@molecule/api-spaced-repetition

Pure-function SM-2 spaced-repetition algorithm for molecule.dev.

Implements Piotr Wozniak's SM-2 algorithm exactly as published in "Optimization of repetition spacing in the course of learning" (1990). No I/O, no DB, no clock reads — every scheduling decision is a pure function of (state, quality, options.now). This keeps it equally usable from API handlers, AI study agents, mock-server fixtures, and frontend test harnesses.

Used by flashcard-app and language-learning today, and by any future app that needs spaced-repetition scheduling. Future algorithms (FSRS / SM-15) can be added as additional named exports without breaking the SM-2 API.

Auto-generated, AI-first package reference for the molecule.dev ecosystem. It is written to be read by coding agents as much as by people, and is generated from this package's source — edit src/index.ts JSDoc, not this file.

Quick Start

import { initialSm2State, reviewSm2 } from '@molecule/api-spaced-repetition'

let state = initialSm2State()
state = reviewSm2(state, 5) // first correct review → interval 1d
state = reviewSm2(state, 4) // second correct review → interval 6d
state = reviewSm2(state, 5) // mature card → interval ≈ 6 * EF
state = reviewSm2(state, 1) // failure → reps reset, interval = 1d, lapse++

// Deterministic scheduling for tests / replays:
const state = reviewSm2(card, 3, { now: new Date('2026-01-01T00:00:00Z') })
// state.next_review is exactly 24h after the supplied `now`.

Type

utility

Installation

npm install @molecule/api-spaced-repetition

API

Interfaces

SpacedRepetitionState

Persisted state for a card / item being scheduled by SM-2.

next_review is the absolute time at which the item becomes due. It is computed as now + interval_days * 24h — i.e. an exact 24-hour multiple, NOT a calendar-day boundary in any timezone. This keeps the algorithm timezone-independent: callers that want "midnight in the user's local timezone" can post-process next_review themselves.

interface SpacedRepetitionState {
  /**
   * Multiplier applied to the previous interval once a card has been
   * reviewed at least twice. Floor of `1.3` per Wozniak. SM-2 default
   * for a brand-new card is `2.5`.
   */
  ease_factor: number
  /**
   * Number of days until the next review. `0` for a card that has
   * never been reviewed. After a successful first review this becomes
   * `1`; after a successful second review it becomes `6`; subsequent
   * reviews multiply by `ease_factor`.
   */
  interval_days: number
  /**
   * Count of consecutive successful reviews (grade `>= 3`). Resets to
   * `0` on any failed review.
   */
  repetitions: number
  /**
   * Lifetime count of failed reviews (grade `< 3`). Never decreases.
   * Useful for surfacing "leech" cards that lapse repeatedly.
   */
  lapses: number
  /**
   * Absolute time at which this card is next due for review. Compared
   * with `Date.now()` to determine due cards.
   */
  next_review: Date
}

ReviewOptions

Optional inputs for {@link reviewSm2}.

interface ReviewOptions {
  /**
   * Override the "current time" used to compute `next_review`. Useful
   * for deterministic tests and replaying review logs. Defaults to
   * `new Date()`.
   */
  now?: Date
}

Types

SpacedRepetitionGrade

SM-2 review quality / grade scale, as defined in Wozniak (1990).

• 0 — Complete blackout. No recognition.
• 1 — Incorrect; the correct answer felt familiar once shown.
• 2 — Incorrect; the correct answer seemed easy in hindsight.
• 3 — Correct, but recalled with serious difficulty.
• 4 — Correct, recalled with some hesitation.
• 5 — Perfect recall.

Grades < 3 are treated as failures: repetitions reset to 0 and the interval resets to 1 day. Grades >= 3 advance the schedule.

type SpacedRepetitionGrade = 0 | 1 | 2 | 3 | 4 | 5

Functions

initialSm2State(now)

Build a default state for a card that has never been reviewed. The returned state is dueAt the supplied now (or right now if omitted), so a brand-new card is immediately eligible for review.

function initialSm2State(now?: Date): SpacedRepetitionState

• now — Reference time for next_review. Defaults to new Date().

Returns: A fresh, unreviewed-card state.

reviewSm2(state, quality, options)

Apply one SM-2 review to an item. Pure function — does no I/O, reads no clocks except via the optional options.now.

Algorithm:

1. Update ease factor: EF' = max(1.3, EF + (0.1 - (5 - q) * (0.08 + (5 - q) * 0.02)))
2. If quality < 3 → reset repetitions = 0, interval = 1, increment lapses.
3. Else → repetitions += 1; first repetition gives interval = 1, second gives interval = 6, subsequent multiply previous interval by EF'.
4. next_review = now + interval * 24h.

function reviewSm2(
  state: SpacedRepetitionState,
  quality: SpacedRepetitionGrade,
  options?: ReviewOptions,
): SpacedRepetitionState

• state — Current persisted state of the item being reviewed.
• quality — Grade 0..5 describing the user's recall performance.
• options — Optional clock override (options.now).

Returns: The updated state. The input state is not mutated.

Constants

DEFAULT_EASE_FACTOR

Default starting ease factor for a fresh card, per Wozniak.

const DEFAULT_EASE_FACTOR: 2.5

MIN_EASE_FACTOR

Lower bound on the ease factor. SM-2 forbids easing below this.

const MIN_EASE_FACTOR: 1.3