Parameters, variables, constraints and the objective

These four blocks carry the math, and given: names what the math reads from another file. Each takes an optional description:, free text that the typeset legend prints.

parameters

A parameter declares a shape. The numbers arrive by name with the data.

dimensions:
  snapshot: { dtype: int }
parameters:
  load:
    dims: [snapshot]
  discount_rate:
    dims: [] # a scalar

Field
dims	required. The dimensions it is indexed by. [] means a scalar
dtype	float, int, bool, str	default float
description	free text	default null

The column has to match the dtype:

declared	the column
float	a float column, or an integer one
int	an integer column
bool	a boolean column	1 and 0 are not booleans. Cast the column
str	a string column

Only float and int are values. A str parameter is a label and a bool parameter is a mask: each selects rows in a where, and writing either as a coefficient, a term or a divisor is a load error. A 0 or 1 that is meant to be multiplied by is declared dtype: int.

variables

A variable is what the solver decides. There is one column per coordinate of dims.

dimensions:
  snapshot: { dtype: int }
  generator: { dtype: str }
parameters:
  capacity: { dims: [generator] }
variables:
  dispatch:
    dims: [snapshot, generator]
    where: "capacity > 0"
    bounds:
      lower: 0
      upper: capacity

Field
dims	required. The dimensions it is indexed by
where	which coordinates exist (absence)	default null
bounds.lower / bounds.upper	a finite number, or the name of a float or int parameter. null leaves that side open	default null
domain	continuous, integer or binary. binary carries fixed 0/1 bounds	default continuous
absence	undefined or zero: what a masked-out coordinate means (absence)	default undefined
description	free text	default null

An open side is null. A bound is never infinite: .inf and -.inf are refused, with null named as the rewrite.

A bound is a name or a number: upper: capacity is accepted, and upper: -rating is refused. Ship the negated column as data.

Equal bounds pin a variable (fix a quantity). A pinned variable is still a variable.

given

given: holds what this file reads and does not build: data under parameters:, columns under variables:, named expressions under expressions:, and row families under constraints:. It takes those four keys and no other. A file with a given: block loads and prints on its own.

given: parameters

A given parameter is data this file reads and another file declares.

dimensions:
  snapshot: { dtype: int }
  generator: { dtype: str }
given:
  parameters:
    gen_cost: { dims: [generator], description: what one unit of output costs }
    gen_on: { dims: [generator], dtype: bool }
  variables:
    gen_p: { dims: [snapshot, generator] }
constraints:
  off_units_idle:
    dims: [snapshot, generator]
    where: not gen_on
    expression: gen_p <= 0
objective:
  sense: minimize
  expression: sum(gen_p * gen_cost)

Field
dims	required. The dimensions the parameter is indexed by
dtype	float, int, bool or str	default float
description	free text	default null

A given parameter is read wherever a parameter is: in an expression, a where and a bound. A name declared under both parameters: and given: parameters: is refused. The typeset legend lists a given parameter under Given.

given: variables

A given variable is a column this file reads and another file introduces.

dimensions:
  snapshot: { dtype: int }
  port: { dtype: str }
  generator: { dtype: str }
relations:
  gen_port: { key: generator, values: port }
variables:
  gen_p: { dims: [snapshot, generator], bounds: { lower: 0 } }
given:
  variables:
    flow:
      dims: [snapshot, port]
      description: what a port puts into its bus
constraints:
  gen_injects:
    dims: [snapshot, generator]
    expression: at(flow, by=gen_port, over=port, into=generator) == gen_p

Field
dims	required. The dimensions the column is indexed by
domain	continuous, integer or binary	default continuous
description	free text	default null

There is no bounds and no where. The file that introduces the column owns both.

An expression reads a given variable as it reads any other. A name declared under both variables: and given: variables: is refused. The typeset legend lists a given variable under Given, and prints no domain line for it.

merge folds a given declaration into the declaration of another fragment that introduces the name, so a composed library carries none of them. The folded declaration is the introducer's, and what the reader states has to say the same or less.

Where nothing in this language introduces the column, the program carries the declaration until a host model provides it (what a program does not build).

given: constraints

A given constraint is a row family that another model builds. This file reads its dual.

dimensions:
  snapshot: { dtype: int }
  bus: { dtype: str }
given:
  constraints:
    balance:
      dims: [snapshot, bus]
      description: the host model clears each bus
expressions:
  price:
    expression: dual(balance)

Field
dims	required. The dimensions the row family runs over
description	free text	default null

There is no expression and no sense. dual(name) is the only place a given row family may be named, and the frame gives the reported expression its dimensions. A name declared under both constraints: and given: constraints: is refused.

given: expressions

A given expression is a named expression this file reads and another file defines.

dimensions:
  snapshot: { dtype: int }
  bus: { dtype: str }
given:
  expressions:
    injection:
      dims: [snapshot, bus]
      description: what the components put into a bus
constraints:
  balance:
    dims: [snapshot, bus]
    expression: injection == 0

Field
dims	required. The dimensions the expression runs over
description	free text	default null

There is no body. This file reads the name as it reads a given variable: a quantity over the frame, of degree one. A where does not read it, because a mask is built before any variable exists. A name declared under both expressions: and given: expressions: is refused. The typeset legend lists a given expression under Given.

merge folds a given expression into the definition of another fragment. The dims are an upper bound: a body that carries a dimension they do not name is refused. A body over fewer dimensions is folded, and the composed model decides: it refuses a row that would repeat across the missing dimension, and accepts one where another term carries it. The composed model holds the body to the rules of every place this file reads it: a square of a given expression that is quadratic is refused once folded.

constraints

One block is one rule. The name of the block is the name of the constraint.

dimensions:
  snapshot: { dtype: int }
  generator: { dtype: str }
parameters:
  load: { dims: [snapshot] }
variables:
  dispatch: { dims: [snapshot, generator] }
constraints:
  power_balance:
    dims: [snapshot]
    expression: sum(dispatch, over=generator) == load

Field
dims	required. The rows this rule builds
expression	required. It uses exactly one of <=, >= or ==
where	which rows are built (absence)	default null
description	free text	default null

The dimensions of the expression must equal its dims (how dimensions combine).

At least one side of the comparator carries a variable. A comparison between numbers and parameters alone is refused at load.

dims: [] gives one scalar row. A scalar variable may not carry a where; put the condition on the constraints that use it.

Two regimes of one rule are two blocks, each under its own where: (state a rule that differs by regime).

objective

The objective is a single block with no name.

dimensions:
  generator: { dtype: str }
parameters:
  cost: { dims: [generator] }
variables:
  dispatch: { dims: [generator] }
objective:
  sense: minimize
  expression: sum(dispatch * cost)

Field
expression	required. Arithmetic, with no comparator
sense	minimize or maximize	default minimize
description	free text	default null

The expression must be scalar. Nothing is summed for you: sum(x * a) + sum(y * b) and sum(x * a + y * b) are both allowed, and they are different models.

There is one objective block. To pursue several goals, weight them into one expression.