Add tasks for all the new languages
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Tina Müller
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Task/Zebra-puzzle/FormulaOne/zebra-puzzle.formulaone
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Task/Zebra-puzzle/FormulaOne/zebra-puzzle.formulaone
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// First, let's give some variables some values:
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Nationality = Englishman | Swede | Dane | Norwegian | German
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Colour = Red | Green | Yellow | Blue | White
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Cigarette = PallMall | Dunhill | BlueMaster | Blend | Prince
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Domestic = Dog | Bird | Cat | Zebra | Horse
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Beverage = Tea | Coffee | Milk | Beer | Water
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HouseOrder = First | Second | Third | Fourth | Fifth
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{
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We use injections to make the array-elements unique.
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Example: 'Pet' is an array of unique elements of type 'Domestic', indexed by 'Nationality'.
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In the predicate 'Zebra', we use this injection 'Pet' to define the array-variable 'pet'.
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The symbol used is the '->>'. 'Nationality->>Domestic' can be read as 'Domestic(Nationality)' in "plain array-speak";
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the difference being that the elements are by definition unique.
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So, in FormulaOne we use a formula like: 'pet(Swede) = Dog', which simply means that the 'Swede' (type 'Nationality')
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has a 'pet' (type 'Pet', which is of type 'Domestic', indexed by 'Nationality'), which appears to be a 'Dog' (type 'Domestic').
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Or, one could say that the 'Swede' has been mapped to the 'Dog' (Oh, well...).
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}
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Pet = Nationality->>Domestic
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Drink = Nationality->>Beverage
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HouseColour = Nationality->>Colour
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Smoke = Nationality->>Cigarette
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Order = HouseOrder->>Nationality
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pred Zebra(houseColour::HouseColour, pet::Pet, smoke::Smoke, drink::Drink, order::Order) iff
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// For convenience sake, some temporary place_holder variables are used.
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// An underscore distinguishes them:
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houseColour(green_house) = Green &
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houseColour(white_house) = White &
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houseColour(yellow_house) = Yellow &
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smoke(pallmall_smoker) = PallMall &
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smoke(blend_smoker) = Blend &
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smoke(dunhill_smoker) = Dunhill &
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smoke(bluemaster_smoker) = BlueMaster &
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pet(cat_keeper) = Cat &
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pet(neighbour_dunhill_smoker) = Horse &
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{ 2. The English man lives in the red house: }
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houseColour(Englishman) = Red &
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{ 3. The Swede has a dog: }
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pet(Swede) = Dog &
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{ 4. The Dane drinks tea: }
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drink(Dane) = Tea &
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{ 'smoke' and 'drink' are both nouns, like the other variables.
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One could read the formulas like: 'the colour of the Englishman's house is Red' ->
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'the Swede's pet is a dog' -> 'the Dane's drink is tea'.
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}
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{ 5. The green house is immediately to the left of the white house: }
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{ The local predicate 'LeftOf' determines the order: }
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LeftOf(green_house, white_house, order) &
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{ 6. They drink coffee in the green house: }
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drink(green_house) = Coffee &
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{ 7. The man who smokes Pall Mall has birds: }
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pet(pallmall_smoker) = Bird &
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{ 8. In the yellow house they smoke Dunhill: }
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smoke(yellow_house) = Dunhill &
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{ 9. In the middle house they drink milk: }
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drink(order(Third)) = Milk &
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{10. The Norwegian lives in the first house: }
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order(First) = Norwegian &
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{11. The man who smokes Blend lives in the house next to the house with cats: }
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{ Another local predicate 'Neighbour' makes them neighbours:}
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Neighbour(blend_smoker, cat_keeper, order) &
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{12. In a house next to the house where they have a horse, they smoke Dunhill: }
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Neighbour(dunhill_smoker, neighbour_dunhill_smoker, order) &
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{13. The man who smokes Blue Master drinks beer: }
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drink(bluemaster_smoker) = Beer &
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{14. The German smokes Prince: }
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smoke(German) = Prince &
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{15. The Norwegian lives next to the blue house: }
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{10. The Norwegian lives in the first house,
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so the blue house is the second house }
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houseColour(order(Second)) = Blue &
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{16. They drink water in a house next to the house where they smoke Blend: }
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drink(neighbour_blend_smoker) = Water &
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Neighbour(blend_smoker, neighbour_blend_smoker, order)
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{ A simplified solution would number the houses 1, 2, 3, 4, 5
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which makes it easier to order the houses.
