HSL ~2022.2 %hw5
Homework #5 for Hoon School Live.

One of the most common kinds of cores in Hoon is the door. A door is sort of a gate-builder, which uses its arms to produce gates on demand (e.g. for particular types/auras/molds).

You have learned about the following runes:

- `|_` barcab, for producing a door
- `%~` censig, to "pull an arm" in a door, or use a door to build a new gate and evaluate it
- `|^` barket, for producing a core with a `$` default arm
- `|.` bardot, for producing a trap to be evaluated at a later time
- `|:` barccol, for producing a gate with a custom sample
- `!: zapcol, to turn on debugging in a library or generator file
- `$_` buccab, to define a default sample (other than the bunt) in a core
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What is your planet or comet? (Type "our" in the Dojo of your ship to identify if you're not sure—your ship, not your fakeship.) *
Write a gate named ++decrement that implements decrement without using the standard library functions of ++sub or ++dec. (Hint: Count up to one less than the input value using recursion). *
A prime number is a number which is only divisible by itself and one (it has no factors), such as 2, 3, 5, 7, and 11. Write a gate named ++primes which produces the Euler primes as a list. The Euler primes are given by k²-k+n (for k = 1 to n-1). (Note: Your program will produce a set of primes if given one of "Euler's lucky numbers": 1, 2, 3, 5, 11, 17, or 41.) *
Consider the gate `|=(a=@ud (add 1 a))`. What is the compiled battery of this gate? *
Write a gate named ++factorial which calculates the factorial of a value. Make its default sample value for the input be 1 using either `$_` or `|:`. Make sure that 0! results in the value 1. *
Write a door (named calc if used in Dojo) that takes a @ud sample. It should have four arms to handle multiplication, subtraction, addition, and division against this value. For instance, you should be able to build an addition gate with `~(add calc 3)` and use it with `(~(add calc 3) 5)` to result in 8. *
What are your biggest remaining concerns, points of misunderstanding or fuzzy understanding, or other feedback on Lesson 5?
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