e s«# DASGraph — Discrete Relation Practice

Local-only React + TypeScript app for exam-style discrete mathematics practice. The app is organized by relation family (closures, composition, structures) and submode (construct, multiple-choice, review).

Architecture (Strict Separation)

• src/math/: Pure relation logic. Normalization, closures, composition, transpose, property checks, checking utilities.
• src/layout/: Deterministic geometry generation (seeded), no relation logic.
• src/render/: SVG path utilities, arrow markers, export helpers.
• src/parser/: JSON parsing + runtime validation; outputs normalized, typed data with warnings.
• src/components/: React UI and diagram composition.
• src/state/: JSON editor state + study mode defaults.
• src/examples/: Family + submode examples.

Single source of truth: normalized relation data. Layouts only affect geometry.

Run Locally

npm install
npm run dev

Global Study Mode

• Practice (default): hides solutions by default.
• Review: reveals solutions by default.

JSON Input Formats (Family + Submode)

Closures / Construct

{
  "family": "closures",
  "submode": "construct",
  "task": "transitive",
  "set": ["1","2","3","4"],
  "relation": [["1","2"],["2","3"]],
  "layoutPreset": "irregular-exam",
  "seed": 12
}

Closures / Multiple-Choice

{
  "family": "closures",
  "submode": "multiple-choice",
  "task": "transitive",
  "set": ["1","2","3","4"],
  "relation": [["1","2"],["2","3"]],
  "correctOptionId": "B",
  "options": [
    { "id": "A", "relation": [["1","2"],["2","3"]] },
    { "id": "B", "relation": [["1","2"],["2","3"],["1","3"]] },
    { "id": "C", "relation": [["1","2"],["2","3"],["3","1"]] },
    { "id": "D", "relation": [["1","2"],["2","3"],["1","4"]] }
  ],
  "layoutPreset": "compact-exam",
  "seed": 12
}

Composition / Construct

{
  "family": "composition",
  "submode": "construct",
  "X": ["1","2","3"],
  "Y": ["1","2","3"],
  "Z": ["1","2","3"],
  "R": [["1","2"],["2","3"]],
  "S": [["2","1"],["3","2"]],
  "allowTraceAssist": true
}

Composition / Multiple-Choice

{
  "family": "composition",
  "submode": "multiple-choice",
  "X": ["1","2","3"],
  "Y": ["1","2","3"],
  "Z": ["1","2","3"],
  "R": [["1","2"],["2","3"]],
  "S": [["2","1"],["3","2"]],
  "correctOptionId": "C",
  "options": [
    { "id": "A", "relation": [["1","1"]] },
    { "id": "B", "relation": [["2","2"]] },
    { "id": "C", "relation": [["1","1"],["2","2"]] },
    { "id": "D", "relation": [["1","2"],["2","1"]] }
  ]
}

Structures / True-False

{
  "family": "structures",
  "submode": "true-false",
  "set": ["1","2","3","4","5","6","7","8"],
  "relation": [["1","2"],["2","3"],["3","4"]],
  "askAboutSquaredRelation": true,
  "layoutPreset": "polygon",
  "seed": 7
}

Structures / Multiple-Choice

{
  "family": "structures",
  "submode": "multiple-choice",
  "prompt": "Choose the correct graph for R ∘ R",
  "set": ["1","2","3","4"],
  "relation": [["1","2"],["2","3"]],
  "correctOptionId": "B",
  "options": [
    { "id": "A", "relation": [["1","2"],["2","3"]] },
    { "id": "B", "relation": [["1","3"]] },
    { "id": "C", "relation": [["3","1"]] },
    { "id": "D", "relation": [["1","1"],["2","2"]] }
  ],
  "derivedTask": "square-relation"
}

Validation Rules (Runtime)

• Elements accept strings or numbers (normalized to internal string ids).
• Relation pairs must be 2-element arrays.
• Relations must be subsets of the intended Cartesian product.
• Duplicate labels (after normalization) are rejected.
• Multiple-choice inputs warn if the marked correct option disagrees with computed results.

Tests

npm run test

Coverage includes:

• closure/composition checking utilities
• property checking
• correct-option validation warnings
• study mode defaults
• deterministic layouts
• opposite-direction edge routing
• label centering defaults