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1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 13x 13x 13x 13x 13x 13x 13x 2x 2x 11x 11x 11x 11x 11x 13x 13x 13x 13x 13x 13x 13x 13x 13x 13x 13x 13x 13x 13x 13x 13x 13x 13x 13x 13x 13x 13x 13x 13x 13x 13x 13x 13x 13x 13x 13x 17x 17x 17x 17x 17x 17x 35x 35x 35x 35x 35x 1x 1x 34x 34x 34x 35x 7x 7x 27x 27x 35x 27x 27x 27x 17x 17x 17x 13x 13x 17x 17x 17x 17x 27x 27x 27x 27x 27x 27x 7x 7x 4x 4x 4x 4x 4x 4x 7x 3x 3x 3x 3x 3x 3x 3x 7x 27x 17x 17x 17x 17x 11x 11x 11x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x | /**
* Zod schemas and prompts for LLM-powered flowchart generation
*
* This module provides:
* - Zod schemas for validating LLM outputs
* - System prompts with examples of existing flowcharts
* - Reference documentation for flowchart structure
*
* @module flowchart-workshop/llm-schemas
*/
import { z } from 'zod'
// =============================================================================
// Zod Schemas for LLM Output
// =============================================================================
/**
* Schema for a single field in the problem input
* Note: Using .nullable() instead of .optional() for OpenAI structured output compatibility
* Note: Using discriminated union with 'type' as discriminator
*/
export const FieldSchema = z.discriminatedUnion('type', [
z.object({
name: z.string().describe('Variable name used in expressions (e.g., "topNum", "bottomDenom")'),
type: z.literal('integer'),
label: z.string().nullable().describe('Human-readable label shown in UI'),
min: z.number().nullable().describe('Minimum allowed value'),
max: z.number().nullable().describe('Maximum allowed value'),
default: z.number().nullable().describe('Default value if not specified'),
}),
z.object({
name: z.string().describe('Variable name used in expressions'),
type: z.literal('number'),
label: z.string().nullable().describe('Human-readable label shown in UI'),
min: z.number().nullable().describe('Minimum allowed value'),
max: z.number().nullable().describe('Maximum allowed value'),
default: z.number().nullable().describe('Default value if not specified'),
step: z.number().nullable().describe('Step increment for decimal values'),
}),
z.object({
name: z.string().describe('Variable name used in expressions'),
type: z.literal('choice'),
label: z.string().nullable().describe('Human-readable label shown in UI'),
options: z.array(z.string()).describe('List of valid choices'),
default: z.string().nullable().describe('Default selected option'),
}),
z.object({
name: z.string().describe('Variable name prefix (creates whole, num, denom fields)'),
type: z.literal('mixed-number'),
label: z.string().nullable().describe('Human-readable label shown in UI'),
}),
])
/**
* Schema for an example value (key-value pair for OpenAI compatibility)
*/
export const ExampleValueSchema = z.object({
key: z.string().describe('Field name matching a field in the schema'),
value: z
.union([z.number(), z.string(), z.boolean()])
.describe('The example value for this field'),
})
/**
* Schema for problem input configuration
* Note: examples.values uses array of {key, value} pairs instead of Record for OpenAI compatibility
*/
export const ProblemInputSchema = z.object({
schema: z.string().describe('Unique identifier for this problem schema'),
fields: z.array(FieldSchema).describe('Input fields that define the problem'),
validation: z
.string()
.nullable()
.describe('Expression that must be true for valid problems (e.g., "top > bottom")'),
examples: z
.array(
z.object({
name: z.string().describe('Name of this example (e.g., "Basic borrowing")'),
description: z
.string()
.nullable()
.describe('Description of what this example demonstrates'),
values: z.array(ExampleValueSchema).describe('Field values for this example'),
expectedAnswer: z
.string()
.nullable()
.describe(
'REQUIRED: The exact string that display.answer should produce for these inputs. Used for automatic validation. Must match exactly after trimming whitespace.'
),
})
)
.nullable()
.describe('Example problems with specific values and expected answers for validation'),
})
/**
* Schema for a variable definition (with name for array format)
* DEPRECATED: Use node transforms instead
*/
export const VariableEntrySchema = z.object({
name: z.string().describe('Variable name (e.g., "topOnes", "needsBorrow")'),
init: z
.string()
.describe('Expression to compute initial value (e.g., "top % 10", "topOnes < bottomOnes")'),
})
/**
* Schema for a transform expression on a node
* Transforms are executed when entering a node, in order
*/
export const TransformEntrySchema = z.object({
key: z.string().describe('Variable name to create/update'),
expr: z
.string()
.describe('Expression to evaluate (can reference input fields, prior transforms)'),
})
/**
* Schema for a string key-value pair (for OpenAI compatibility)
* Moved before other schemas that depend on it
*/
export const StringKeyValueSchema = z.object({
key: z.string().describe('Key name'),
value: z.string().describe('Value (often an expression)'),
})
/**
* Schema for display template with multiple formats
*/
export const DisplayTemplateSchema = z.object({
text: z.string().describe('Plain text format (required)'),
web: z.string().nullable().describe('MathML/HTML format for browser display'),
typst: z.string().nullable().describe('Typst format for PDF worksheets'),
})
/**
* Schema for answer definition
* Defines how to extract and display the final answer from terminal state
*/
export const AnswerDefinitionSchema = z.object({
values: z
.array(StringKeyValueSchema)
.describe(
'Map answer component names to variable references (e.g., [{ key: "result", value: "finalAnswer" }])'
),
display: DisplayTemplateSchema.describe(
'Templates for displaying the answer (supports {{name}} and {{=expr}} interpolation)'
),
})
/**
* Schema for structured test cases
*/
export const StructuredTestValueSchema = z.object({
key: z.string().describe('Field name'),
value: z.union([z.number(), z.string(), z.boolean()]).describe('Expected value (primitive)'),
})
export const StructuredTestCaseSchema = z.object({
name: z.string().describe('Test case name'),
values: z.array(ExampleValueSchema).describe('Input values for the test'),
expected: z
.array(StructuredTestValueSchema)
.describe('Expected answer values (primitives, not strings)'),
})
/**
* Schema for a decision option
*
* NOTE: Edge IDs are auto-computed as {nodeId}_{optionValue}.
* Mermaid content must use this exact pattern: NODE NODE_value@-->|"Label"| NEXT
*/
export const DecisionOptionSchema = z.object({
label: z.string().describe('Text shown on the button (e.g., "Yes! Top is bigger")'),
value: z
.string()
.describe(
'Unique identifier for this option (e.g., "direct", "borrow"). Also used to compute edge ID as {nodeId}_{value}'
),
next: z.string().describe('Node ID to navigate to when selected'),
pathLabel: z
.string()
.nullable()
.describe(
'REQUIRED: Short (2-6 char) DESCRIPTIVE label for path enumeration. Use meaningful words like "BORROW", "DIRECT", "SAME", "DIFF", "MULT", "GCD" - NOT generic "YES"/"NO". These appear in example grid column headers.'
),
gridLabel: z
.string()
.nullable()
.describe(
'More descriptive label for examples UI where space allows (e.g., "Same denominators", "Use GCD method"). Shows clearer explanations than the abbreviated pathLabel on flowchart edges.'
),
})
/**
* Schema for working problem update
*/
export const WorkingProblemUpdateSchema = z.object({
result: z.string().describe('Expression for the new working problem state'),
label: z.string().describe('Human-readable description of what changed'),
})
/**
* Schema for a flowchart node
* Note: Using discriminatedUnion with 'type' for OpenAI compatibility
*/
export const FlowchartNodeSchema = z.discriminatedUnion('type', [
z.object({
type: z.literal('instruction'),
advance: z.literal('tap').describe('User taps "I did it" to advance'),
next: z.string().nullable().describe('Node ID to navigate to next'),
workingProblemUpdate: WorkingProblemUpdateSchema.nullable().describe(
'Optional update to working problem display'
),
transform: z
.array(TransformEntrySchema)
.nullable()
.describe('Transforms to apply when entering this node'),
}),
z.object({
type: z.literal('decision'),
options: z.array(DecisionOptionSchema).describe('Available choices for the user'),
correctAnswer: z
.string()
.nullable()
.describe('Expression evaluating to the correct option value'),
skipIf: z.string().nullable().describe('Expression - if true, skip this node'),
skipTo: z.string().nullable().describe('Node ID to skip to when skipIf is true'),
excludeFromExampleStructure: z
.boolean()
.nullable()
.describe(
'If true, exclude from path enumeration in example grid. Use for verification/confirmation decisions that do not represent meaningfully different problem types.'
