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* Skill Extraction Utility
*
* Extracts skill identifiers from the tutorial system's UnifiedInstructionSequence.
* Maps pedagogical decomposition rules to the SkillSet schema used in mastery tracking.
*/
import type { PedagogicalSegment, UnifiedInstructionSequence } from './unifiedStepGenerator'
/**
* Skill identifier format matches the player_skill_mastery.skill_id column
* Examples:
* - "basic.directAddition"
* - "fiveComplements.4=5-1"
* - "tenComplements.9=10-1"
*/
export type SkillId = string
/**
* Detailed skill usage information extracted from a segment
*/
export interface ExtractedSkill {
/** The skill identifier (e.g., "fiveComplements.4=5-1") */
skillId: SkillId
/** The pedagogical rule that triggered this skill */
rule: 'Direct' | 'FiveComplement' | 'TenComplement' | 'Cascade'
/** The place value where this skill was applied (0=ones, 1=tens, etc.) */
place: number
/** The digit being added/subtracted */
digit: number
/** The segment ID this skill was extracted from */
segmentId: string
}
/**
* Extract skills from a unified instruction sequence
*
* @param sequence - The instruction sequence from generateUnifiedInstructionSequence
* @returns Array of extracted skill information
*/
export function extractSkillsFromSequence(sequence: UnifiedInstructionSequence): ExtractedSkill[] {
const skills: ExtractedSkill[] = []
for (const segment of sequence.segments) {
const extractedSkills = extractSkillsFromSegment(segment)
skills.push(...extractedSkills)
}
// Post-process: detect cascading carries/borrows from consecutive ten complements
// This catches cases where the unified step generator processes each place independently
// but the pattern across adjacent places indicates cascading
const cascadingSkills = detectCascadingFromTenComplements(skills)
skills.push(...cascadingSkills)
return skills
}
/**
* Detect cascading carry/borrow from consecutive ten complement operations
*
* When 2+ consecutive place values all use ten complements, this indicates
* a cascading carry (addition) or cascading borrow (subtraction).
*
* Example: 1000 - 999 = 1
* - Place 2 (hundreds): TenComplement subtraction
* - Place 1 (tens): TenComplement subtraction
* - Place 0 (ones): TenComplement subtraction
* All 3 are consecutive ten complements = cascading borrow
*/
function detectCascadingFromTenComplements(skills: ExtractedSkill[]): ExtractedSkill[] {
const cascadingSkills: ExtractedSkill[] = []
// Already has cascading skills? Don't add duplicates
if (skills.some((s) => s.skillId.startsWith('advanced.cascading'))) {
return cascadingSkills
}
// Group ten complement skills by whether they're subtraction or addition
const tenComplementAdditions = skills.filter(
(s) => s.rule === 'TenComplement' && s.skillId.startsWith('tenComplements.')
)
const tenComplementSubtractions = skills.filter(
(s) => s.rule === 'TenComplement' && s.skillId.startsWith('tenComplementsSub.')
)
// Check for cascading carry (addition)
if (hasConsecutivePlaceValues(tenComplementAdditions)) {
// Find a representative skill to copy segment info from
const representative = tenComplementAdditions[0]
cascadingSkills.push({
skillId: 'advanced.cascadingCarry',
rule: 'Cascade',
place: representative.place,
digit: representative.digit,
segmentId: representative.segmentId,
})
}
// Check for cascading borrow (subtraction)
if (hasConsecutivePlaceValues(tenComplementSubtractions)) {
// Find a representative skill to copy segment info from
const representative = tenComplementSubtractions[0]
cascadingSkills.push({
skillId: 'advanced.cascadingBorrow',
rule: 'Cascade',
place: representative.place,
digit: representative.digit,
segmentId: representative.segmentId,
})
}
return cascadingSkills
}
/**
* Check if skills span 2+ consecutive place values
*/
function hasConsecutivePlaceValues(skills: ExtractedSkill[]): boolean {
if (skills.length < 2) return false
// Get unique place values and sort them
const places = [...new Set(skills.map((s) => s.place))].sort((a, b) => a - b)
// Check for at least 2 consecutive places
for (let i = 0; i < places.length - 1; i++) {
if (places[i + 1] === places[i] + 1) {
return true // Found 2 consecutive places
}
}
return false
}
/**
* Extract skills from a single pedagogical segment
*/
function extractSkillsFromSegment(segment: PedagogicalSegment): ExtractedSkill[] {
const skills: ExtractedSkill[] = []
const { digit, place, plan } = segment
// Get the primary rule from the segment's plan
