Hilbert

Do you know the one best language in this world?

I believe mathematics (logic) is absolutely that language.

How can we deal something as great as mathematics in a discrete world?

Hilbert is the answer.

Hilbert lets you have a sense of mathematics using a keyboard, the same as you would with a pen.

+---Discrete world---+                    +------Mathematics-------+
|        Ruby        |                    |        axiom           |
|        TeX         |<----  Hilbert ---->|    Uncountable noun    |
|       Python       |                    |  real number topology  |
+--------------------+                    +------------------------+

Demo

The code below is input and output for the Hilbert interpreter. (You can try it with hilbert -i.)

Logic

P -> Q 
Q -> R
(P -> R)?
=> TRUE

P | Q # P or Q
~P    # not P
Q?    # Q is TRUE?
=> TRUE

Differentiate

d/dx(cos(x))
=> ( - sin( x ) )

# You can omit parentheses

d/dx log(x)
=> ( 1 / x )

d/dy xy
=> ( x )

d/dx e^x
=> e ^ x

Integrate

S(log(x)dx)[0..1]
=> - oo

S(sin(x)dx)[0..pi]
=> 2.0

S(cos(x)dx)[0..pi]
=> 0.0

Limit

lim[x->oo] (1 + 1/x)^x
=> 2.7182682371744895

lim[x->0] 1/x
=> oo

Sigma

∑[x=0,10] x
=> 55.0

Matrix

(1 2 3; 4 5 6)
=> (1 2 3; 4 5 6)

(1 2 3; 4 5 6) + (1 2 3; 4 5 6)
=> (2 4 6; 8 10 12)

(1 2 3; 4 5 6) * (1 2 3)
=> (14 32)

Function

f(x, y) = xy
f(1, 2)
=> 2

How to use

Install the hilbert gem.

$ gem install hilbert

Note to OS X Users: If the above gem command does not work with the stock version of Ruby (due to not being able to build a target indicated in the Makefile), then you will need to install a version of Ruby that includes the appropriate header files. Using homebrew (brew install ruby) will suffice.

Interpreter

$ hilbert -i
Enjoy! ->

Use as native language

Compile into R

$ hilbert -r foo.hr

Compile into Ruby

$ hilbert -rb foo.hr

Compile into Python

$ hilbert -py foo.hr

Use as math template within other langs

class ExampleClass
  def example_method
    #your Ruby codes
    ......

I love mathematics.
  a = (1 3 4)
  # your Hilbert codes
Q.E.D

  end
end

$ hilbert -rb example.rb

class ExampleClass
  def example_method
    #your Ruby codes
    ......

    a = Vector[1, 3, 4]

  end
end

Contributing

Any PRs or issues are welcome. (Please make them to the develop branch.)

You can become a committer, even if you only commit once.

Tech-Curriculums/Hilbert