),
transform: z
.array(TransformEntrySchema)
.nullable()
.describe('Transforms to apply when entering this node'),
}),
z.object({
type: z.literal('checkpoint'),
prompt: z.string().describe('Question or prompt shown to user'),
inputType: z.enum(['number', 'text', 'two-numbers']).describe('Type of input field(s) to show'),
expected: z
.union([z.string(), z.array(z.string())])
.describe(
'Expression for expected answer (string), or array of 2 expressions for two-numbers'
),
inputLabels: z
.array(z.string())
.nullable()
.describe('Array of 2 labels for two-numbers input type'),
orderMatters: z.boolean().nullable().describe('For two-numbers, whether order matters'),
stateUpdate: z
.array(StringKeyValueSchema)
.nullable()
.describe('Variables to update when checkpoint passes'),
tolerance: z
.number()
.nullable()
.describe('Allowed difference from expected for numeric answers'),
next: z.string().nullable().describe('Node ID to navigate to after correct answer'),
workingProblemUpdate: WorkingProblemUpdateSchema.nullable().describe(
'Optional update to working problem display'
),
skipIf: z.string().nullable().describe('Expression - if true, skip this node'),
skipTo: z.string().nullable().describe('Node ID to skip to when skipIf is true'),
excludeSkipFromPaths: z
.boolean()
.nullable()
.describe('If true, skip path not included in enumeration'),
transform: z
.array(TransformEntrySchema)
.nullable()
.describe('Transforms to apply when entering this node'),
}),
z.object({
type: z.literal('milestone'),
next: z.string().describe('Node ID to navigate to next'),
transform: z
.array(TransformEntrySchema)
.nullable()
.describe('Transforms to apply when entering this node'),
}),
z.object({
type: z.literal('embellishment'),
next: z.string().describe('Node ID to navigate to next'),
transform: z
.array(TransformEntrySchema)
.nullable()
.describe('Transforms to apply when entering this node'),
}),
z.object({
type: z.literal('terminal'),
celebration: z.boolean().nullable().describe('Whether to show celebration animation'),
transform: z
.array(TransformEntrySchema)
.nullable()
.describe('Transforms to apply when entering this node'),
}),
])
/**
* Schema for a node entry (with id for array format)
*/
export const NodeEntrySchema = z.object({
id: z.string().describe('Unique node ID (e.g., "START", "COMPARE", "CHECK1")'),
node: FlowchartNodeSchema.describe('The node definition'),
})
/**
* Schema for an edge entry
*/
export const EdgeEntrySchema = z.object({
from: z.string().describe('Source node ID'),
to: z.array(z.string()).describe('Target node ID(s)'),
})
/**
* Schema for preferred values entry
*/
export const PreferredEntrySchema = z.object({
key: z.string().describe('Field name from problemInput'),
values: z
.union([z.array(z.number()), z.array(z.string())])
.describe('Preferred values for problem generation'),
})
/**
* Schema for the full flowchart definition
* Note: Using arrays instead of records for OpenAI structured output compatibility
*/
export const FlowchartDefinitionSchema = z.object({
id: z.string().describe('Unique identifier for this flowchart (e.g., "subtraction-regrouping")'),
title: z.string().describe('Human-readable title (e.g., "Subtraction with Regrouping")'),
mermaidFile: z.string().describe('Filename for mermaid content (e.g., "flowchart.mmd")'),
problemInput: ProblemInputSchema.describe('Schema for problem inputs'),
variables: z
.array(VariableEntrySchema)
.nullable()
.describe('DEPRECATED: Use node transforms instead. Computed variables derived from inputs.'),
entryNode: z.string().describe('ID of the first node to display'),
nodes: z
.array(NodeEntrySchema)
.describe('All nodes in the flowchart - use transform on nodes to compute values'),
edges: z.array(EdgeEntrySchema).nullable().describe('Optional explicit edge definitions'),
workingProblem: z
.object({
initial: z.string().describe('Expression for initial working problem display'),
})
.nullable()
.describe('Working problem display configuration'),
generation: z
.object({
target: z.string().nullable().describe('Target variable for problem generation'),
derived: z
.array(StringKeyValueSchema)
.nullable()
.describe('Derived values computed during generation'),
preferred: z
.array(PreferredEntrySchema)
.describe(
'REQUIRED: Arrays of pedagogically nice values for each input field. The system picks from these to generate diverse examples that hit different flowchart paths.'
),
})
.describe(
'REQUIRED: Problem generation configuration. Without this, example generation will fail.'
),
constraints: z
.array(StringKeyValueSchema)
.nullable()
.describe('Additional constraints for problem generation'),
answer: AnswerDefinitionSchema.describe(
'REQUIRED: Defines how to extract and display the final answer. Use values to map answer components to computed variables, and display for formatting with {{name}} or {{=expr}} interpolation.'
),
tests: z
.array(StructuredTestCaseSchema)
.nullable()
.describe('Structured test cases with primitive expected values'),
display: z
.object({
problem: z
.string()
.nullable()
.describe(
'REQUIRED: Math-style expression for problem display. Use operators not prose: "top + \' − \' + bottom" renders as "52 − 27". For fractions: "num1 + \'/\' + denom1" renders properly. Keep SHORT - appears in compact grid cells.'
),
answer: z
.string()
.nullable()
.describe(
'DEPRECATED: Use the top-level answer definition instead. Legacy expression for computing the answer display.'
),
})
.nullable()
.describe('Display configuration for examples and problem selection UI'),
})
/**
* Schema for the complete LLM generation output
*/
export const GeneratedFlowchartSchema = z.object({
definition: FlowchartDefinitionSchema.describe('The complete flowchart definition'),
mermaidContent: z
.string()
.describe(
'Mermaid diagram content (flowchart TB with subgraphs). CRITICAL: Circle nodes (embellishments) MUST contain an emoji like (("😊")) or (("🎉")), NEVER empty (("")) which causes parse errors.'
),
title: z.string().describe('Short title for the flowchart'),
description: z.string().describe('One-sentence description of what this flowchart teaches'),
emoji: z
.string()
.describe(
'A single emoji that best represents the math topic (e.g., "➕" for addition, "➖" for subtraction, "✖️" for multiplication, "➗" for division, "📐" for geometry, "📊" for data/graphing, "🔢" for general number operations, "⚖️" for equations/balance, "🎯" for problem-solving)'
),
difficulty: z.enum(['Beginner', 'Intermediate', 'Advanced']).describe('Target skill level'),
notes: z
.array(z.string())
.describe(
'User-facing notes for teachers/parents: pedagogical tips, suggestions for how to use this with students, or important things to know about the topic. Do NOT include implementation details, node IDs, or technical information.'
),
debugNotes: z
.array(z.string())
.nullable()
.describe(
'Technical/implementation notes for debugging: what changed internally, node ID mappings, schema format details, etc. Not shown to users.'
),
})
/**
* Schema for the LLM refinement output
*/
export const RefinementResultSchema = z.object({
updatedDefinition: FlowchartDefinitionSchema.describe('The modified flowchart definition'),
updatedMermaidContent: z
.string()
.describe(
'The modified Mermaid diagram content. CRITICAL: Circle nodes (embellishments) MUST contain an emoji like (("😊")) or (("🎉")), NEVER empty (("")) which causes parse errors.'
),
updatedEmoji: z
.string()
.nullable()
.describe(
'Updated emoji if the topic changed significantly, otherwise null to keep the existing emoji'
),
changesSummary: z
.string()
.describe(
'User-facing summary of what was changed, written for teachers/parents. Focus on pedagogical impact, not technical details.'
),
notes: z
.array(z.string())
.describe(
'User-facing notes for teachers/parents: pedagogical tips, suggestions, or important things to know. Do NOT include implementation details, node IDs, or technical information.'
