/**
 * Identity cleanup taps: tiny, exactly-preserving rules that clear the
 * residue other moves leave behind (a stranded 0 in a sum, a 1 in a
 * product, x^1, x^0). All are tap gestures — no drop target.
 *
 * Note on definedness: like additive-cancellation, these can erase a
 * subexpression's undefinedness hole (x^0 ~> 1 is defined even where x is
 * not). The engine-wide soundness contract is truth-where-both-defined,
 * which these preserve exactly.
 */
import { type NodeId } from "../expr.js";
import { type Rule } from "../rule.js";
export interface DropTermParams {
    readonly termId: NodeId;
}
/** x + 0 ~> x (also accepts the canonical −0, Neg(Integer 0)). */
export declare const dropZeroTerm: Rule<DropTermParams>;
/** x · 1 ~> x (strictly the literal 1; −1 is not an identity). */
export declare const dropOneFactor: Rule<DropTermParams>;
/** x^1 ~> x; the base survives by identity. */
export declare const powerOne: Rule<Record<string, never>>;
/** x^0 ~> 1 (0^0 = 1 under the exact evaluator). */
export declare const powerZero: Rule<Record<string, never>>;
/** 0 · x ~> 0: a product with a literal-zero factor is zero. (Unconditionally
 *  exact — 0·anything is 0 — like the other identity cleanups.) Pairs with
 *  drop-zero-term to clear a vanished term, e.g. after 2x + (−2)x folds to 0x. */
export declare const multiplyByZero: Rule<Record<string, never>>;
export declare const pullOutNegative: Rule<Record<string, never>>;
/** (−a)·(−b) ~> a·b: two negative factors in a product cancel. Exact and
 *  unconditional. Common after distributing a negative over a difference, e.g.
 *  (−2)(x − y) → (−2)x + (−2)(−y), where the second term is (−2)(−y) → 2y. */
export declare const cancelNegatives: Rule<Record<string, never>>;
/** −(a + b) ~> −a + (−b): distribute a negation across a sum. Exact and
 *  unconditional. Needed by elimination's subtract step, where α·A + (−1)·B
 *  produces −(B's sum) — e.g. (x + y) − (x − y) has the −(x − y) term. */
export declare const distributeNegation: Rule<Record<string, never>>;
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