fancylojban challenges

Lojban is supposed to be a logical language, so why not practice translating some common mathematical statements, or algorithms

Additional challenge: Don't use mekso with VUhU. Or use them, if you prefer the challenge of wrangling with mekso grammar...

Fermat's Last Theorem

(The statement, not the proof, of course!)

"No three positive integers a, b, and c can satisfy the equation aⁿ + bⁿ = cⁿ for any integer value of n greater than two."

Subproblem #1: How to explicitly make letter pronouns or ko'a-series existential, without having to assign {daxivo goi ny} e.g.?

Solution by la zipcpi (doesn't solve subproblem #1)

Euclid's Algorithm for Greatest Common Divisor

function gcd(a, b)
    if b = 0
       return a
    else
       return gcd(b, a mod b)

Also try a non-recursive version, but we'd probably need a new brivla for while-loop, and {tu'e...tu'u} in NU.

Subproblem #1: come up with a better brivla to define than one based on the abbreviation "gcd"

Recursive [zipcpi: solution-gcd-1|solution] by la zipcpi (doesn't solve subproblem #1)

Non-recursive solution by la zipcpi (uses {zvailu} for while-loop, {goilka'i} as suggested below, and {tu'e...tu'u} in NU)

Towers of Hanoi

x1 is the sequence of moves that move discs from x2 to x3 using x4 as temporary storage.

Recursive solution by la xalbo

While-loop brivla - English and Lojban definitions

In the vein of ifle, we might need brivla suitable for describing while-loops...

While-loop:

As long as x1 (du'u proposition) is true, x2 (action/event) repeatedly happens

Do-while-loop:

x1 (action/event) happens, then repeats as long as x2 (du'u proposition) is true.

With ko'oi / gau ko / ko gasnu lo nu turning it into a command that the agent (whether it's a computer or a person) should follow.

Question: Can Lojban, as designed, actually handle this? Can KOhA and letteral variables be reinterpreted in an existing du'u-proposition, or does the proposition remain the same even if the variables get goi-ed to something else?

Thoughts: Perhaps, don't use {goi}. {goi} is problematic for any use other than assigning nonce pronouns anyway, due to ambiguity of directionality. Instead, for something like "var x = 1; x = x + 1", we use brivla that says that x is a variable *standing in* for some object (e.g. something like {ko'oi la .xys. cu goilka'i li pa .i ko'oi la .xys. cu goilka'i le sumji be [la'e?] la .xys. bei li pa}) . This allows the variables to change without actually changing the objects themselves, and allows the truth value of that du'u-proposition to change.

goilka'i tentative definition

goilka'i: x1 (quoted-pronoun or object) is a variable representing x2 (any sumti).

{goi} is a special case where {zo ko'a} (e.g.) becomes a goilka'i of something. However the main use of goilka'i is to allow {ko'a (bi'u)} or {la .xys.}, not {zo ko'a}, to be variables.

Informal algorithms

Instructional texts like cookbooks or game rules, that might have use for certain programming-language-like structures, but which might not need to be specified to the last detail like programming languages...