Operators

An expression is one of four things:

An operator node always has op and args. Some operators take extra named fields — wrt on D, output_idx/ranges on faq, regions/values on makearray — which are listed on each operator’s page.

Text

k * A * B

JSON

{ "op": "*", "args": ["k", "A", "B"] }

Two tiers

Evaluable core (closed). The operators in the index below have a defined evaluator in every binding. The set is closed: adding one is a specification change. That closure is what lets a conforming reader in any language evaluate any document without executing author-supplied code.

Rewrite-target (open). grad, div, laplacian, integral, a D with a spatial wrt, and any operator you invent have no evaluator. They must be eliminated by a template rewrite before evaluation. A document may load with them present; one that reaches evaluation still carrying them is rejected with unlowered_operator.

A rewrite-target operator gets no privileges: its result dimension is unknown until it is lowered, and no binding may special-case its name. A custom op carries its scheme parameters in attrs rather than in dedicated fields.

Text form

Every example on these pages is one expression shown two ways: a block labelled Text, the notation an author writes, followed by a block labelled JSON, the node it denotes. They are not two different examples, and they are not independent — each pair is checked with the shipped parse_expression and to_ascii, which are inverses, so the text parses to exactly the JSON shown and the JSON prints back to exactly the text.

Multiplication is always explicit (k * A, never kA), because identifiers are multi-letter.

A JSON block with no Text partner is a form the text notation cannot spell today. broadcast and enum have no surface of their own — the first prints as the operator it applies, the second as a dotted name that re-parses as a scoped variable reference. neg shares the surface of unary -. And a few forms lose a field on the way out: a D carrying trailing boundary operands, a grad carrying dim, and an overlap join. Whole .esm documents are shown as JSON throughout; the text notation covers expressions and equations, not files.

Index

Arity structural means the operator’s operands live in dedicated fields rather than in args, and are described on its own page.

The operators esm 2.0.0 removed (fn, table_lookup, skolem, rank, the argmin/argmax operator forms, the two polygon operators, and aggregate, the old spelling of faq) are rejected at load with removed_op; removed operators lists the standard-library template that replaces each, and geometry covers polygon overlap areas.

Rewrite-target sugar — grad, div, laplacian, integral, and a spatial D — is covered on the calculus page. It is not part of the set above.

Dimensional rules

Dimensional analysis follows the operator, and findings are warnings: a dimensional problem never makes a document invalid.

Everything else either propagates its operands’ dimension (+, -, min, max, ifelse) or combines them (*, /, ^). A rewrite-target operator has no rule, so a checker reports unknown and skips the enclosing check.