Compiles a validated ExDatalog.Program into an ExDatalog.IR program.

The compiler transforms the high-level AST (rules, atoms, terms, constraints) into a deterministic, engine-neutral intermediate representation suitable for evaluation by any backend that implements ExDatalog.Engine.

Compilation steps

1. Validate — calls ExDatalog.Validator.validate/1 to ensure the program is structurally and semantically correct.

2. Assign strata — uses ExDatalog.Compiler.Stratifier to determine which stratum each rule belongs to.

3. Canonicalize — sorts relations, facts, and rules into deterministic order. Rule IDs are assigned monotonically in canonical order.

4. Convert — transforms AST types (Term, Atom, Constraint) into IR types (IRTerm, IRAtom, IRConstraint), replacing {:const, value} with tagged IR values ({:const, {:int, n}}, {:const, {:atom, a}}, etc.).

The output is a %ExDatalog.IR{} struct that is deterministic for a given input program: compiling the same program twice produces identical IR.

After compilation, the IR is validated against structural invariants: unique rule IDs, stratum bounds, rule-in-stratum consistency, and relation reference integrity. Violations raise an error — these indicate a bug in the compiler, not an invalid program (programs are validated before compilation).

Examples

iex> alias ExDatalog.{Program, Rule, Atom, Term, Compiler}
iex> program =
...>   Program.new()
...>   |> Program.add_relation("parent", [:atom, :atom])
...>   |> Program.add_relation("ancestor", [:atom, :atom])
...>   |> Program.add_fact("parent", [:alice, :bob])
...>   |> Program.add_rule(
...>     Rule.new(
...>       Atom.new("ancestor", [Term.var("X"), Term.var("Y")]),
...>       [{:positive, Atom.new("parent", [Term.var("X"), Term.var("Y")])}]
...>     )
...>   )
iex> {:ok, ir} = Compiler.compile(program)
iex> length(ir.rules) == 1 and length(ir.relations) == 2
true