The modeling DSL: model do ... end with variable/constraint/objective.

import Optex.DSL

m =
  model sense: :min do
    variable x, lb: 0.0
    variable y[i], i <- [1, 2, 3], lb: 0.0
    variable z, type: :bin

    constraint 2 * x + sum(y[i], i <- [1, 2, 3]) <= 10
    constraint x - y[1] >= 0
    constraint sum(y[i], i <- [1, 2, 3], i > 1) == 4

    objective x + 2 * y[1] + z
  end

Indexed families use one generator clause per index. A single index keys the family map by the bare index (y[i]); multiple indices use an explicit tuple key (w[{i, j}], declared as variable w[{i, j}], i <- 1..2, j <- 1..2), because Elixir's parser rejects w[i, j] outright.

Constraints accept the same trailing generator/filter clauses to declare a whole family at once, one constraint per binding:

constraint sum(ship[{p, mk}], mk <- markets) <= supply[p], p <- plants
constraint y[i] <= y[i + 1], i <- [1, 2]

Two conventions worth knowing:

• In if: {b, 0} (indicator active when the binary is off), a 2-tuple whose second element is the literal 0 or 1 is always read as the negation form. To reference an indexed binary in if:, use the access form (if: open[s]), never a raw name tuple.
• Defined variables (variable t = abs(e) / pwl(e, points) / max(args...) / min(args...)) with non-bare arguments introduce machinery: a free auxiliary variable named {t, :arg} pinned by an equality row named {t, :def} (position-indexed {t, {:arg, i}} / {t, {:def, i}} for the multi-argument min/max forms). These are real model variables and appear in solution values (their value is the argument expression's value, often useful when debugging). min/max accept numbers among their arguments (folded into one constant operand) and are a Gurobi-only capability.