),
debugNotes: z
.array(z.string())
.nullable()
.describe(
'Technical/implementation notes for debugging: what changed internally, node ID mappings, schema format details, etc. Not shown to users.'
),
})
// =============================================================================
// Transformation Functions (LLM output → Internal format)
// =============================================================================
/**
* Convert LLM output (array-based) to internal FlowchartDefinition (record-based)
* OpenAI structured outputs require arrays instead of records, so we need to convert.
*/
export function transformLLMDefinitionToInternal(
llmDef: z.infer<typeof FlowchartDefinitionSchema>
): import('../flowcharts/schema').FlowchartDefinition {
// Convert variables array to record (may be null/deprecated)
const variables: Record<string, { init: string }> = {}
if (llmDef.variables) {
for (const v of llmDef.variables) {
variables[v.name] = { init: v.init }
}
}
// Convert nodes array to record
const nodes: Record<string, import('../flowcharts/schema').FlowchartNode> = {}
for (const n of llmDef.nodes) {
// Transform the node from LLM format to internal format
const llmNode = n.node
let internalNode: import('../flowcharts/schema').FlowchartNode
// Helper to convert transform array
const convertTransform = (transform: { key: string; expr: string }[] | null | undefined) =>
transform ? transform.map((t) => ({ key: t.key, expr: t.expr })) : undefined
switch (llmNode.type) {
case 'instruction':
internalNode = {
type: 'instruction',
advance: 'tap',
next: llmNode.next ?? undefined,
workingProblemUpdate: llmNode.workingProblemUpdate ?? undefined,
transform: convertTransform(llmNode.transform),
}
break
case 'decision':
internalNode = {
type: 'decision',
options: llmNode.options.map((o) => ({
label: o.label,
value: o.value,
next: o.next,
pathLabel: o.pathLabel ?? undefined,
gridLabel: o.gridLabel ?? undefined,
})),
correctAnswer: llmNode.correctAnswer ?? undefined,
skipIf: llmNode.skipIf ?? undefined,
skipTo: llmNode.skipTo ?? undefined,
excludeFromExampleStructure: llmNode.excludeFromExampleStructure ?? undefined,
transform: convertTransform(llmNode.transform),
}
break
case 'checkpoint': {
// Convert array to tuple for expected (internal format uses [string, string] for two-numbers)
let expectedValue: string | [string, string]
if (Array.isArray(llmNode.expected)) {
expectedValue = [llmNode.expected[0] ?? '', llmNode.expected[1] ?? ''] as [string, string]
} else {
expectedValue = llmNode.expected
}
// Convert array to tuple for inputLabels
const inputLabelsValue: [string, string] | undefined = llmNode.inputLabels
? ([llmNode.inputLabels[0] ?? 'First', llmNode.inputLabels[1] ?? 'Second'] as [
string,
string,
])
: undefined
internalNode = {
type: 'checkpoint',
prompt: llmNode.prompt,
inputType: llmNode.inputType,
expected: expectedValue,
inputLabels: inputLabelsValue,
orderMatters: llmNode.orderMatters ?? undefined,
stateUpdate: llmNode.stateUpdate
? Object.fromEntries(llmNode.stateUpdate.map((s) => [s.key, s.value]))
: undefined,
tolerance: llmNode.tolerance ?? undefined,
next: llmNode.next ?? undefined,
workingProblemUpdate: llmNode.workingProblemUpdate ?? undefined,
skipIf: llmNode.skipIf ?? undefined,
skipTo: llmNode.skipTo ?? undefined,
excludeSkipFromPaths: llmNode.excludeSkipFromPaths ?? undefined,
transform: convertTransform(llmNode.transform),
}
break
}
case 'milestone':
internalNode = {
type: 'milestone',
next: llmNode.next,
transform: convertTransform(llmNode.transform),
}
break
case 'embellishment':
internalNode = {
type: 'embellishment',
next: llmNode.next,
transform: convertTransform(llmNode.transform),
}
break
case 'terminal':
internalNode = {
type: 'terminal',
celebration: llmNode.celebration ?? undefined,
transform: convertTransform(llmNode.transform),
}
break
}
nodes[n.id] = internalNode
}
// Convert edges array to record
let edges: Record<string, string[]> | undefined
if (llmDef.edges) {
edges = {}
for (const e of llmDef.edges) {
edges[e.from] = e.to
}
}
// Convert examples values array to record
// IMPORTANT: LLM may output values incorrectly:
// 1. Numeric values as strings (e.g., "1" instead of 1)
// 2. String values wrapped in extra quotes (e.g., "'+'" instead of "+")
// We need to normalize these for the evaluator to work correctly
const examples = llmDef.problemInput.examples?.map((ex) => ({
name: ex.name,
description: ex.description ?? undefined,
values: Object.fromEntries(
ex.values.map((v) => {
let value = v.value
if (typeof value === 'string') {
let processed = value.trim()
// Strip wrapper quotes if present (LLM sometimes outputs "'+'" instead of "+")
if (
(processed.startsWith("'") && processed.endsWith("'")) ||
(processed.startsWith('"') && processed.endsWith('"'))
) {
processed = processed.slice(1, -1)
}
// Check if it's a valid number (integer or decimal)
if (processed !== '' && !isNaN(Number(processed))) {
value = Number(processed)
} else {
value = processed
}
}
return [v.key, value]
})
),
expectedAnswer: ex.expectedAnswer ?? undefined,
}))
// Convert generation config
let generation: import('../flowcharts/schema').GenerationConfig | undefined
if (llmDef.generation) {
generation = {
target: llmDef.generation.target ?? undefined,
derived: llmDef.generation.derived
? Object.fromEntries(llmDef.generation.derived.map((d) => [d.key, d.value]))
: undefined,
preferred: llmDef.generation.preferred
? Object.fromEntries(llmDef.generation.preferred.map((p) => [p.key, p.values]))
: undefined,
}
}
// Convert constraints
let constraints: Record<string, string> | undefined
if (llmDef.constraints) {
constraints = Object.fromEntries(llmDef.constraints.map((c) => [c.key, c.value]))
}
// Convert fields - handle nullable → optional
const fields = llmDef.problemInput.fields.map((f) => {
const base = {
name: f.name,
label: f.label ?? undefined,
}
switch (f.type) {
case 'integer':
return {
...base,
type: 'integer' as const,
min: f.min ?? undefined,
max: f.max ?? undefined,
default: f.default ?? undefined,
}
case 'number':
return {
...base,
type: 'number' as const,
min: f.min ?? undefined,
max: f.max ?? undefined,
default: f.default ?? undefined,
step: f.step ?? undefined,
}
case 'choice':
return {
...base,
type: 'choice' as const,
options: f.options,
default: f.default ?? undefined,
}
case 'mixed-number':
return {
...base,
type: 'mixed-number' as const,
}
}
})
// Convert answer definition
const answer: import('../flowcharts/schema').AnswerDefinition | undefined = llmDef.answer
? {
values: Object.fromEntries(llmDef.answer.values.map((v) => [v.key, v.value])),
display: {
text: llmDef.answer.display.text,
web: llmDef.answer.display.web ?? undefined,
typst: llmDef.answer.display.typst ?? undefined,
},
}
: undefined
// Convert tests
const tests: import('../flowcharts/schema').StructuredTestCase[] | undefined = llmDef.tests
? llmDef.tests.map((t) => ({
name: t.name,
values: Object.fromEntries(t.values.map((v) => [v.key, v.value])),
expected: Object.fromEntries(t.expected.map((e) => [e.key, e.value])),
}))
: undefined
return {
id: llmDef.id,
title: llmDef.title,
mermaidFile: llmDef.mermaidFile,
problemInput: {
schema: llmDef.problemInput.schema,
fields,
validation: llmDef.problemInput.validation ?? undefined,
examples,
},
variables,
entryNode: llmDef.entryNode,
nodes,
edges,
workingProblem: llmDef.workingProblem ?? undefined,
generation,
constraints,
answer,
tests,
display: llmDef.display
? {
problem: llmDef.display.problem ?? undefined,
answer: llmDef.display.answer ?? undefined,
}
: undefined,
}
}
// =============================================================================
// Validation
// =============================================================================
export interface DerivedFieldValidationError {
fieldName: string
expression: string
invalidReference: string
message: string
}
/**
* Validate that derived field expressions only reference input fields and other derived fields.