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'right in the center' would become 3; 'in the first house', 1
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But we stick to the original puzzle and use some local predicates.
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}
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local pred Neighbour(neighbour1::Nationality, neighbour2::Nationality, order::Order)iff
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neighbour1 <> neighbour2 &
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order(house1) = neighbour1 &
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order(house2) = neighbour2 &
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( house1 = house2 + 1 |
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house1 = house2 - 1 )
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local pred LeftOf(neighbour1::Nationality, neighbour2::Nationality, order::Order) iff
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neighbour1 <> neighbour2 &
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order(house1) = neighbour1 &
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order(house2) = neighbour2 &
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house1 = house2 - 1
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{
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The 'all'-query in FormulaOne:
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all Zebra(houseColour, pet, smokes, drinks, order)
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gives, of course, only one solution, so it can be replaced by:
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one Zebra(houseColour, pet, smokes, drinks, order)
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}
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// The compacted version:
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Nationality = Englishman | Swede | Dane | Norwegian | German
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Colour = Red | Green | Yellow | Blue | White
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Cigarette = PallMall | Dunhill | BlueMaster | Blend | Prince
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Domestic = Dog | Bird | Cat | Zebra | Horse
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Beverage = Tea | Coffee | Milk | Beer | Water
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HouseOrder = First | Second | Third | Fourth | Fifth
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Pet = Nationality->>Domestic
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Drink = Nationality->>Beverage
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HouseColour = Nationality->>Colour
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Smoke = Nationality->>Cigarette
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Order = HouseOrder->>Nationality
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pred Zebra(houseColour::HouseColour, pet::Pet, smoke::Smoke, drink::Drink, order::Order) iff
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houseColour(green_house) = Green &
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houseColour(white_house) = White &
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houseColour(yellow_house) = Yellow &
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smoke(pallmall_smoker) = PallMall &
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smoke(blend_smoker) = Blend &
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smoke(dunhill_smoker) = Dunhill &
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smoke(bluemaster_smoker) = BlueMaster &
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pet(cat_keeper) = Cat &
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pet(neighbour_dunhill_smoker) = Horse &
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houseColour(Englishman) = Red &
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pet(Swede) = Dog &
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drink(Dane) = Tea &
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LeftOf(green_house, white_house, order) &
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drink(green_house) = Coffee &
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pet(pallmall_smoker) = Bird &
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smoke(yellow_house) = Dunhill &
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drink(order(Third)) = Milk &
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order(First) = Norwegian &
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Neighbour(blend_smoker, cat_keeper, order) &
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Neighbour(dunhill_smoker, neighbour_dunhill_smoker, order) &
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drink(bluemaster_smoker) = Beer &
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smoke(German) = Prince &
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houseColour(order(Second)) = Blue &
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drink(neighbour_blend_smoker) = Water &
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Neighbour(blend_smoker, neighbour_blend_smoker, order)
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local pred Neighbour(neighbour1::Nationality, neighbour2::Nationality, order::Order)iff
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neighbour1 <> neighbour2 &
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order(house1) = neighbour1 & order(house2) = neighbour2 &
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( house1 = house2 + 1 | house1 = house2 - 1 )
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local pred LeftOf(neighbour1::Nationality, neighbour2::Nationality, order::Order) iff
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neighbour1 <> neighbour2 &
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order(house1) = neighbour1 & order(house2) = neighbour2 &
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house1 = house2 - 1
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