Algebraic types demystified

In programming, a type is what a variable is allowed to represent.  Typical types are character, integer, and floating point number.  These are the usual atomic types, meaning they hold and represent only one value.  Typical collection types are lists (of one type) and strings (lists of characters).

Functional programmers like to talk about algebraic types.  They wrap these concepts in mystery and superstition, because they originated in mathematics.  They call them "product" and "sum" types.  But really, they're remarkably simple collections of other types.  

Product type = AND collection

A product type is a fixed length, ordered list of various types, where you must fill each element.  A and B and C and D.  It is better known in programming as a tuple.  If you name what each type represents, it is a struct or record.  For those working with an object-oriented language, this is a class.

Sum type = OR collection

A sum type is a set or list of various types, from which you must choose exactly one element to fill.  E or F or G or H.  It is better known as an enum (when referencing elements of a single type) or union (when referencing elements of disparate types).

You can combine these two concepts with each other and the atomic and basic collection types to produce arbitrarily complex data structures.  Some languages even allow types to be recursive, and include themselves as an element.

Contrived example:

type NameOrNumber = union [string, int]    # can be either but not both

var myGirl1, myGirl2: NameOrNumber

myGirl1 = "Jenny"

myGirl2 = 8675309

Overly Contrived Example:

type Lowercase = enum [`a ... `z]    # sum type

type Uppercase = enum [`A ... `Z]    # sum type

type NameFormat =  record       # product type

    initial: Uppercase

    rest: list[Lowercase]

type PersonName = record        # product type

    firstName: NameFormat

    middleInitial: Uppercase

    lastName: NameFormat

type PersonInitials = record        # product type

    firstInitial, middleInitial, lastInitial: Uppercase

type Person = union [PersonName, PersonInitials]    # sum type

var generalName: PersonName        # create a variable

generalName.firstName.initial = `G

generalName.firstName.rest = [`e, `o, `r, `g, `e]

generalName.middleInitial = `S

generalName.lastName.initial = `P

generalName.lastName.rest = [`a, `t, `t, `o, `n]

var nationName: PersonInitials        # create a completely different variable

nationName.firstInitial = `U

nationName.middleInitial = `S

nationName.lastInitial = `A

var name1, name2: Person        # create two variables of the same union type

name1 = generalName               # which are used

name2 = nationName                 # in different ways

How stupid the lies are

Zelensky, dictator of Ukraine, recently claimed that they have lost a total of 31,000 men so far in their war with Russia.

Bwehahahaha -wheeze- hahahahha!  

They lost 1,500 dead and 1,000 captured in just the two day rout from Avdiivka.

I'm sure this announcement had nothing to do with the cancellation of all future elections.

Remember:  They announced last November that they'd lost over 1.1 million men so far.  Which, when you take into account their population of less than 25 million, means they've lost around 10% of their total number of men.  Naturally, they immediately arrested the people responsible for accidentally leaking the (likely) true figures.

The five basic principles

There seem to be five basic rules, or principles, of the universe.  They are simple, yet have remarkably profound consequences.

1. The total energy at every point is a constant.

2. There is no such thing as negative energy.

3. Spacetime is the field governing motion.

4. Time is the source of all potential energy.

5. Proper time is a type of spin.

All else follows. There are no infinities. There are no singularities. There are no contradictions. Proper time appears to be left handed, except for antimatter.

"Proper time" is the time you feel, by the way.  It is the time that affects you.  Photons have no proper time. 

Black holes are hollow shells of maximal density surrounding absolute nothingness.  All the energy has been taken from the center by the mass and energy of the shell, leaving nothing for anything else to exist.  This is how black holes can rotate and move about the galaxy.  The hole grows as energy density increases, pushing everything out into a spheroid shell.

What are you testing for?

I am very intelligent.  I was a counterintelligence agent, which is the opposite of intelligence, which means I have been specially trained how to be stupid!

I am very well educated.  I dropped out of college twice!

I score very well on most tests.  Except...

When I first joined the military, back when Reagan was President, I went to Pensacola after basic training.  As part of the in processing, every Army trainee on this Navy base where dentists were also trained got two fillings, whether you needed them or not.  Ah, the joys of taking a typing test (real typewriters, following a program on real punch tape) while wearing heavy headphones immediately after getting two fillings.

We also had to participate in this new personality profile test.  I guess it was part of the counterintelligence program, but I'm not certain about that.  The Navy was just weird, sometimes, especially from a Soldier's perspective.

I had already done something like this in high school, as part of the vocational advisement program.  It showed that I was neither suited for nor interested in any profession.  Oddly enough, the vocational test had nothing in it about wanting to join the military, the only thing I had really wanted to do since I was 8 years old or so.

So I took the Navy's personality test.  A few days later, I was ordered to take a different one.  They were sort of silly, but something to do while I waited for my class cycle to start.

A couple days after taking the second test, I was called to the office of the testing program manager.  He railed at me for a while.  He accused me of cheating on the tests.  He asked me who I thought I was?  Who sent me?  What am I really doing there on the base?  Who did I really work for?

I had no answers to these questions, and no idea what he was going on about.  So I asked what the real problem was.  He told me that I must have been specially prepared by someone, because both tests indicated that I had no discernible personality.

New books!

I hate writing blurbs for books.  I'm terrible at it.  So here are a few new (and new to me) books I enjoyed, so you might, as well.

Harrier and Murder

Ice

The Sumire Series

Doctor Inferno

The Arcane Casebook Series

It's goundhog day... again

Well, the day is happening again.  Once again, we entrust our fate to a large, generally ill tempered rodent.

Happy groundhog day, everyone!

Don't drive angry.

Gang warfare

Large gangs cannot be effectively fought by police using normal, civil rights focused procedures. Large gangs are alternate governments, with their own laws, taxes, police, courts, intelligence, and military forces. They are insurgencies. They must be fought with heavy handed policing in conjunction with military force. Anything less is a waste of men, money, and time.

Fighting a gang is fighting a civil war.