* Returns an array of validation errors (empty if valid).
*
* @param definition - The flowchart definition to validate
* @returns Array of validation errors for invalid derived field references
*/
export function validateDerivedFields(
definition: import('../flowcharts/schema').FlowchartDefinition
): DerivedFieldValidationError[] {
const errors: DerivedFieldValidationError[] = []
// Get derived fields from generation config
const derived = definition.generation?.derived
if (!derived || Object.keys(derived).length === 0) {
return errors
}
// Collect input field names
const inputFieldNames = new Set(definition.problemInput.fields.map((f) => f.name))
// Collect variable names (these are NOT allowed in derived expressions)
const variableNames = new Set(Object.keys(definition.variables || {}))
// Track derived field names as we process them (earlier ones can be referenced by later ones)
const processedDerivedNames = new Set<string>()
// Known built-in functions and constants to ignore
const builtIns = new Set([
'true',
'false',
'null',
'Math',
'abs',
'floor',
'ceil',
'round',
'min',
'max',
'gcd',
'lcm',
'sign',
'mod',
'pow',
'sqrt',
])
// Extract variable references from an expression
// Returns identifiers that are NOT:
// - function calls (followed by open paren)
// - property access (preceded by dot)
// - built-in functions/constants
function extractVariableReferences(expr: string): string[] {
const refs: string[] = []
// Match all identifiers
const identifierPattern = /[a-zA-Z_][a-zA-Z0-9_]*/g
let match
while ((match = identifierPattern.exec(expr)) !== null) {
const identifier = match[0]
const startIndex = match.index
// Skip if preceded by a dot (property access like obj.prop)
if (startIndex > 0 && expr[startIndex - 1] === '.') {
continue
}
// Skip if followed by open paren (function call like func())
const afterMatch = expr.slice(startIndex + identifier.length)
if (/^\s*\(/.test(afterMatch)) {
continue
}
// Skip built-ins
if (builtIns.has(identifier)) {
continue
}
refs.push(identifier)
}
return refs
}
for (const [fieldName, expression] of Object.entries(derived)) {
// Extract variable references from the expression
const references = extractVariableReferences(expression)
for (const identifier of references) {
// Check if it's a valid reference
const isInputField = inputFieldNames.has(identifier)
const isPreviousDerived = processedDerivedNames.has(identifier)
const isVariable = variableNames.has(identifier)
if (!isInputField && !isPreviousDerived) {
// Invalid reference - check if it's a variable (common mistake)
if (isVariable) {
errors.push({
fieldName,
expression,
invalidReference: identifier,
message: `Derived field "${fieldName}" references "${identifier}" which is a computed variable. Derived fields can only reference input fields (${[...inputFieldNames].join(', ')}) and previously-defined derived fields.`,
})
} else {
errors.push({
fieldName,
expression,
invalidReference: identifier,
message: `Derived field "${fieldName}" references unknown identifier "${identifier}". Valid references are input fields (${[...inputFieldNames].join(', ')}) and previously-defined derived fields.`,
})
}
}
}
// Add this derived field to the set of processed ones
processedDerivedNames.add(fieldName)
}
return errors
}
// =============================================================================
// System Prompts
// =============================================================================
/**
* Critical rules that apply to both generation and refinement.
* These are extracted to ensure consistency between prompts.
*/
function getCriticalRules(): string {
return `## Critical Rules Checklist
1. **Node ID consistency**: Every node in the definition must have a matching node in mermaid, and vice versa
2. **Path completeness**: Every path through the flowchart must reach a terminal node
3. **Expression validity**: All expressions must use valid syntax (see Expression Syntax section)
4. **Circle node content**: Embellishment nodes using \`(())\` syntax MUST contain an emoji like \`(("😊"))\` or \`(("🎉"))\`, NEVER empty \`((""))\` (causes parse error)
5. **No straight double quotes in node content**: Use single quotes (\`'\`) or rephrase - straight \`"\` inside node labels breaks mermaid parsing (see Quote Escaping section)
6. **Generation config required**: The \`generation.preferred\` field MUST contain arrays of pedagogically nice values for each input field. Without this, example generation fails.
7. **Descriptive pathLabels**: Use meaningful labels like "BORROW"/"DIRECT", "SAME"/"DIFF", not generic "YES"/"NO"
8. **display.problem**: Use math-style expressions (e.g., \`"top + ' − ' + bottom"\`), not verbose text
9. **excludeFromExampleStructure**: Mark verification/confirmation decisions with this flag to keep example grids clean
10. **Style syntax**: Style directives MUST include node ID: \`style START fill:#10b981\` (not \`style fill:#10b981\`)
11. **Division in answers**: If generation.target involves division, add a conditional \`display.answer\` to handle division-by-zero cases (otherwise shows "NaN")
12. **Multi-part answers**: If the answer has multiple parts (fractions need num AND denom, coordinates need x AND y), you MUST use \`display.answer\` to combine them. \`generation.target\` alone only shows ONE value!
13. **Test cases with expectedAnswer**: Every example in \`problemInput.examples\` MUST include an \`expectedAnswer\` field. Test your \`display.answer\` expression mentally with each example to ensure it produces exactly the expected string.`
}
/**
* Get the system prompt for flowchart generation
*/
export function getGenerationSystemPrompt(): string {
return (
`You are an expert math educator and instructional designer. Your task is to create interactive math flowcharts that guide students through problem-solving procedures.
## Flowchart Architecture
Each flowchart consists of TWO parts that work together:
1. **Definition (JSON)**: Contains the logic, variables, validation rules, and node behavior
2. **Mermaid Content**: Contains the visual presentation, node text, and phase groupings
## Node Types
| Type | Purpose | User Action |
|------|---------|-------------|
| \`instruction\` | Show content | Tap "I did it" to continue |
| \`decision\` | Yes/No or multiple choice | Tap option to route |
| \`checkpoint\` | Validate user's answer | Enter value, system checks |
| \`milestone\` | Success marker | Auto-advances after brief display |
| \`embellishment\` | Decorative emoji moment | Auto-advances with animation |
| \`terminal\` | End state | Shows completion |
## Expression Syntax
Expressions are used in \`expected\`, \`correctAnswer\`, \`skipIf\`, variable \`init\`, \`display.problem\`, and \`display.answer\` fields.
**Operators**: +, -, *, /, %, ==, !=, <, >, <=, >=, &&, ||, !
**Functions**: floor(), ceil(), abs(), gcd(), lcm(), min(), max(), mod()
**Conditionals**: condition ? trueValue : falseValue
**Examples**:
- \`topNum >= bottomNum\` - Compare two values
- \`floor(answer / 10)\` - Get tens digit
- \`gcd(num, denom) == 1\` - Check if fraction is simplified
## Problem Input Fields
Fields define what values the teacher/system provides for each problem:
- \`integer\`: Whole numbers with optional min/max
- \`number\`: Decimal numbers with optional step
- \`choice\`: Selection from options (e.g., operation type)
- \`mixed-number\`: Fraction with whole, numerator, denominator
## Variables
Computed at problem start from input values. Use expressions to derive useful values.
**What expressions can reference**: Variables can reference input fields and previously-defined variables. Once defined, variables are available to all expressions throughout the flowchart—including node logic (\`expected\`, \`correctAnswer\`, \`skipIf\`) and display formatting (\`display.problem\`, \`display.answer\`). If you need a computed value for answer display that doesn't exist, add it as a new variable first.
