🟢🟡🔴 Jello 🔴🟡🟢

Description

A Python script for wrapping the Jellyfish (a fork of Jelly) executable so you can more easily play with the language.

Links

Jelly(fish) Links

• Jelly GitHub Repo
• Jelly Online Interpreter
• Jellyfish Repo 🪼

Livestreams

• Jello LiveStream I
• Jello LiveStream II
• Jello LiveStream III
• Jello LiveStream IV (Top 10)
• Jello LiveStream V (PWC)
• Jello LiveStream VI (bits, keep, cuts.md, --find-by-example)
• Jello LiveStream VII (maxs, cuts, Combinators i.e. Φ.₂)

YouTube Videos

• BQN vs Jelly

Chain Patterns

Special Chain Names

• LCC: Leading Constant Chain
• LDC: Leading Dyadic Chain (described in the first bullet here)
• JL: Just use Left Arg (as v)

Monadic Chains

Q: What makes my chain monadic?
A: If you only pass it one argument (aka ω)

	Chain pattern	New v value	Chain Type	Name	IC	SC
1	+ F ...	v+F(ω)	2-1	dyad-monad	S	Φ
2	+ 1 ...	v+1	2-0	dyad–nilad	d	Δ
3	1 + ...	1+v	0-2	nilad-dyad	d	D
4	+ ...	v+ω	2	dyad	W	Σ
5	F ...	F(v)	1	monad	m	B

• IC = Initial Combinator
• SC = Subsequent Combinator
• m = Monadic function application
• d = Dyadic function application

Dyadic Chains

Q: What makes my chain dyadic?
A: If you pass it two arguments (aka λ and ρ)

	Chain pattern	New v value	Chain Type	Name	IC	SC
1	+ × 1 ...	(v+ρ)×1*	2-2-0	dyad-dyad-nilad
2	+ × ...	v+(λ×ρ)	2-2	dyad-dyad	Φ₁	Φ₁
3	+ 1 ...	v+1	2-0	dyad-nilad	Kd	ε
4	1 + ...	1+v	0-2	nilad-dyad	πd	E
5	+ ...	v+ρ	2	dyad	d	ε'
6	F ...	F(v)	1	monad	Km	B₁

Combinator Table (WIP)

Combinator	Chain Spelling
S	2-1 monadic
B₁	2-1 dyadic
E
ε

Examples

Example 1 (from Section 1)

+H can be called monadically or dyadically, and is a 2-1 chain.

• If called monadically, its a 2-1 monadic train, aka the S combinator.
• If called dyadically, it is a JL+5+6, which ends up being the B₁ combinator.

Example 2 (from Section 4.2)

+²× can be called monadically or dyadically, and it is a 2-1-2 chain.

• If called monadically, S forms a monadic function, that is then used in Σ
• If called dyadically, the 2-1 is the B₁ combinator, and then used in a Φ₁ where the left dyadic function is ⊢.

Example 3 (from Section 4.3)

+×÷H can be called monadically and dyadically, and it is a 2-2-2-1 chain.

• If called monadically, apply W is applied, then evalaate the 2-2 part as repeated (or 2) S combinators, and then the 2-1 chain at the end matches the S combinator.
• If called dyadically, we have a LDC, which means the 2-2-2 forms the Φ₁ which yield a binary function that is then used in the sits inside a B₁ along with the final monadic operation.