const primaryRule = plan[0]?.rule
if (!primaryRule) return skills
// Detect subtraction by checking segment ID suffix or step operations
// Subtraction segments have IDs ending in '-sub'
const isSubtraction = segment.id.endsWith('-sub')
// Check if any rule in the plan is 'Cascade' - this indicates cascading carries/borrows
const hasCascade = plan.some((p) => p.rule === 'Cascade')
switch (primaryRule) {
case 'Direct':
// Direct addition/subtraction - check what type
if (isSubtraction) {
if (digit <= 4) {
skills.push({
skillId: 'basic.directSubtraction',
rule: 'Direct',
place,
digit,
segmentId: segment.id,
})
} else if (digit === 5) {
skills.push({
skillId: 'basic.heavenBeadSubtraction',
rule: 'Direct',
place,
digit,
segmentId: segment.id,
})
} else {
// 6-9 without complements means simple combinations
skills.push({
skillId: 'basic.simpleCombinationsSub',
rule: 'Direct',
place,
digit,
segmentId: segment.id,
})
}
} else {
if (digit <= 4) {
skills.push({
skillId: 'basic.directAddition',
rule: 'Direct',
place,
digit,
segmentId: segment.id,
})
} else if (digit === 5) {
skills.push({
skillId: 'basic.heavenBead',
rule: 'Direct',
place,
digit,
segmentId: segment.id,
})
} else {
// 6-9 without complements means simple combinations
skills.push({
skillId: 'basic.simpleCombinations',
rule: 'Direct',
place,
digit,
segmentId: segment.id,
})
}
}
break
case 'FiveComplement': {
if (isSubtraction) {
// Five's complement subtraction: -d = -5 + (5-d)
const fiveComplementSubKey = getFiveComplementSubKey(digit)
if (fiveComplementSubKey) {
skills.push({
skillId: `fiveComplementsSub.${fiveComplementSubKey}`,
rule: 'FiveComplement',
place,
digit,
segmentId: segment.id,
})
}
} else {
// Five's complement addition: +d = +5 - (5-d)
const fiveComplementKey = getFiveComplementKey(digit)
if (fiveComplementKey) {
skills.push({
skillId: `fiveComplements.${fiveComplementKey}`,
rule: 'FiveComplement',
place,
digit,
segmentId: segment.id,
})
}
}
break
}
case 'TenComplement': {
if (isSubtraction) {
// Ten's complement subtraction (borrow): -d = +(10-d) - 10
const tenComplementSubKey = getTenComplementSubKey(digit)
if (tenComplementSubKey) {
skills.push({
skillId: `tenComplementsSub.${tenComplementSubKey}`,
rule: 'TenComplement',
place,
digit,
segmentId: segment.id,
})
}
} else {
// Ten's complement addition: +d = +10 - (10-d)
const tenComplementKey = getTenComplementKey(digit)
if (tenComplementKey) {
skills.push({
skillId: `tenComplements.${tenComplementKey}`,
rule: 'TenComplement',
place,
digit,
segmentId: segment.id,
})
}
}
break
}
case 'Cascade': {
// Cascade is triggered by TenComplement with consecutive 9s/0s
// The underlying skill is still TenComplement (addition) or TenComplementSub (subtraction)
// Also emit the advanced.cascading* skill to track this pattern
if (isSubtraction) {
const cascadeSubKey = getTenComplementSubKey(digit)
if (cascadeSubKey) {
skills.push({
skillId: `tenComplementsSub.${cascadeSubKey}`,
rule: 'Cascade',
place,
digit,
segmentId: segment.id,
})
}
// Also emit cascading borrow skill
skills.push({
skillId: 'advanced.cascadingBorrow',
rule: 'Cascade',
place,
digit,
segmentId: segment.id,
})
} else {
const cascadeKey = getTenComplementKey(digit)
if (cascadeKey) {
skills.push({
skillId: `tenComplements.${cascadeKey}`,
rule: 'Cascade',
place,
digit,
segmentId: segment.id,
})
}
// Also emit cascading carry skill
skills.push({
skillId: 'advanced.cascadingCarry',
rule: 'Cascade',
place,
digit,
segmentId: segment.id,
})
}
break
}
}
// If any rule in the plan was 'Cascade' but we didn't already emit a cascading skill
// (e.g., when primaryRule is 'TenComplement' but plan also contains 'Cascade'),
// emit the cascading skill now
if (hasCascade && primaryRule !== 'Cascade') {
if (isSubtraction) {
skills.push({
skillId: 'advanced.cascadingBorrow',
rule: 'Cascade',
place,
digit,
segmentId: segment.id,
})
} else {
skills.push({
skillId: 'advanced.cascadingCarry',
rule: 'Cascade',
place,
digit,
segmentId: segment.id,
})
}
}
return skills
}
/**
* Map a digit to its five's complement skill key
* Five's complements are used when adding 1-4 and there's not enough earth beads
* +4 = +5 - 1, +3 = +5 - 2, +2 = +5 - 3, +1 = +5 - 4
*/
function getFiveComplementKey(digit: number): string | null {
const mapping: Record<number, string> = {
4: '4=5-1',
3: '3=5-2',
2: '2=5-3',
1: '1=5-4',
}
return mapping[digit] ?? null
}
/**
* Map a digit to its ten's complement skill key
* Ten's complements are used when adding causes a carry
* +9 = +10 - 1, +8 = +10 - 2, etc.