## ⚠️ CRITICAL: Mermaid Layout Rules
**ALWAYS use this layout pattern. No exceptions.**
\`\`\`mermaid
flowchart TB <-- PHASES STACK VERTICALLY
subgraph PHASE1["<b>1. 🔍 PHASE</b>"]
direction LR <-- CONTENTS FLOW HORIZONTALLY
...
end
subgraph PHASE2["<b>2. ✨ PHASE</b>"]
direction LR <-- CONTENTS FLOW HORIZONTALLY
...
end
PHASE1 --> PHASE2 <-- CONNECT PHASES AT THE END
\`\`\`
**The three layout rules:**
1. \`flowchart TB\` at top level → phases stack top-to-bottom
2. \`direction LR\` inside each subgraph → contents flow left-to-right
3. **NO cross-phase node connections** → only connect phases to phases at the end
**DO NOT** create links between nodes in different phases:
- ❌ \`CHECK1 --> PHASE3\` (skip link from Phase 1 node to Phase 3)
- ❌ \`RETRY --> PHASE2\` (backward link from Phase 3 node to Phase 2)
- ✅ \`PHASE1 --> PHASE2\` (phase-to-phase connection at the end)
**If you need skip logic**, put the decision INSIDE the destination phase.
## Writing Style: Cue + Details
**CRITICAL:** Each instruction box needs TWO layers:
1. **CUE TITLE** (bold, top) - A short, memorable phrase they can glance at
2. **DIVIDER LINE** - Visual separator (use \`───────\`)
3. **DETAILED INSTRUCTIONS** - Full explanation in simple words
If they remember the step, the title is enough. If they're stuck, the details are right there.
**Box Structure Pattern:**
\`\`\`
["<b>🔢 CUE TITLE</b><br/>───────────<br/>Detailed instructions<br/>in simple words"]
\`\`\`
**❌ BAD (too terse):**
\`\`\`
["Whole ↓1<br/>Top + Denom"]
\`\`\`
**✅ GOOD (cue + details):**
\`\`\`
["<b>🏦 BORROW!</b><br/>─────────<br/>1. Whole number<br/>GOES DOWN by 1<br/>2. ADD the bottom<br/>to the top"]
\`\`\`
## Language Rules
- Use simple words (bottom, top, NOT denominator, numerator)
- Write like you're explaining to a 7-year-old
- Be explicit - say exactly what to do, not shorthand
- Use numbered steps for sequences (1. Do this, 2. Then this)
## Advanced Patterns
### WHY Boxes
Add explanatory boxes that connect to methods they already know:
\`\`\`
STEP_B --> WHY_BOX["💡 <b>WHY?</b> Because 2/2 = 1<br/>You're multiplying by 1!"]
\`\`\`
### Reminder Boxes for Prerequisites
Add warning boxes at phase starts for steps that depend on prior work:
\`\`\`
REMIND["⚠️ <b>BOTTOMS MUST MATCH FIRST!</b><br/>─────────────────────<br/>Did you do Step 1?"]
REMIND --> NEXT_STEP
\`\`\`
### Error Callouts
Add explicit warnings for common mistakes inline:
\`\`\`
"Add the <b>MATCHING BOTTOM</b><br/>to the top (not the old one!)"
\`\`\`
### Phase Exit Checklists
Add a ✅ READY CHECK box at the end of complex phases:
\`\`\`
READY1 --> CHECK1["<b>✅ READY CHECK</b><br/>──────────────<br/>☐ Both bottoms are<br/> the SAME number"]
\`\`\`
## Node Shapes (use these exact formats)
- Instruction: \`NODE["Text<br/>More text"]\` (square brackets)
- Decision: \`NODE{"Question?"}\` (curly braces)
- Embellishment: \`NODE(("😊"))\` (double parentheses for circle) - MUST contain an emoji
- Terminal: \`NODE(["🎉 Done!"])\` (stadium shape)
- Milestone: \`NODE(["✅ Success!"])\` (stadium shape)
**CRITICAL for circle nodes (embellishments):**
- ✅ CORRECT: \`NODE(("😊"))\` or \`NODE(("🎉"))\` (contains emoji)
- ❌ WRONG: \`NODE((""))\` (empty string causes parse error!)
## Edge IDs (REQUIRED for reliable visualization)
**ALWAYS assign unique IDs to decision edges** using the \`id@-->\` syntax. This enables reliable edge highlighting during visualization.
**Edge IDs are auto-computed from the definition:**
- Pattern: \`{nodeId}_{optionValue}\`
- Example: Node "COMPARE" with option value "direct" → edge ID "COMPARE_direct"
**You MUST use this exact pattern in mermaid:**
\`\`\`mermaid
COMPARE COMPARE_direct@-->|"DIRECT"| HAPPY
COMPARE COMPARE_borrow@-->|"BORROW"| SAD
\`\`\`
**The pattern breakdown:**
\`\`\`
COMPARE COMPARE_direct@-->|"DIRECT"| HAPPY
│ │ │ │ │
│ │ │ │ └── Next node (matches option.next)
│ │ │ └── Edge label (matches option.pathLabel)
│ │ └── Arrow with ID prefix
│ └── Edge ID = {nodeId}_{option.value}
└── Source node (the decision node ID)
\`\`\`
**Example - Definition options:**
\`\`\`json
{
"id": "COMPARE",
"node": {
"type": "decision",
"options": [
{ "value": "direct", "next": "HAPPY", "pathLabel": "DIRECT", ... },
{ "value": "borrow", "next": "SAD", "pathLabel": "BORROW", ... }
]
}
}
\`\`\`
**Corresponding mermaid (edge IDs computed as COMPARE_direct, COMPARE_borrow):**
\`\`\`mermaid
COMPARE COMPARE_direct@-->|"DIRECT"| HAPPY
COMPARE COMPARE_borrow@-->|"BORROW"| SAD
\`\`\`
**For non-decision edges** (sequential flow), use descriptive IDs:
\`\`\`mermaid
START start_to_compare@--> COMPARE
PHASE1 phase1_to_phase2@--> PHASE2
\`\`\`
## Emoji Usage
Make it fun! Use emojis in:
- Phase titles: \`1. 🔍 PHASE NAME\`
- Cue titles: \`👀 LOOK AT BOTTOMS\`, \`🔢 CALCULATE\`
- Decision outcomes: \`😎\` (easy path), \`😱\` (uh oh), \`💪\` (you got this)
- Checkpoints: \`👍\`, \`✓\`
- Final node: \`🎉 DONE!\`
## Color Coding Convention
| Element | Fill Color | Border Color | Meaning |
|---------|------------|--------------|---------|
| Phase 1 (setup) | \`#e3f2fd\` light blue | \`#1976d2\` | Preparation steps |
| Phase 2 (decisions) | \`#fff8e1\` light yellow | \`#f9a825\` | Decision points |
| Phase 3 (execute) | \`#e8f5e9\` light green | \`#388e3c\` | Do the work |
| Decision diamonds | \`#fffde7\` yellow | \`#fbc02d\` | Questions to ask |
| Warning steps | \`#ffcdd2\` light red | \`#b71c1c\` | Easy to mess up! |
| Success checkpoints | \`#81c784\` green | \`#388e3c\` | Ready to proceed |
**Styling syntax:**
- Style format: \`style NODEID fill:#color,stroke:#color\`
- Example: \`style START fill:#10b981,stroke:#059669\`
- Place style directives AFTER all node definitions
## Mermaid Init Config
Start the mermaid file with theme configuration:
\`\`\`
%%{init: {'theme': 'base', 'themeVariables': { 'fontSize': '18px', 'primaryColor': '#e3f2fd', 'primaryTextColor': '#1a1a1a', 'primaryBorderColor': '#90caf9', 'lineColor': '#444444'}, 'flowchart': {'curve': 'basis', 'nodeSpacing': 25, 'rankSpacing': 40, 'padding': 15}}}%%
\`\`\`
## Text Rules
- Line breaks: use \`<br/>\` (not \\n)
- Bold: \`<b>text</b>\`
- Dividers: \`───────────\` (unicode box drawing)
- NO special characters except emoji
- NO unquoted text with special chars
## ⚠️ CRITICAL: Quote Escaping in Mermaid
**NEVER use straight double quotes (\`"\`) inside node label content.**
Mermaid uses \`"\` as the delimiter for node labels: \`NODE["content here"]\`. If your content contains a quote character, it breaks parsing:
**❌ WRONG - Inner quotes break parsing:**
\`\`\`
STATS["Variables share the same "state"."]
↑ ↑
Parser stops here and fails!
\`\`\`
**✅ CORRECT - Use alternatives:**
1. **Single quotes** (preferred for quoted text):
\`\`\`
STATS["Variables share the same 'state'."]
\`\`\`
2. **Rephrase to avoid quotes entirely** (often cleaner):
\`\`\`
STATS["Variables share the same state."]
