Arcangel

Arcangel is a programming language and agent for solving ARC. It's a first step on a path to the world's first system 2 compiler and, eventually, AGI.

Language

The language will certainly change as we experiment with various tradeoffs between expressiveness, compactness, etc.

So, arcangel is a language for solving ARC, so it's fundamentally about colored grids. But also the colors produce structure, so we need something more flexible than just grid. Let's just brainstorm some primitives:

• field
• point
• row
• column
• boundary
• line
• ray
• shape
• color
• direction
• predicate
• region
• set
• box
• coordinate

What about LLM primitives like maybe "system" or "message" or "natural language"? Or conversation?

• system
• message
• model
• language
• conversation
• agent

Or maybe the agent is another language altogether?

What about ARC primitives that aren't about the Grid?

• task
• pair
• rule

What about primitives for exploration?

• fork
• merge
• select
• expand
• generate
• evolution
• simulate
• commit

Is this another language as well?

• git
• agent
• arc

And these languages interact with eachother?

---

So I think we have

• Point := (x, y, energy)

• Set := Predicate

• Predicate (Grid, Point) -> Boolean

• Property Grid -> Boolean

• Relation Grid, Grid -> Boolean

• Invariant Grid[] -> Boolean

Point, Set

1P:1P 1P:NP 1P:1S 1P:NS NP:1P NP:NP NP:1S NP:NS 1S:1S 1S:NS 1S:1P 1S:NP NS:1S NS:NS NS:1P NS:NP

the set of all points within 1 unit from (x, y)

the set of all blue points

predicate isRay conditions isField isBlue isGood description "" signature (set, point) function // do stuff end

NW N NE W (x, y) E SW S SE

iter ray (point, dir) => { // } end

with X ray (2, 3), NE do |point| // do stuff end

kw exp exp exp end

kw
exp name exp name exp end

(a: Type, b: Type, c: Type): Type => { return ... }

def set func call struct sequence read write map filter reduce if and or switch

switch if x === 10 then ... else ... end

if x === 10 then ... else ... end

end

case y => y < 0: ... case z => z > 0: ... end

map numbers

do

end end

filter numbers

do

end end

reduce numbers

func

end

init end

def X with: Field select: (Field, P) -> boolean (Field, P) -> boolean end

kw1 exp kw2 exp kw3 exp end

SIGNATURE IS DIFF

fn signature

end

CALL DATA IS DIFF

def x exp end

set x exp end

func signature ... end

call f a exp b exp ... end

struct key k value v end key k2 value v2 end ... end

sequence exp exp exp ... end

read o v end

write o k v end

@ name a1 exp1 a2 exp2 a3 exp3 end

seq exp exp exp exp exp ... end

def obj struct key x value ... end

key y value ... end end

read x v end

write x vvv end

struct key x value y end

key x value z end end

sequence

read o key k end

write o key y value ... end

read structObj or seqObj do key whatever value thing end

key other value other value end end

write structObj or seqObj do key whatever value thing end

key other value other value end end

def name do ... end

kw exp kw exp kw exp kw exp ...

do exp exp exp ... end

and exp exp exp ... end

or exp exp exp ... end

do def piped do map y do double end end

let piped do map piped do decrement end end

let piped do reduce piped do sum end end end

with thing map y do ... filter thing do ... end

• Point := (x, y, z)
• Set := Point, Point, ...
• Iterator := Set -> Sequence
• Sequence := Point[]
• Predicate := Set => Boolean
• Type := Predicate, Predicate, Predicate...
• Structure := (Set, Type)

TODO

I need to think just a little bit more about what are the primitives. I mean, I'm not even 100% sure I have it clear in my head what makes a good primitive set. The more keywords you have the more "domain knowledge" you need in your head but also your programs will be short. What is the sweet spot for a human programmer? What is the sweet spot for an LLM? Is there a difference?

map, filter, reduce

A Set starts out Unknown -> -> add predicates -> Workable (or whatever)

type X = predicate 1 predicate 2 predicate 3 predicate 4

do

end

and () end () end () end () end () end end

---

time language dsl language dialogue language state tree

you have a language you have a program you have a history you have an engine

def options with goal do 'do this thing'

'do that thing'

'do something else' end

def best_option filter options do succeeded? quickly? end

// with arc

inputs -> outputs

what is the rule?

the rule is basically

what properties do the inputs have? what language do the inputs speak? what properites do the outputs have? what language do the outputs speak? what is a description of the relationship between the two? what is a program written in

type Coordinate = number;

type Energy = number;

type Dimension = number;

type Time = number;

type Datum = { t: Time; x: Coordinate; y: Coordinate; energy: Energy; }

type Set := unordered

type Sequence := ordered

type Field = { height: Dimension; width: Dimension; data: Set; }

Primitive Types

• Void
• Null
• Number
• Boolean
• String
• Map
• Array
• Struct

Named Parameters

kw name exp name exp name exp end

Ordered Parameters

kw exp exp exp end

Function Call

@name name => exp name => exp name => exp end

Function Definition

fn (a: C: b: C c: C): P do

end

Struct

@struct id => String name => String end

Type

...TODO...

Map Literal

{}

Array Literal

[]

Numerical Operators

+, *, /, -,

Boolean Operators

&&, ||, !

Comments

"hash"

Feedback, Commentary, Thoughts

...TODO...

return do

end end

def x 10

def symbol x end value 10 end end

def x y + 10

if when x > 10 end then x end else null end end

Keywords

• {}
• keys
• []
• ...
• def
• let (redef)
• () => {}
• @ (call)
• do
• if
  • when
  • then
  • else
• switch
  • when
  • then
• return

read, write, def, () => {}, do, for, call, struct, map, array, return

def x 5 end

def y

do x + x end end

rows grid end

columns grid end

call f a n b n c v