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optimize

with_unique_lhs(f, root, bindings)

Ensures all left-hand sides (LHS) of queries are unique by inserting new tensors.

Source code in src/finch/autoschedule/factorizer/optimize.py 
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def with_unique_lhs(
    f, root: LogicStatement, bindings: dict[Alias, TensorFType]
) -> tuple[LogicStatement, dict[Alias, TensorFType]]:
    """
    Ensures all left-hand sides (LHS) of queries are unique by inserting new
    tensors.
    """

    spc = Namespace(root)
    for var in bindings:
        spc.freshen(var.name)
    renames: dict[Alias, Alias] = {}
    bound = set(bindings.keys())
    writes: dict[Alias, Alias] = {}

    def rule_0(node):
        match node:
            case Query(Table(Alias() as lhs, idxs), rhs):
                if lhs in bound:
                    var = Alias(spc.freshen(lhs.name))
                    renames[lhs] = var
                    if lhs in bindings:
                        writes[lhs] = var
                    return Query(Table(var, idxs), rhs)
                bound.add(lhs)
                return None
            case Alias() as a if a in renames:
                return renames[a]
            case Produces(args):
                return Produces(args + tuple(writes.values()))

    root = Rewrite(PostWalk(rule_0))(root)
    root, bindings = f(root, bindings)

    unrenames = {v: k for k, v in renames.items()}

    # Some produces may be renamed during the optimization,
    # so we need to be a bit careful here.
    def rule_1(node):
        match node:
            case Produces(args):
                n_writes = len(writes)
                v_post_list = args[-n_writes:] if n_writes else ()

                bodies: list[LogicStatement] = []
                for (k, _v_pre), v_post in zip(
                    writes.items(), v_post_list, strict=True
                ):
                    idxs = tuple(
                        Field(spc.freshen("i")) for _ in range(bindings[k].ndim)
                    )
                    bodies.append(Query(Table(k, idxs), Table(v_post, idxs)))

                v_post_to_k = dict(zip(v_post_list, writes.keys(), strict=True))
                args_2 = tuple(
                    v_post_to_k.get(a, unrenames.get(a, a))
                    for a in args[: len(args) - n_writes]
                )
                return Plan(tuple(bodies) + (Produces(args_2),))

    return (Rewrite(PostWalk(rule_1))(root), bindings)