(apologies for the lengthy post, but I would really appreciate some feedback)

Rome: A thesis for Lisp in the 4th dimension, with fewer parenthesis

Introduction

In the course of it's development, the LISP system went through several stages of simplification and eventually came to be based on a scheme for representing the partial recursive functions of a certain class of symbolic expressions...and it now seems expedient to expound the system by starting with the class of expressions called S-expressions.

-- John McCarthy in the seminal paper that introduced Lisp to the world in April 1960.

Also, from the paper:

An S-expression is then simply an ordered pair, the terms of which may be atomic symbols or simpler S-expressions.

This statement can be expressed symbolically as:

S := (S . S)

Any of the S on the right hand side can either be a terminal symbol that cannot be further expanded called an atom or it be expanded recursively in the same manner, as another (S. S).

Turtles all the way down.

The whole of Lisp is built up from this scheme of S-expressions.

Hmm....So an S-expression is simply an ordered pair (yes, and recursive...)

But why a pair? (Reminds me of Key-Value pair).

Why not three? (Like you know: Key, Relation, Value, like in RDF triplets? )

You know what, better stil...Why not four?

4-tuples. Key, relation, value + time? (like in Datomic clojure DB and datalog etc).

O-expressions

What if, instead of S-expressions, we start with ....say O-expressions

O := (O . O . O . O)

Where each O can be:

expanded further as (O . O . O .O)

or it can be a terminal symbol.

an S expression (maybe I am not sure about this).

Will we end up with a Lisp like language that's somehow more expressive? In the same manner, RDF triplets are more expressive than key-value pairs.

Will we be able to programmatically play with time?

Like how including time in the 4-tuple gives datomic time travelling capabilities?

Well, we will find out I guess....

What's in a name

For fun and for clarity, I am using the uppercase greek symbol of Omicron to represent the O in the O-expression.

And I came up with a fun acronym too:

ROME stands for Recursive Omicron Meta Evaluator (ha!) This is the name of the compiler/translator itself.

and the language itself to be called:

Roman: Recursive Omicron Meta Algebraic Notation. (ha ha!).

(In the long tradition of functional languages, everything will be an Expression in Rome, no statements vs expressions dilemmas.

Please...can we at least not have as many parenthesis?

What if we express function composition as:

x f g to mean the same as (g(f(x)))

Look ma! fewer parenthesis.

Lisp uses prefix notation

(add a b)

where a and b are the arguments to the function.

Let's go ahead and use this format for function calls

a b add

Also we need one last thing. Take a leaf out of Elixir/ELM/ReasonML pipe operator. |> We will be using this too in our approach to have fewer parentheses.

Examples of how Rome might look:

Assign 5 to a.

a = 5 def

Check if a is greather than b

a > b ?

Let it be a fact that the symbol a is greather than b.

a > b def

Nested expressions

(11 19 *) < (9 23 *) ?

or

11 19 *
, <
, 9 23 *
, ?

assign it to. value

a = (11 19 *, 9 23 *, +) def

Define a function to add 3 to any number

add3 (a) (a 3 +) fn

or using the lambda method (=> stands in for lambda)

add3 = ((a) (a 3 +) =>) def

Yeah you can't get rid of all the brackets I think.

Function calls:

4 add3 .

with assigns

a = 4 add3

Find b.

b > a def
, b < c def
, a = 1 def
, c = 3 def
, b ?

What if the above ended with , b . instead. Well we'll come to that soon I hope.

Piping function outputs.

3 add3
|> add3
|> 2 add

will eval to

7 2 add

Conditionals

x if (x > 0) ?

Can we do else case like this?

x if (x > 0) or else -x ?

x if (x > 0 ?) else 0 if (x = 0 ?) else -x if (x < 0 ?) or else 1000000 ?

Quote

(+ 2 3)'

O.0: (+ 2 3)

Maybe we can use '.' to send it "into" the system, along the z-axis to evaluate it.

And use - to connect with other fellow functions in the same "plane" of abstraction.

But those are wild ideas, I don't want to get into now.

Can we use @ to denote apply?

apply @
eval |
quote '
bind &

x = (1 2 3)' def

Get h, t, r, e, s, p

(x 1 2 3)'t

Time

We havent defined any explicit timeline manipulating symbols/procedures but def can be seen as saying to the system "From now on, let it be known to this system that the following is a fact.."

and ? in a > b ? can be seen as "Tell me, as of now, is a > b etc etc".

