Created basic data structures and methods for dealing with a collection of surreal...

[surreal-numbers] / chapter-1-experiments / ch1-breeding-numbers.go

// (c) 2020 Aaron Taylor <ataylor at subgeniuskitty dot com>
// See LICENSE.txt file for copyright and license details.

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() {
    // 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)
}

// =============================================================================