PrimalForm

Authors: Jacob Adley (jadley08), Lalo Viduarri (eduvidau)

Description

Racket domain specific language that uses integers in their prime factorization form.

Goal

Setup Instructions

Note: There will probably be some errors while installing, but they are just test failures and the language ?should? still work.

DrRacket Package Manager

1. Open package manager and install via url (add '.git' at the end).
2. Language line at top of file should be #lang primal-form.
3. Good to go!

Manual

1. Clone the repo.
2. Use raco pkg install at the root of the directory to install as a package.
3. Language line at top of file should be #lang primal-form.
4. Good to go!

Syntax

Data Type

For directly inputting integers in their primal form: Literals: ^ : ( ) Variables: x, w ∈ ℤ; y, z ∈ ℕ

(x)
(x y)
(x : y)
(x ^ y)
(x ^ y w)
(x ^ y : w)
(x ^ y : w ^ z)
(x ^ y w ^ z)

The : is an optional separator of primal divisors of input number. The ^ denotes exponentiation from one integer to a Natural.

No kidding operator !t

Usage of this operator disables checking when making a primal number. Increases efficiency for not having to check primality. Relies on user not making an error.

(!t x)
(!t x y)
(!t x : y)
(!t x ^ y)
(!t x ^ y w)
(!t x ^ y : w)
(!t x ^ y : w ^ z)
(!t x ^ y w ^ z)
(!t ...)

The int operator

Use this operator applied to a number and returns the normal base 10 representation of the number such as in regular Racket. Does not perform any prime factorization computation.

x ∈ ℤ

(int x)
  → x

Match

[(fac num >> a b) body] ;; Binds a and b if num is a factor in the thing matched
[(pow num >> a b) body] ;; Binds a and b if there is a factor raised to the num power
[(to-the num1 num2 >> a b) body] ;; Binds a and b if num1 is a factor raised to the num2 power

Implemented Functions

primal-+
primal--
primal-add1
primal-sub1
primal->integer
integer->primal
primal-divisible?
intersection ∩
union ∪
primal-/
primal-*
primal-zero?
primal?
primal=?
cardinality
disjoint?
partition?

Future Implementation

Variables in primal number construction

Want to allow expressions that evaluate to valid integers or naturals to be allowed in primal number construction as described in Data Type.

(define x 5)
(define y 2)
(x ^ y)

Modulo

Want to define at the top of the file the integers we will be using mod n.

Print nice representation, not implementation

Efficiency