The three languages

Language	What it is	Reach for it when
Volt	A notation that parses into a graph	The job is “this, for all of those, then combine”
Ohm	Lua 5.4 where LaTeX maths is executable syntax	You need real control flow, or the full 49 operators
Bolt	English, translated by a local model	You would rather describe it than write it

Volt — the program is a graph

Every line names a thing, and the names are the edges. Building the graph is pure, so it is safe to do on every keystroke and on a program you have not read. Because it is a graph rather than a script, the independent work is concurrent, re-running recomputes only what changed, and the cost is countable before anything executes.

# Two companies, two questions. The whole program.

sites  = [apple, nvidia]
topics = [latest earnings, layoffs]
jobs   = sites × topics

found = search(jobs, k: 3)
brief = summarize(found, words: 60)

table(brief)

volt/04-verbs.volt — summarize takes one note, so it maps. join takes the whole list, so it folds. The operator’s own signature decides.

Ohm — mathematics as syntax

Lua 5.4, in which LaTeX mathematics is executable. $ ... $ is an expression; $$ ... $$ holds statements — assignment, loops, conditionals, operators. Maths and Lua share one set of variables; neither is a guest in the other.

-- Maths and Lua share one set of variables.
local A = {3, 1, 4, 1, 5, 9, 2, 6}

$$
  |A|                          % length
  \sum_{x \in A} x             % sum over a list
  \max_{x \in A} x
  \frac{\sum_{x \in A} x}{|A|} % mean
  sq := x \mapsto x^2          % a lambda
  \forall x \in A : sq(x)       % map over a list
  \{1, \dots, 5\}              % a range
$$

-- …and an AI operator is something you compose.
$$
  answer := \Cite_{\Gamma} \circ \Ground_{\Gamma}(\Summarize_{\Psi}(pages); C)
$$

The Math view — One file, three ways: the code you type, the mathematics it renders as, and the Lua it compiles to

49 operators, in five families

Each documented once, in the registry, and rendered everywhere from there. They compose with ∘, × and ∥ the way operators in a notation should.

Family	For	Some of them
`\Psi`	Reasoning	Ask, CoT, ToT, GoT, Plan, Reflect, Critique, Summarize
`\Gamma`	Context	Search, Fetch, Retrieve, Rank, Filter, Compress, Ground, Cite
`\mathcal{M}`	Memory	MemRead, MemWrite, MemSearch, MemSummarize, MemForget
`\Sigma`	Aggregation	Join, Vote, Debate, Cross, Flatten, Sort, Pick, Zip
`\Lambda`	Agents	ReAct, Verify, Fork, Chat

Bolt — English, but it has to compile

Describe the job and a local model writes the program. The model is bounded rather than trusted: it produces source, and source can be checked.

The output must pass the real compiler before it is allowed to run.
Compiler errors are fed back for a fix; if it still fails you get the broken source and an error, not a run.
You see the program it wrote before it executes.
The translation is cached by source and prompt, so the second run never asks the model at all — and a cached translation that no longer compiles is thrown away.

bolt/compare.bolt — Bolt source. English is an input method here — never the program, and never the record.