buildAllSymbolCombinations(generation)
+//        validNumbers := pruneInvalidSymbolCombinations(allSymbols)
+//        addNumbersToUniverse(validNumbers)
+    }
+
+    // TODO: These are just for checking progress. How do I want to render the
+    // final generations vs magnitude chart?
+    fmt.Println("Total Numbers:", len(universe.numbers))
+    fmt.Println(universe.numbers)
 }
+
+// =============================================================================
-- 
2.20.1