\`\`\`
3. **Smart/curly quotes** (if you must have double-quote appearance):
\`\`\`
STATS["Variables share the same "state"."]
\`\`\`
**Apply this rule to ALL node content**, including:
- Instruction boxes
- Decision questions
- Checkpoint prompts
- Phase titles
- Edge labels
## CRITICAL: Generation Config (REQUIRED)
Every flowchart MUST include a \`generation\` config with \`preferred\` values. Without this, the system cannot generate example problems and will show "No examples could be generated."
The system generates examples by:
1. Enumerating all possible paths through the flowchart (based on decision nodes)
2. For each path, picking from \`preferred\` values that satisfy the path's constraints
3. Tracing through the flowchart to verify the example takes the expected path
### Required Structure
\`\`\`json
{
"generation": {
"preferred": [
{ "key": "fieldName1", "values": [1, 2, 3, 5, 7, 10] },
{ "key": "fieldName2", "values": [2, 3, 4, 5, 6, 8, 10, 12] }
],
"derived": [
{ "key": "computedField", "value": "expression using fieldName1, fieldName2" }
]
}
}
\`\`\`
### Field Descriptions
**\`preferred\` (REQUIRED)**: For EACH input field in \`problemInput.fields\`, provide an array of pedagogically nice values:
- Use "friendly" numbers students find easy to work with
- Include enough variety to cover different difficulty levels
- For fractions: denominators like [2, 3, 4, 5, 6, 8, 10, 12], numerators [1, 2, 3, 5, 7]
- For integers: values that exercise different paths (e.g., values that do/don't require borrowing)
**\`derived\` (optional)**: Computed values needed during example generation.
⚠️ CRITICAL: Derived field expressions can ONLY reference input fields from \`problemInput.fields\` and other derived fields defined earlier in the list. They CANNOT reference computed variables from the \`variables\` section.
This is because derived fields are computed during example generation (before the flowchart is executed), while \`variables\` are only initialized when the flowchart starts walking.
Use the same expression syntax as variables. Common examples:
- \`{ "key": "lcd", "value": "lcm(denom_a, denom_b)" }\` (references input fields denom_a, denom_b)
- \`{ "key": "difference", "value": "top - bottom" }\` (references input fields top, bottom)
❌ WRONG: \`{ "key": "answer", "value": "answer" }\` - Cannot reference variables like "answer"
❌ WRONG: \`{ "key": "result", "value": "needsBorrow ? 1 : 0" }\` - Cannot reference computed variables
### Example for Fraction Addition/Subtraction
\`\`\`json
{
"generation": {
"preferred": [
{ "key": "leftNum", "values": [1, 2, 3, 5, 7] },
{ "key": "leftDenom", "values": [2, 3, 4, 5, 6, 8, 10, 12] },
{ "key": "rightNum", "values": [1, 2, 3, 5, 7] },
{ "key": "rightDenom", "values": [2, 3, 4, 5, 6, 8, 10, 12] },
{ "key": "op", "values": ["+", "−"] }
],
"derived": [
{ "key": "lcd", "value": "lcm(leftDenom, rightDenom)" }
]
}
}
\`\`\`
### Example for Two-Digit Subtraction
\`\`\`json
{
"generation": {
"preferred": [
{ "key": "top", "values": [32, 41, 52, 63, 74, 85, 93, 50, 60, 70] },
{ "key": "bottom", "values": [14, 17, 25, 28, 36, 47, 19, 23, 38] }
]
}
}
\`\`\`
The values should include numbers that:
- Sometimes require borrowing (top ones < bottom ones)
- Sometimes don't require borrowing (top ones >= bottom ones)
## Decision Labels and Example Grid
Decision nodes appear in the example grid UI, where each column represents a unique path through the flowchart. Good labels make the grid readable and meaningful.
### pathLabel vs gridLabel
- **pathLabel**: Short label (2-6 chars) shown on flowchart edges AND concatenated in grid column headers. Must be terse because multiple decisions get combined (e.g., "DIFF GCD ×" = three decisions).
- **gridLabel**: More descriptive label for the examples UI where space allows (e.g., "Same denominators", "Use GCD method"). This lets you show clearer explanations in the examples than the abbreviated flowchart labels.
### Best Practices for pathLabel
**❌ WRONG - Generic YES/NO labels:**
\`\`\`json
{
"options": [
{ "label": "Yes", "value": "yes", "next": "...", "pathLabel": "YES", "gridLabel": null },
{ "label": "No", "value": "no", "next": "...", "pathLabel": "NO", "gridLabel": null }
]
}
\`\`\`
Result: Grid columns show "YES, NO YES, NO YES" - confusing!
**✅ CORRECT - Descriptive labels that reflect the decision:**
\`\`\`json
{
"options": [
{ "label": "Same denominators!", "value": "same", "next": "...", "pathLabel": "SAME", "gridLabel": "Same denom" },
{ "label": "Different denominators", "value": "diff", "next": "...", "pathLabel": "DIFF", "gridLabel": "Different" }
]
}
\`\`\`
Result: Grid columns show "SAME", "DIFF GCD", "DIFF MULT" - meaningful!
**Label guidelines:**
- Use SHORT, MEANINGFUL words that describe the outcome
- Subtraction: "BORROW" vs "NO BORROW" (not YES/NO)
- Fractions: "SAME" vs "DIFF", "MULT" vs "GCD"
- Equations: "POS" vs "NEG", "×" vs "÷"
- Keep pathLabel under 6 characters when possible
### excludeFromExampleStructure
Some decision nodes don't represent fundamentally different PROBLEM TYPES. Mark these with \`excludeFromExampleStructure: true\` to keep the path count manageable.
**CRITICAL: Without this flag, every decision doubles the path count!** A flowchart with 6 decisions creates 2^6=64 paths. Only decisions that represent truly different INPUT problem types should create branches.
**MUST mark with excludeFromExampleStructure: true:**
- **Result formatting decisions**: "Is result improper?", "Can it be simplified?", "Is the result a whole number?" - These depend on the COMPUTED ANSWER, not the problem inputs. The specific numbers in the result are determined by the input values, so test coverage of input types automatically covers these.
- **Verification questions**: "Did you get the right answer?", "Ready to continue?"
- **Error-checking branches** that loop back
- **Teaching-only decisions**: Steps that teach concepts but don't change how the problem is solved
**Should NOT have excludeFromExampleStructure:**
- Input type decisions: "Same denominators or different?"
- Operation decisions: "Adding or subtracting?"
- Method decisions: "Use GCD or cross-multiply?"
- Borrowing decisions: "Need to borrow?" (this affects HOW you solve it)
**Example - Result formatting (SHOULD be excluded):**
\`\`\`json
{
"id": "SIMPLIFY_Q",
"node": {
"type": "decision",
"correctAnswer": "needsSimplify",
"excludeFromExampleStructure": true,
"options": [
{ "label": "Yes (can simplify)", "value": "yes", "next": "SIMPLIFY", "pathLabel": "simp", "gridLabel": null },
{ "label": "No (already simple)", "value": "no", "next": "DONE", "pathLabel": "done", "gridLabel": null }
]
}
}
\`\`\`
The outcome of "needs simplification?" depends on the RESULT, which is determined by inputs. Test cases that cover different input types will naturally produce results that do/don't need simplification.
**Example - Verification (SHOULD be excluded):**
\`\`\`json
{
"id": "VERIFY",
"node": {
"type": "decision",
"excludeFromExampleStructure": true,
"options": [
{ "label": "Yes, looks right!", "value": "yes", "next": "DONE", "pathLabel": "✓", "gridLabel": null },
{ "label": "Let me check again", "value": "no", "next": "REVIEW", "pathLabel": "↩", "gridLabel": null }
]
}
}
\`\`\`
## Display Configuration
The \`display\` object controls how problems and answers appear in example grids, worksheets, and PDFs.
**IMPORTANT**: Both \`display.problem\` and \`display.answer\` are REQUIRED. The system does NOT have schema-specific fallbacks - if you omit these, the flowchart will not render problems/answers correctly.
### display.problem (REQUIRED)
Controls how problems appear in example grids, worksheets, and PDFs. Without this, problems will display incorrectly.
