Maailmantutkija

Date: 2025-10-18

Summary

Implemented comprehensive distribution system for the Shapes Game with all 27 rules (12 existing + 15 new). Each rule now has pedagogically designed positive and negative example generators with built-in validation.

Game Structure

Input: Sequence of 4 (color, type) pairs in left-to-right order

• Colors: red, blue, green, purple, black, yellow (6 total)
• Types: circle, square, triangle, star, heart, plus (6 total)
• Rules: 27 total (s1-s27)

What Was Implemented

1. Distribution Generators (shapes-distributions.js)

Created 19 distribution generator functions:

Basic Generators (1-7):

1. uniformRandom() - 4 random (color, type) pairs
2. allSameColor(color) - All 4 shapes same color, random types
3. allSameType(type) - All 4 shapes same type, random colors
4. allDifferentColors() - 4 different colors
5. allDifferentTypes() - 4 different types
6. exactlyKColors(k) - Exactly k distinct colors (1-4)
7. exactlyKTypes(k) - Exactly k distinct types (1-4)

Positional Generators (8-11):

1. firstAndLastSame(attribute) - First and last match on ‘color’ or ‘type’
2. specificAtPosition(pos, color, type) - Specific shape at position
3. colorPattern(pattern) - Specific color sequence (e.g., [red, blue, red, blue])
4. typePattern(pattern) - Specific type sequence

Counting Generators (12-13):

1. atLeastK(attribute, value, k) - At least k shapes with specific color/type
2. exactlyK(attribute, value, k) - Exactly k shapes with specific color/type

Complexity Generators (14-19):

1. increasingCorners() - Corner count strictly increasing
2. nonDecreasingCorners() - Corner count non-decreasing
3. symmetricColors() - Palindromic color sequence
4. symmetricTypes() - Palindromic type sequence
5. noAdjacentSameColor() - No two adjacent shapes same color
6. noAdjacentSameType() - No two adjacent shapes same type

2. Rule Additions (shapes-rules.js)

Existing Rules (s1-s12):

• s1: All same color
• s2: All same type
• s3: All different colors
• s4: Contains green
• s5: First and last same color
• s6: Exactly two colors
• s7: All different types
• s8: Contains triangle
• s9: At least two circles
• s10: Exactly two types
• s11: First is red circle
• s12: Corner count strictly increasing

New Rules (s13-s27):

• s13: First and last different colors
• s14: Color palindrome (positions 0==3, 1==2)
• s15: Exactly three colors
• s16: No two adjacent same color
• s17: Type palindrome
• s18: Exactly three types
• s19: At least three circles
• s20: No two adjacent same type
• s21: Corner count non-decreasing
• s22: First and last same corner count
• s23: All same corner count
• s24: Same color → same type (logical implication)
• s25: If red exists, blue exists (logical implication)
• s26: First and third identical (both color AND type)
• s27: Exactly two pairs of identical shapes

3. Distribution Design Patterns

Pattern used: 20% random + 80% conceptual near-misses

Example Near-Miss Designs:

s1 (All same color):

• ✓ Positive: allSameColor(randomColor)
• ✗ Negative near-misses:
  • 40% exactly 3 colors (near-miss!)
  • 40% exactly 2 colors (near-miss!)

s12 (Corners strictly increasing):

• ✓ Positive: increasingCorners() → [circle, triangle, square, star]
• ✗ Negative near-misses:
  • 40% nonDecreasingCorners() (allows equal - near-miss!)
  • 40% allDifferentTypes() (random corners)

s14 (Color palindrome):

• ✓ Positive: symmetricColors() → [red, blue, blue, red]
• ✗ Negative near-misses:
  • 40% firstAndLastSame('color') (only ends match - near-miss!)
  • 40% symmetricTypes() (wrong attribute - near-miss!)

s16 (No adjacent same color):

• ✓ Positive: noAdjacentSameColor()
• ✗ Negative near-misses:
  • 40% allSameColor() (extreme opposite)
  • 40% exactlyKColors(2) (likely has adjacent)

s24 (Same color → same type):

• ✓ Positive:
  • 50% allDifferentColors() (vacuously true)
  • 50% uniformRandom() (some satisfy)
• ✗ Negative:
  • 60% exactlyKColors(2) (likely violates)
  • 40% allSameColor() with different types

4. Game Logic Updates (shapes-game.js)

Added methods:

1. generateShapesForRule(shouldSatisfy)
   • Uses distribution specs from rule definitions
   • Handles different generator signatures
   • Falls back to random generation if no distribution
2. generateShapesFallback(shouldSatisfy)
   • Fallback random generation with retry logic
   • Ensures generated shapes match desired satisfaction status

Added validation:

• Logs console warnings if positive example doesn’t satisfy rule
• Logs warnings if negative example satisfies rule
• Helps identify distribution bugs during development

Corner Count System

Corner counts used for ordering rules:

• circle, heart: 0 corners
• triangle: 3 corners
• square, plus: 4 corners
• star: 5 corners

This enables rules about increasing/decreasing/equal corner counts.

Logical Implication Rules

s24: “Same color → same type”

• Checks: For all pairs (i,j), if color[i] == color[j], then type[i] == type[j]
• Vacuously true when all colors different

s25: “If red exists, blue exists”

• Checks: hasRed → hasBlue (equivalent to !hasRed OR hasBlue)
• Vacuously true when no red shapes

Testing Checklist

• [✓] 27 rules with distributions
• [✓] 19 generators produce valid 4-shape sequences
• [✓] Validation logs warnings for incorrect examples
• Browser testing at /saannon-keksiminen.html
• Near-misses are pedagogically useful (verify in testing)

Files Modified/Created

1. /shapes/shapes-distributions.js (CREATED, 450 lines)
2. /shapes/shapes-rules.js (UPDATED, 550 lines)
3. /shapes/shapes-game.js (UPDATED, added validation + distributions)
4. /shapes/SHAPES_IMPLEMENTATION.md (THIS FILE)

Design Philosophy

Pedagogical value: Near-misses help students refine understanding by testing:

• Boundary cases: “Almost all same color” vs “all same color”
• Attribute confusion: Color palindrome vs type palindrome
• Count variations: Exactly 2 vs exactly 3 distinct colors
• Logical near-misses: Only ends match vs full palindrome

Validation-first: Always validate generated examples match expected satisfaction status.

Flexibility: System gracefully falls back to random generation if distributions aren’t specified.

Next Steps

1. Test in browser at http://localhost:4000/saannon-keksiminen.html
2. Select “Shapes” game
3. Play through several rules (especially new ones s13-s27)
4. Verify:
   • Examples generate correctly
   • Validation warnings (if any) in console
   • Near-misses are pedagogically useful
   • Corner-based rules work correctly
   • Logical implication rules (s24, s25) work

Version

All files use ?v7 query parameter for cache busting.