Pulling Ourselves Up By Our Bootstraps

Pulling Ourselves Up By Our Bootstraps

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But Why Would You Even Do This?	Pulling Ourselves Up By Our Bootstraps	Pulling Some Strings

Encoding The Basic Data Types

Using only the characters in our close-to-minimal alphabet, we can immediately represent two basic JavaScript objects:

• [] The empty list, and
• {} The empty object

By performing different combinations of type coercion on these simple values, we can derive the primitive Boolean values of true and false; from which we can then derive the integer values 0 and 1.

Primitive Values

By performing numeric coercion on an empty list, we obtain integer 0

By performing Boolean coercion on an empty list, we obtain the Boolean primitive false

If we then perform Boolean negation on ![] we obtain true

Finally, we can derive integer 1 by performing numeric coercion on !![]

Counting Numbers

We have seen above that when a Boolean value appears in an arithmetic expression, false is coerced to 0 and true is coerced to 1. Knowing this we can now derive the counting numbers.

Since 2 is 1 + 1, we can rewrite 1 + 1 as true + true and still get 2.

Further, we know from above that true can be encoded as !![]; therefore 1 + 1 can be rewritten as:

So now we can generate the first 10 counting numbers:

+[]                                                           // 0
+!![]                                                         // 1
!![] + !![]                                                   // 2
!![] + !![] + !![]                                            // 3
!![] + !![] + !![] + !![]                                     // 4
!![] + !![] + !![] + !![] + !![]                              // 5
!![] + !![] + !![] + !![] + !![] + !![]                       // 6
!![] + !![] + !![] + !![] + !![] + !![] + !![]                // 7
!![] + !![] + !![] + !![] + !![] + !![] + !![] + !![]         // 8
!![] + !![] + !![] + !![] + !![] + !![] + !![] + !![] + !![]  // 9