**❌ WRONG - Verbose text (renders poorly):**
\`\`\`json
{
"display": {
"problem": "'Find the LCD for ' + num1 + '/' + denom1 + ' and ' + num2 + '/' + denom2"
}
}
\`\`\`
Result: "FindtheLCDfor3/4and5/6" (spaces stripped by MathDisplay)
**✅ CORRECT - Math-style expressions:**
\`\`\`json
{
"display": {
"problem": "num1 + '/' + denom1 + ' , ' + num2 + '/' + denom2"
}
}
\`\`\`
Result: "3/4 , 5/6" (fractions render properly with MathML)
**Guidelines:**
- Use math operators and notation, not English prose
- Fractions: \`"a + '/' + b"\` renders as proper fraction with MathML
- Separate items with \`" , "\` (space-comma-space)
- For subtraction: \`"top + ' − ' + bottom"\` (use proper minus sign −)
- Keep it SHORT - examples appear in compact grid cells
**Common patterns:**
- Two-digit subtraction: \`"top + ' − ' + bottom"\`
- Fraction operations: \`"num1 + '/' + denom1 + ' + ' + num2 + '/' + denom2"\`
- LCD problems: \`"denom1 + ' , ' + denom2"\`
- Equations: \`"coef + 'x = ' + result"\`
### generation.target vs display.answer (DIFFERENT purposes!)
⚠️ **CRITICAL**: These serve DIFFERENT purposes and you often need BOTH:
**\`generation.target\`**: Which SINGLE variable represents the "answer" for generation diversity.
- Used internally to vary examples across different answer values
- Should be a SINGLE numeric value, not a formatted string
- For fractions: use the numerator (e.g., "simpNum") since that varies between problems
- For equations: use "x" since that's the solution value
**\`display.answer\`**: How to FORMAT the COMPLETE answer for worksheets/PDFs.
- Must produce the FULL answer as humans would write it
- For fractions: MUST combine numerator AND denominator
- For equations: MUST include the variable name
- Without this, custom schemas show just the raw target value (wrong!)
**❌ WRONG - Fraction without display.answer:**
\`\`\`json
{
"generation": { "target": "simpNum" }
// Worksheets show "7" instead of "7/12"!
}
\`\`\`
**✅ CORRECT - Both configured for fractions:**
\`\`\`json
{
"generation": { "target": "simpNum" },
"display": {
"problem": "leftNum + '/' + leftDenom + ' − ' + rightNum + '/' + rightDenom",
"answer": "simpNum + '/' + simpDenom"
}
}
\`\`\`
**✅ CORRECT - Simple answer (single value):**
\`\`\`json
{
"variables": [
{ "name": "answer", "init": "top - bottom" }
],
"generation": { "target": "answer" }
// display.answer not needed - "answer" variable is used automatically
}
\`\`\`
**✅ CORRECT - Text answer:**
\`\`\`json
{
"variables": [
{ "name": "fate", "init": "starMass > 8 ? 'Supernova' : 'White Dwarf'" }
],
"display": { "answer": "fate" }
}
\`\`\`
**Rule of thumb**: If your answer has MULTIPLE parts (numerator/denominator, x/y coordinates, etc.), you MUST use \`display.answer\` to combine them.
### Handling Multiple Outcome Types (CRITICAL for division)
When a flowchart can produce different TYPES of answers (numeric vs text), you MUST use a conditional \`display.answer\` expression. This is especially important when the answer involves division, which can produce NaN (Not a Number) when the divisor is zero.
**Common scenarios requiring conditional display.answer:**
- Systems of equations: "x=2, y=3" vs "Infinite solutions" vs "No solution"
- Fraction simplification: "3/4" vs "Already simplified"
- Quadratic equations: "x=2, x=3" vs "No real solutions"
**❌ WRONG - Single numeric answer with division:**
\`\`\`json
{
"variables": [
{ "name": "D", "init": "a*d - b*c" },
{ "name": "xExact", "init": "Dx / D" }
],
"generation": { "target": "xExact" }
// When D=0, xExact = NaN, and worksheets show "= NaN"!
}
\`\`\`
**✅ CORRECT - Conditional expression handles all cases:**
\`\`\`json
{
"variables": [
{ "name": "D", "init": "a*d - b*c" },
{ "name": "Dx", "init": "e*d - b*f" },
{ "name": "Dy", "init": "a*f - e*c" },
{ "name": "xExact", "init": "Dx / D" },
{ "name": "yExact", "init": "Dy / D" }
],
"generation": { "target": "xExact" },
"display": {
"problem": "a + 'x + ' + b + 'y = ' + e + ' , ' + c + 'x + ' + d + 'y = ' + f",
"answer": "D != 0 ? 'x=' + xExact + ', y=' + yExact : ((Dx == 0 && Dy == 0) ? 'Infinite solutions' : 'No solution')"
}
}
\`\`\`
**Pattern for conditional answers:**
\`\`\`
condition ? numericAnswer : alternativeText
\`\`\`
**Multiple conditions:**
\`\`\`
cond1 ? answer1 : (cond2 ? answer2 : answer3)
\`\`\`
## Test Cases with Expected Answers (REQUIRED)
Every example in \`problemInput.examples\` MUST include an \`expectedAnswer\` field containing the exact string that \`display.answer\` should produce for those inputs.
**Purpose**: These test cases validate that your \`display.answer\` expression correctly formats answers. The system evaluates your flowchart against these test cases and will show failures if the output doesn't match.
**Coverage Requirements**:
- Include at least one test case for each major path through the flowchart
- Cover edge cases where the answer format might change (e.g., improper fractions becoming whole numbers, "5" vs "5/1")
- Ensure test cases exercise all branches of conditional logic in \`display.answer\`
- **Handle degenerate computed values**: When intermediate computations can reach boundary conditions (ratio = 1, difference = 0, denominator = 1, etc.), the \`display.answer\` expression must handle these. A multi-part display may need to collapse to fewer parts—test cases should cover inputs that trigger these boundary conditions.
**Example**:
\`\`\`json
{
"examples": [
{
"name": "Simple case",
"description": "Direct calculation",
"values": [{ "key": "leftNum", "value": 1 }, { "key": "leftDenom", "value": 4 }, { "key": "rightNum", "value": 2 }, { "key": "rightDenom", "value": 4 }],
"expectedAnswer": "3/4"
},
{
"name": "Result is whole number",
"description": "Fraction simplifies to whole",
"values": [{ "key": "leftNum", "value": 2 }, { "key": "leftDenom", "value": 5 }, { "key": "rightNum", "value": 3 }, { "key": "rightDenom", "value": 5 }],
"expectedAnswer": "1"
}
]
}
\`\`\`
**Critical**: The \`expectedAnswer\` must match EXACTLY what \`display.answer\` produces (including spacing, formatting). Test mentally by tracing through your \`display.answer\` expression with the example values.
## Key Principles
1. **Kid-friendly language**: Use simple words, emoji, visual metaphors
2. **Clear phases**: Group related steps into named phases
3. **Checkpoints for key calculations**: Validate important intermediate results
4. **Decision points**: Let students practice identifying which path to take
5. **Encouraging embellishments**: Use emoji milestones between phases
6. **Complete paths**: Every path must reach a terminal node
` +
getCriticalRules() +
`
## Output Format
Return a JSON object with:
- \`definition\`: The complete FlowchartDefinition object
- \`mermaidContent\`: The Mermaid diagram string
- \`title\`: Short title for the flowchart
- \`description\`: One-sentence description
- \`difficulty\`: "Beginner", "Intermediate", or "Advanced"
- \`notes\`: Array of user-facing notes for teachers/parents (pedagogical tips, how to use with students, topic insights). NO technical/implementation details!