*/
function getTenComplementKey(digit: number): string | null {
const mapping: Record<number, string> = {
9: '9=10-1',
8: '8=10-2',
7: '7=10-3',
6: '6=10-4',
5: '5=10-5',
4: '4=10-6',
3: '3=10-7',
2: '2=10-8',
1: '1=10-9',
}
return mapping[digit] ?? null
}
/**
* Map a digit to its five's complement subtraction skill key
* Five's complement subtraction: -d = -5 + (5-d)
* -4 = -5 + 1, -3 = -5 + 2, -2 = -5 + 3, -1 = -5 + 4
*/
function getFiveComplementSubKey(digit: number): string | null {
const mapping: Record<number, string> = {
4: '-4=-5+1',
3: '-3=-5+2',
2: '-2=-5+3',
1: '-1=-5+4',
}
return mapping[digit] ?? null
}
/**
* Map a digit to its ten's complement subtraction skill key
* Ten's complement subtraction (borrow): -d = +(10-d) - 10
* -9 = +1 - 10, -8 = +2 - 10, etc.
*/
function getTenComplementSubKey(digit: number): string | null {
const mapping: Record<number, string> = {
9: '-9=+1-10',
8: '-8=+2-10',
7: '-7=+3-10',
6: '-6=+4-10',
5: '-5=+5-10',
4: '-4=+6-10',
3: '-3=+7-10',
2: '-2=+8-10',
1: '-1=+9-10',
}
return mapping[digit] ?? null
}
/**
* Get unique skill IDs from an instruction sequence
* Useful for tracking which skills were exercised in a problem
*/
export function getUniqueSkillIds(sequence: UnifiedInstructionSequence): SkillId[] {
const skills = extractSkillsFromSequence(sequence)
return [...new Set(skills.map((s) => s.skillId))]
}
/**
* Extract skills from a problem's term transitions
*
* For practice problems with multiple terms, this extracts skills
* for each term transition (currentValue -> currentValue + term)
*
* @param terms - Array of terms in the problem
* @param generateSequence - Function to generate instruction sequence
* @returns Map of term index to extracted skills
*/
export function extractSkillsFromProblem(
terms: number[],
generateSequence: (start: number, target: number) => UnifiedInstructionSequence
): Map<number, ExtractedSkill[]> {
const skillsByTerm = new Map<number, ExtractedSkill[]>()
let currentValue = 0
for (let i = 0; i < terms.length; i++) {
const term = terms[i]
const targetValue = currentValue + term
try {
const sequence = generateSequence(currentValue, targetValue)
const skills = extractSkillsFromSequence(sequence)
skillsByTerm.set(i, skills)
} catch {
// If sequence generation fails (e.g., subtraction not implemented),
// store empty skills for this term
skillsByTerm.set(i, [])
}
currentValue = targetValue
}
return skillsByTerm
}
/**
* Flatten skills from all terms into a single array
*/
export function flattenProblemSkills(
skillsByTerm: Map<number, ExtractedSkill[]>
): ExtractedSkill[] {
const allSkills: ExtractedSkill[] = []
for (const skills of skillsByTerm.values()) {
allSkills.push(...skills)
}
return allSkills
}
/**
* Get the category of a skill ID (e.g., "fiveComplements" from "fiveComplements.4=5-1")
*/
export function getSkillCategory(skillId: SkillId): string {
const dotIndex = skillId.indexOf('.')
return dotIndex >= 0 ? skillId.substring(0, dotIndex) : skillId
}
/**
* Get the specific skill key (e.g., "4=5-1" from "fiveComplements.4=5-1")
*/
export function getSkillKey(skillId: SkillId): string {
const dotIndex = skillId.indexOf('.')
return dotIndex >= 0 ? skillId.substring(dotIndex + 1) : skillId
}
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