We will try to build up the syntax and semantics of playing with time in later chapters. For now, let's use the following symbol scheme to denote a point in time or a tick (specifically a lamport's time stamp but we will come to that later).

We will represent what NASA calls T0 as .0 or . to denote now. And T+1 as .1 T-1 as .-1 or ~1

.-1
-- is same as
~1
-- not the same as
.1 - 1 ? --: .0
-- now is
.0
-- same as
.

What is your wildest programming language idea? This could be fun (silly) ideas or really cool and useful ones.

Go!

Also on le twatter: https://twitter.com/replit/status/1275525512861900800

In one line: extending Lisp to the 4th dimension.

(apologies for the lengthy post, but I would really appreciate some feedback)

## Rome: A thesis for Lisp in the 4th dimension, with fewer parenthesis

## Introduction

Also, from the paper:

This statement can be expressed symbolically as:

Any of the

`S`

on the right hand side can either be a terminal symbol that cannot be further expanded called an atom or it be expanded recursively in the same manner, as another`(S. S)`

.## Turtles all the way down.

The whole of Lisp is built up from this scheme of S-expressions.

Hmm....So an S-expression is simply an ordered pair (yes, and recursive...)

But why a pair? (Reminds me of Key-Value pair).

Why not three? (Like you know: Key,

Relation, Value, like in RDF triplets? )You know what, better stil...Why not four?

4-tuples. Key, relation, value + time? (like in Datomic clojure DB and datalog etc).

## O-expressions

What if, instead of S-expressions, we start with ....say O-expressions

Where each

`O`

can be:Will we end up with a Lisp like language that's somehow more expressive?

In the same manner, RDF triplets are more expressive than key-value pairs.

Will we be able to programmatically play with time?

Like how including time in the 4-tuple gives datomic time travelling capabilities?

Well, we will find out I guess....

## What's in a name

For fun and for clarity, I am using the uppercase greek symbol of Omicron to represent the O in the O-expression.

And I came up with a fun acronym too:

ROME stands for Recursive Omicron Meta Evaluator (ha!) This is the name of the compiler/translator itself.

and the language itself to be called:

Roman: Recursive Omicron Meta Algebraic Notation. (ha ha!).

(In the long tradition of functional languages, everything will be an Expression in Rome, no statements vs expressions dilemmas.

## Please...can we at least not have as many parenthesis?

What if we express function composition as:

Look ma! fewer parenthesis.

Lisp uses prefix notation

(add a b)

where a and b are the arguments to the function.

Let's go ahead and use this format for function calls

Also we need one last thing. Take a leaf out of Elixir/ELM/ReasonML pipe operator. |> We will be using this too in our approach to have fewer parentheses.

## Examples of how Rome might look:

Assign

`5`

to`a`

.Check if a is greather than b

Let it be a fact that the symbol a is greather than b.

Nested expressions

or

assign it to. value

Define a function to add 3 to any number

or using the lambda method (=> stands in for lambda)

Yeah you can't get rid of

allthe brackets I think.Function calls:

with assigns

Find

`b`

.What if the above ended with

`, b .`

instead. Well we'll come to that soon I hope.Piping function outputs.

will eval to

## Conditionals

Can we do else case like this?

## Quote

Maybe we can use '.' to send it "into" the system, along the z-axis to evaluate it.

And use - to connect with other fellow functions in the same "plane" of abstraction.

But those are wild ideas, I don't want to get into now.

Can we use

`@`

to denote apply?Get h, t, r, e, s, p

## Time

We havent defined any explicit timeline manipulating symbols/procedures but

`def`

can be seen as saying to the system "From now on, let it be known to this system that the following is a fact.."and

`?`

in`a > b ?`

can be seen as "Tell me, as ofnow, is a > b etc etc".We will try to build up the syntax and semantics of playing with time in later chapters. For now, let's use the following symbol scheme to denote a point in time or a tick (specifically a lamport's time stamp but we will come to that later).

We will represent what NASA calls T0 as

`.0`

or`.`

to denotenow. And T+1 as`.1`

T-1 as`.-1`

or`~1`