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J Incunabulum
What is the t variable really tracking?
The t variable is the type of the array. In the Incunabulum there are only 2 types: unboxed, and boxed. See https://www.jsoftware.com/papers/AIOJ/typedefA.htm
How does one create a multi-dimensional array easily?
d=3,2
a=d#~6
What are some interesting programs one can run with this mini-interpreter?
Not any that couldn't be run with any other APL. Imo, the main value of the Incunabulum is just how it works.