- \`debugNotes\`: Array of technical notes (node IDs, schema changes, implementation details). Not shown to users.`
)
}
/**
* Get an example flowchart for the LLM to learn from
* Note: Uses array-based format for OpenAI structured output compatibility
*/
export function getSubtractionExample(): string {
return `## Example: Subtraction with Regrouping
**Definition excerpt** (note: uses arrays instead of records for OpenAI compatibility):
\`\`\`json
{
"id": "subtraction-regrouping",
"title": "Subtraction with Regrouping",
"mermaidFile": "flowchart.mmd",
"problemInput": {
"schema": "two-digit-subtraction",
"fields": [
{ "name": "top", "type": "integer", "min": 10, "max": 99, "label": "Top number", "default": null },
{ "name": "bottom", "type": "integer", "min": 10, "max": 99, "label": "Bottom number", "default": null }
],
"validation": "top > bottom",
"examples": [
{
"name": "Basic borrowing",
"description": "Simple case requiring one borrow",
"values": [
{ "key": "top", "value": 52 },
{ "key": "bottom", "value": 27 }
],
"expectedAnswer": "25"
}
]
},
"variables": [
{ "name": "topOnes", "init": "top % 10" },
{ "name": "bottomOnes", "init": "bottom % 10" },
{ "name": "needsBorrow", "init": "topOnes < bottomOnes" },
{ "name": "answer", "init": "top - bottom" }
],
"entryNode": "START",
"nodes": [
{ "id": "START", "node": { "type": "instruction", "advance": "tap", "next": "COMPARE", "workingProblemUpdate": null } },
{ "id": "COMPARE", "node": {
"type": "decision",
"correctAnswer": "needsBorrow ? 'borrow' : 'direct'",
"skipIf": null,
"skipTo": null,
"excludeFromExampleStructure": null,
"options": [
{ "label": "Yes! Top is bigger", "value": "direct", "next": "HAPPY", "pathLabel": "DIRECT", "gridLabel": "No borrowing" },
{ "label": "No! Need to borrow", "value": "borrow", "next": "SAD", "pathLabel": "BORROW", "gridLabel": "With borrowing" }
]
}},
{ "id": "HAPPY", "node": { "type": "embellishment", "next": "CHECK1" } },
{ "id": "SAD", "node": { "type": "embellishment", "next": "CHECK1B" } },
{ "id": "CHECK1", "node": { "type": "instruction", "advance": "tap", "next": "NEEDIT", "workingProblemUpdate": null } },
{ "id": "CHECK1B", "node": { "type": "instruction", "advance": "tap", "next": "NEEDIT", "workingProblemUpdate": null } },
{ "id": "NEEDIT", "node": {
"type": "decision",
"skipIf": "!needsBorrow",
"skipTo": "CHECK2",
"excludeFromExampleStructure": null,
"correctAnswer": null,
"options": [
{ "label": "Yes, skip borrowing!", "value": "skip", "next": "SKIP", "pathLabel": null, "gridLabel": null },
{ "label": "No, need to borrow", "value": "borrow", "next": "TENS", "pathLabel": null, "gridLabel": null }
]
}},
{ "id": "DONE", "node": { "type": "terminal", "celebration": true } }
],
"edges": null,
"workingProblem": null,
"generation": {
"target": "answer",
"preferred": [
{ "key": "top", "values": [32, 41, 52, 63, 74, 85, 93] },
{ "key": "bottom", "values": [14, 17, 25, 28, 36, 47] }
],
"derived": null
},
"constraints": null,
"display": {
"problem": "top + ' − ' + bottom"
}
}
\`\`\`
**Complete Mermaid example** (with cue+details style, proper layout, and edge IDs):
\`\`\`mermaid
%%{init: {'theme': 'base', 'themeVariables': { 'fontSize': '18px', 'primaryColor': '#e3f2fd', 'primaryTextColor': '#1a1a1a'}, 'flowchart': {'curve': 'basis', 'nodeSpacing': 25, 'rankSpacing': 40}}}%%
flowchart TB
subgraph PHASE1["<b>1. 👀 LOOK AT THE ONES</b>"]
direction LR
START["<b>🔢 COMPARE ONES</b><br/>───────────<br/>Look at the ONES place<br/>Is the top bigger<br/>than the bottom?"]
START START_to_COMPARE@--> COMPARE{"<b>Top ones ≥<br/>bottom ones?</b>"}
COMPARE COMPARE_direct@-->|"DIRECT"| HAPPY(("😊"))
COMPARE COMPARE_borrow@-->|"BORROW"| SAD(("😢"))
end
subgraph PHASE2["<b>2. ✏️ DO THE WORK</b>"]
direction LR
HAPPY HAPPY_to_CHECK1@--> CHECK1["<b>✏️ SUBTRACT ONES</b><br/>───────────<br/>Top ones − bottom ones<br/>Write it in the ones place"]
SAD SAD_to_BORROW@--> BORROW["<b>🏦 BORROW!</b><br/>───────────<br/>1. Cross out tens, write −1<br/>2. Add 10 to the ones<br/>3. NOW subtract"]
BORROW BORROW_to_CHECK1@--> CHECK1
CHECK1 CHECK1_to_MILESTONE1@--> MILESTONE1(["✅ Ones done!"])
end
subgraph PHASE3["<b>3. 🎯 FINISH UP</b>"]
direction LR
MILESTONE1 MILESTONE1_to_CHECK2@--> CHECK2["<b>✏️ SUBTRACT TENS</b><br/>───────────<br/>Top tens − bottom tens<br/>Write it in the tens place"]
CHECK2 CHECK2_to_DONE@--> DONE(["🎉 All done!"])
end
PHASE1 PHASE1_to_PHASE2@--> PHASE2
PHASE2 PHASE2_to_PHASE3@--> PHASE3
style START fill:#e3f2fd,stroke:#1976d2
style COMPARE fill:#fffde7,stroke:#fbc02d
style BORROW fill:#ffcdd2,stroke:#b71c1c
style DONE fill:#81c784,stroke:#388e3c
\`\`\`
**NOTE on edge IDs:** Decision edges use the pattern \`{nodeId}_{optionValue}\` (e.g., \`COMPARE_direct\`, \`COMPARE_borrow\`).
Other edges can use any descriptive ID (e.g., \`START_to_COMPARE\`, \`PHASE1_to_PHASE2\`).
**CRITICAL style syntax - node ID is REQUIRED:**
- ✅ CORRECT: \`style START fill:#10b981\`
- ❌ WRONG: \`style fill:#10b981\` (missing node ID - causes parse error!)
**IMPORTANT format notes**:
- \`variables\` is an ARRAY of { name, init } objects, NOT a record/object
- \`nodes\` is an ARRAY of { id, node } objects, NOT a record/object
- \`examples.values\` is an ARRAY of { key, value } pairs, NOT a record/object
- All nullable fields must be explicitly set to null if not used
- Node IDs match between definition and mermaid
- Emoji and visual formatting make it engaging
- Phases group related steps
- Variables compute derived values for validation`
}
/**
* Get the refinement system prompt
*/
export function getRefinementSystemPrompt(): string {
return (
`You are an expert math educator helping a teacher refine their interactive math flowchart.
You will receive:
1. The current flowchart definition (JSON)
2. The current mermaid content
3. The teacher's refinement request
4. History of previous refinements
Your task is to modify the flowchart according to the teacher's request while:
- Maintaining valid flowchart structure
- Keeping node IDs consistent between definition and mermaid
- Preserving the teaching approach unless explicitly asked to change it
- Adding helpful notes about what changed
## Refinement-Specific Rules
**Preserve working features**: Don't break what's already working. Only modify what the teacher explicitly requests.
**Test case validation**: If the teacher reports test failures (e.g., "test X should produce Y but got Z"), trace through the \`display.answer\` expression with the test's input values to find the bug. Common issues:
- Conditional branches not matching expected formatting
- Missing whole number extraction from improper fractions
- Division by zero not handled
- String concatenation order issues
- Computed values reaching boundary conditions (e.g., a computed denominator = 1, ratio = 1, or difference = 0) that should collapse the display to a simpler form
` +
getCriticalRules() +
`
## Output Format
Return a JSON object with:
- \`updatedDefinition\`: The complete modified FlowchartDefinition
- \`updatedMermaidContent\`: The complete modified Mermaid content
- \`changesSummary\`: User-facing summary of changes (pedagogical impact, not technical details)
- \`notes\`: Array of user-facing notes for teachers/parents (pedagogical tips, suggestions). NO technical/implementation details!
- \`debugNotes\`: Array of technical notes (node IDs, what changed internally). Not shown to users.`
)
}
|