The limits of the language

A model can only say what the language has words for. This page says which words can be added, and which cannot. Read it before you ask for a new operator, block or keyword. For the rules a model itself has to obey, read the ten rules.

How a new construct enters

A request for something new is one of three kinds, and the kind decides what it costs to add.

• A macro is a template with arguments, written in the file under macros:. Adding one costs nothing: it uses only operators that exist, so no engine has to change. Most requests turn out to be a macro (macros).
• A primitive is an operator built into the language: sum, sum_back, at, shift, and the where comparisons. A file cannot add one. Adding one here is the expensive kind: every engine that builds models has to implement it, and the typesetter has to print it in LaTeX, Typst and Markdown.
• A formulation is a block that states ordinary variables and constraints rather than being one. piecewise: and sos: are the two. It costs as much as a primitive to build, but composes as freely as a macro. A formulation emits variables and constraints, states what it assumes of the data as ordinary assumptions, and emits no parameter — so the same data binds a model and its expansion, and spec.expand() needs no source a reader has to supply.

A request that is none of the three is refused, and the table of refusals records it with what to write instead.

What a new primitive has to satisfy

A macro must be able to call it. Everything a modeller might pass in goes in the value of a keyword argument, such as over=snapshot.

An operator may read the whole table. It pays one full pass over the data. sum(p, over=g) reads one row per generator, and shift(p, along=t, offset=1) reads the row before. Each reads a bounded number of rows per output row, so an engine builds the model one chunk of rows at a time. An operator that reads every row to produce one row costs one full pass before any chunk builds, and a request for such an operator names that price.

An operator that calls itself is refused. Nothing bounds how far it expands.

The operator	Allowed?
filters rows on a column they already carry	yes
joins each row against a parameter or a relation	yes
reads a fixed number of neighbouring rows	yes
reads only the coordinate labels	yes
reads every row	yes, at one full pass before any chunk builds
calls itself	no, and the message names what to write instead

Degree is not a third test. p * q at one coordinate is a join of a table with itself, so the objective and the constraints take it. A product of two sums, sum(x, over=i) * sum(y, over=j), is refused, because the file does not say how many terms either sum has. x[i] * y[j] * a[i, j] is allowed, because the table a says which pairs exist.

A new primitive is finished when lowering builds it, the typesetter prints it in all three formats, and an engine's build of a model that uses it matches the same model written out by hand.

Three kinds of refusal

The language refuses it because…	Examples	Can it change?
one solver cannot take it	indicator constraints; a quadratic constraint. sos: was in this group, and entered: a solver with sets takes it as one, and a model for a solver without is written out first	yes, solver by solver
the file would stop being the artifact	arbitrary Python, whose content no loader can check and no typesetter can print	no
this project puts the work elsewhere	data preparation such as resampling; helpers for one domain; Python that decides which declarations exist	it could; this project does not want it to

Three things never appear inside one model: an if, a loop, and a set of declarations that depends on the data. A dimension computed before the model loads is fine: a cycle basis for Kirchhoff's voltage law is a graph algorithm run in data preparation, and its result arrives as a parameter. What no model can hold is work that needs the solver's answer before it can write the next row, such as cuts added during a solve. A tool can still loop over models: a rolling horizon and Benders decomposition each build a model, solve it, and build the next.

Solver capability

Whether an engine can build the operator is one question. Whether a given solver then accepts the result is a second one, and the language does not answer it. If it did, one solver's limits would be written into the language, and every other solver would inherit them.

• HiGHS has no special-ordered sets. Gurobi does. An engine handing a model to Gurobi passes the set through; one handing it to HiGHS refuses it, and the author writes the set out with spec.expand('sos') first.
• A quadratic constraint is accepted by some solvers only when it is convex, and convexity depends on the numbers, which the file does not have.

So sos: entered the language on the first question alone. Each engine then decides whether it takes a set, and the language decides what a set is written out as.

What counts as data preparation

From inside a model, a column you computed in pandas and a column the language could have derived look the same: a parameter arrives, and a constraint reads it. One sentence tells them apart:

Data preparation computes what the model cannot know. The language derives what it can from data the model already has.

A cycle basis is the first kind. It needs the network's topology, which only the data has, so cycle_incidence arrives as a parameter. A minimum up time is the second kind. min_up_time is a column the model already binds, so sum_back(window=min_up_time) reads the width off the column and you ship no window mask.

Checking a column is neither. p_min <= p_max is a rule two consumers must not answer differently, so the rule is language and the check is the consumer's. The file states the predicate, and whoever binds the numbers runs it.

Deliberate non-primitives

What has been asked for and refused, with the reason and what to write instead. That another tool has a feature is not by itself a reason to add it.

Request	Why refused	Instead
Resampling, clustering, file IO, unit conversion	not math	do it in data preparation, and pass a parameter
Unit checking at load	a unit: MW on a parameter is a claim that nothing checks against the column, and it needs a grammar of units the language then maintains	convert to one unit system in data preparation, and name it in the description:. A range the data has to meet is an assumptions: entry
Array operations such as merge and reindex	there is no end to them	data preparation
Helpers for one domain, such as reduce_carrier_dim	writes one field's vocabulary into the language	a component library of macros over the operators that exist
A vocabulary for tracked metrics: impacts:, effects:, a costs axis	a named expression already does this	an impact dimension and one named expression. Cap it with a constraint, weight it in the objective, read it back after the solve
** with a variable in the base or the exponent	the exponent would decide the degree, and to_spec reads no data	x * x for a square. ** over parameters and numbers is allowed
Normalisation, x / sum(x)	dividing by a variable is not a polynomial, and no solver takes it	write the ratio as a constraint, or fix the denominator
An if, a loop, or declarations that depend on the data	to_spec could no longer read the file without the data	where: masks and dims: dimensions. A tool may loop over models
A Python API for building models	the model is the file you review and diff	YAML, or a dict with the same keys (below)
A where comparing a relation column against the dimension it maps into	the relation already pairs the two, and a mask over the pair is the same fact in a bigger shape	place the quantity with sum(by=), or read it with at(by=) (operators)

Composition (component libraries)

A component library is a set of templates, such as a boiler, a battery and a line, that agree on how ports and flows are named. You merge the templates you need into one file, wire the components together with a connectivity table in the data, and close the system with one sum(by=) balance.

The topology is data. Adding a second battery is a row in a table, so the file grows with the number of component types.

Merging happens before to_spec. Every function here takes a dict as well as a path, so a model assembled in Python is checked exactly as a file is, and Spec.to_yaml() writes the file a reviewer reads. A dict may hold only what a file may hold, so the file itself states no composition. A template names no sibling, and no key says which fragment wins where two declare a p.