This package provides everything necessary to create spaced repetition software using the SM2+ algorithm. The SM2+ algorithm was proposed by "BlueRaja" as an improvement of the SM-2 algorithm, which has been released for free public use when accompanied by the following notice:
Algorithm SM-2, (C) Copyright SuperMemo World, 1991.
For details about the SM2+ algorithm and its purported advantages over the SM-2 algorithm, please refer to the following blog post.
It should be noted that this algorithm produces seemingly illogical behavior, namely that more incorrect answers result in longer intervals than less incorrect answers. Do not use it if this behavior is objectionable to you (as it probably should be). A custom scheduling function for incorrect answers may be provided if one still wishes to use it (with a different incorrect scheduler).
Most notably (versus SM-2), the SM2+ algorithm "rewards" correctly answering more-overdue cards and sorts due items based on the proportion they are overdue, not the absolute amount they are overdue by. Additionally, the initial intervals are 1 day -> 3 days, rather than 1 day -> 6 days.
The building blocks of this package are Card
s and Deck
s. In simple terms, a Card
may be thought of as a single flashcard and a Deck
as a list or collection of Card
s.
{ a | srsData : SRSData }
A Card
represents a single question or unit of knowledge the user will review. In general terms, each would represent a single flashcard. Card
is defined as an extensible record; as such, whatever necessary custom fields for a use case may simply be included in the record, e.g.:
type alias MyFlashcard =
Card { prompt : String, answer : String }
A Card
contains only the information necessary for scheduling and nothing else; all other information should be added as in the above example.
Array (Card a)
A Deck
represents a list of cards to be studied (this might be called a "collection" in other software). It is simply an Array
of Card
and requires no special creation or manipulation. Maintaining the state of a Deck
may be handled by the user of the module or by this module itself. In general, it is probably best not to add a massive quantity of new (unstudied) cards to a deck at once.
A Card
may be created by use of the newSRSData
function, as in the following example:
type alias MyFlashcard =
Card { prompt : String, answer : String }
myFlashcard : MyFlashcard
myFlashcard =
{ prompt = "SYN"
, answer = "SYN-ACK"
, srsData = newSRSData
}
SpacedRepetition.Internal.SMTwoPlus.ReviewHistory
SRSData
contains all data necessary for the SM2+ scheduling algorithm and may be created with the newSRSData
function. It may additionally be saved/loaded using the Json encoder/decoder in this package
newSRSData : SRSData
newSRSData
creates a new SRSData
for inclusion in a Card
.
Since Card
data must necessarily be preserved between sessions, a Json encoder/decoder is provided for SRSData
. It may be utilized as follows:
import Json.Decode as Decode
import Json.Encode as Encode
type alias MyFlashcard =
Card { prompt : String, answer : String }
myFlashcardConstructor : SRSData -> String -> String -> MyFlashcard
myFlashcardConstructor srsData prompt answer =
{ prompt = prompt
, answer = answer
, srsData = srsData
}
myFlashcardToJson : MyFlashcard -> String
myFlashcardToJson myCard =
Encode.encode 0 <|
Encode.object
[ ( "srsData", encoderSRSData myCard.srsData )
, ( "prompt", Encode.string myCard.prompt )
, ( "answer", Encode.string myCard.answer )
]
myFlashcardDecoder : Decode.Decoder MyFlashcard
myFlashcardDecoder =
Decode.map3 myFlashcardConstructor
(Decode.field "srsData" decoderSRSData)
(Decode.field "prompt" Decode.string)
(Decode.field "answer" Decode.string)
jsonToMyFlashcard : String -> Result Decode.Error MyFlashcard
jsonToMyFlashcard str =
Decode.decodeString myFlashcardDecoder str
encoderSRSData : SRSData -> Json.Encode.Value
encoderSRSData
provides a Json encoder for encoding SRSData
from a Card
.
decoderSRSData : Json.Decode.Decoder SRSData
decoderSRSData
provides a Json decoder for decoding SRSData
for a Card
.
The SM2+ algorithm depends on grading answers on a scale from 0.0 to 1.0, with answers of 0.6 and above being correct (and incorrect below that) responses. For some use cases, it may be able to programmatically determine the PerformanceRating
of a user's response. In other cases, however, the user may need to self-report.
SpacedRepetition.Internal.SMTwoPlus.PerformanceRating
The PerformanceRating
type represents how accurate/certain a user's response was to a card and must be passed to answerCard
whenever a Card
is answered. PerformanceRating
is quantitative and must be between 0.0 and 1.0, with values of 0.6 and greater representing a "correct" answer. A PerformanceRating
may be created with the performanceRating
function.
performanceRating : Basics.Float -> PerformanceRating
The performanceRating
function creates a PerformanceRating
. PerformanceRating
is quantitative and must be between 0.0 and 1.0, with values of 0.6 and greater representing a "correct" answer.
answerCardInDeck : Maybe IncorrectSchedulingFunction -> Time.Posix -> PerformanceRating -> Basics.Int -> Deck a -> Deck a
answerCardInDeck
functions analogously to answerCard
but handles maintenance of the Deck
, which is typically what one would desire. When a card is presented to the user and answered, answerCardInDeck
should be called with a Maybe IncorrectSchedulingFunction
, the current time (in the Time.Posix
format returned by the now
task of the core Time
module), a PerformanceRating
, the index of the card in the Deck
, and the Deck
itself. It returns the updated Deck
. Use this function if you simply want to store a Deck
and not worry about updating it manually (which is most likely what you want). Otherwise, use answerCard
to handle updating the Deck
manually. Handling the presentation of a card is the responsibility of the implementing program, as various behaviors might be desirable in different cases. Note that if an invalid (out of bounds) index is passed, the Deck
is returned unaltered. IncorrectSchedulingFunction
may be provided to fix the issue with scheduling incorrect cards inherent in the algorithm. If Nothing
is provided, the algorithm-specified 1 / diffWeight ^ 2
scaling is used that results in questionable behavior.
answerCard : Maybe IncorrectSchedulingFunction -> Time.Posix -> PerformanceRating -> Card a -> Card a
When a card is presented to the user and answered, answerCard
should be called with a Maybe IncorrectSchedulingFunction
, the current time (in the Time.Posix
format returned by the now
task of the core Time
module) and an PerformanceRating
. It returns the updated card, which should replace the card in the Deck
. Use this function if you want to handle updating the Deck
manually; otherwise, use answerCardInDeck
. Handling the presentation of a card is the responsibility of the implementing program, as various behaviors might be desirable in different cases. IncorrectSchedulingFunction
may be provided to fix the issue with scheduling incorrect cards inherent in the algorithm. If Nothing
is provided, the algorithm-specified 1 / diffWeight ^ 2
scaling is used that results in questionable behavior.
Basics.Float -> Basics.Float
IncorrectSchedulingFunction
must take a float as an argument, representing "difficultyWeight" (which is in the interval [1.3, 3.0]), and return a float representing the factor by which the interval should be scaled (which should probably be in the interval [0.0, 1.0]). This function will only be called with incorrect answers, not correct ones. Note that an incorrect interval cannot be less than 1 day, so any factor resulting in a shorter interval will simply result in an interval of 1 day. A custom function may be provided, or the pre-made function oneMinusReciprocalDiffWeightSquared
may be used, which seems a likely correction.
oneMinusReciprocalDiffWeightSquared : Basics.Float -> Basics.Float
oneMinusReciprocalDiffWeightSquared
represents an attempt to "fix" the SM2+ algorithm, scheduling incorrect cards with the more logical behavior of more difficult cards receiving shorter intervals, with the assumption that the original formula 1 / diffWeight ^ 2
was intended to be 1 - 1 / diffWeight ^ 2
. It maps "difficultyWeight" ([1.3, 3.0]) to the interval [0.408, 0.889].
Besides answering cards, this package handles determining which cards in a Deck
are due and require answering.
getDueCardIndices : Time.Posix -> Deck a -> List Basics.Int
getDueCardIndices
takes the current time (in the Time.Posix
format returned by the now
task of the core Time
module) and a Deck
and returns the indices of the subset of the Deck
that is due for review (as List Int
). The returned indices will be sorted in the following order:
Equally due cards are presented in random order.
getDueCardIndices
assumes that a new day begins after 8 hours, e.g. if a card is scheduled to be studied the next day, it will become due after 8 hours of elapsed time. This can of course create edge cases where cards are reviewed too "early" if one studies very early in the morning and again late at night. Still, only very "new" cards would be affected, in which case the adverse effect is presumably minimal.
getDueCardIndicesWithDetails : Time.Posix -> Deck a -> List { index : Basics.Int, queueDetails : QueueDetails }
getDueCardIndicesWithDetails
takes the current time (in the Time.Posix
format returned by the now
task of the core Time
module) and a Deck
and returns the the subset of the Deck
that is due for review (as a list of records), providing their index and which queue they are currently in, with any relevant queue details. The returned indices will be sorted in the following order:
Equally due cards are presented in random order.
getDueCardIndicesWithDetails
assumes that a new day begins after 8 hours, e.g. if a card is scheduled to be studied the next day, it will become due after 8 hours of elapsed time. This can of course create edge cases where cards are reviewed too "early" if one studies very early in the morning and again late at night. Still, only very "new" cards would be affected, in which case the adverse effect is presumably minimal.
If you require specific details for a single card, you may use the provided functionality here. If you need details for all due cards, just use getDueCardIndicesWithDetails
.
QueueDetails
represents the current status of a card.
NewCard
-- A card that has never before been studied (encountered) by the user.ReviewQueue {...}
-- A card that is being reviewed for retention.intervalInDays : Float
-- The interval, in days from the date last seen, that the card is slated for review in.lastSeen : Time.Posix
-- The date and time the card was last reviewed.getCardDetails : Card a -> { queueDetails : QueueDetails }
getCardDetails
returns the current queue status for a given card. If you require this for every due card, simply use getDueCardIndicesWithDetails
.