function 2: transform

transform:
    description:
        transform(sp1, sp2) input-sp
        transform the ingredients in sp1 into those in sp2, providing there are enough ingredients in the input superposition
        eg, process a chemical reaction, or a nuclear reaction, or a trade, etc
        if there are not enough ingredients in input-sp then return it unchanged

    examples:
        -- the first example is make water from hydrogen and oxygen gas:
        make-water (*) #=> transform( 2|H2> + |O2>, 2|H2O> ) |__self>

        -- first try to make water with just hydrogen gas:
        -- and we see the reaction did not proceed:
        make-water 10|H2>
            10|H2>

        -- now try to make 40 molecules of water from 10 molecules of hydrogen gas and 10 of oxygen gas:
        -- and we see we only have enough ingredients to successfully apply the make-water operator 5 times:
        -- ie, 10 molecules of water
        make-water^20 (10|H2> + 10|O2>)
            0|H2> + 5|O2> + 10|H2O>


        -- the next example is going shopping, ie a trade of cash for goods:
        -- first define the shopping list:
        the |shopping list> => 5|apple> + 7|orange> + |milk> + |steak> + |coffee> + |bread>

        -- now define their prices:
        -- note that if an item on your shopping list does not have a defined price, you get it for free
        -- though we can change that behaviour by defining a general rule:
        -- price |*> => |item not for sale>
        -- then if any items do not have a specific price, the shopping will fail
        -- because |item not for sale> is not in the input superposition for the transform operator
        price |apple> => 0.4|dollar>
        price |orange> => 0.6|dollar>
        price |milk> => 2|dollar>
        price |steak> => 9|dollar>
        price |coffee> => 4.5|dollar>
        price |bread> => 2.6|dollar>

        -- now let's define the buy-shopping operator:
        buy-shopping (*) #=> transform(price the |shopping list>, the |shopping list>) |__self>

        -- now let's try to buy our shopping starting with 10 dollars:
        -- and the trade/purchase fails because we don't have enough money:
        buy-shopping 10|dollar>
            10|dollar>

        -- now try again, but this time with 100 dollars:
        buy-shopping 100|dollar>
            75.700000|dollar> + 5|apple> + 7|orange> + |milk> + |steak> + |coffee> + |bread>

        -- of course, we could have saved ourselves trouble, by calculating the cost of our shopping list
        -- before trying to buy it with only 10 dollars:
        price the |shopping list>
            24.300000|dollar>


        -- now let's consider the toy example of fissioning U235:
        -- first, learn some of the possible reactions:
        -- NB: a realistic example would include |MeV> too
        fission-channel-1 |U: 235> => |Ba: 141> + |Kr: 92> + 3|n>
        fission-channel-2 |U: 235> => |Xe: 140> + |Sr: 94> + 2|n>
        fission-channel-3 |U: 235> => |La: 143> + |Br: 90> + 3|n>
        fission-channel-4 |U: 235> => |Cs: 137> + |Rb: 96> + 3|n>
        fission-channel-5 |U: 235> => |I: 131> + |Y: 89> + 16|n>

        -- now learn their operators:
        -- NB: a realistic example would also include their respective probabilities, as coefficients of each of the channels
        list-of-fission-channels |U: 235> => |op: fission-channel-1> + |op: fission-channel-2> + |op: fission-channel-3> + |op: fission-channel-4> + |op: fission-channel-5>

        -- now define a single fission event operator:
        fission |*> #=> apply(weighted-pick-elt list-of-fission-channels |_self>, |_self>)

        -- now let's try out our new fission operator a couple of times:
        fission |U: 235>
            |La: 143> + |Br: 90> + 3|n>

        fission |U: 235>
            |Ba: 141> + |Kr: 92> + 3|n>

        fission |U: 235>
            |Xe: 140> + |Sr: 94> + 2|n>

        -- now, let's define an operator that transforms one neutron and one U235 into fission decay products:
        fission-uranium-235 (*) #=> transform(|n> + |U: 235>, fission |U: 235>) |__self>

        -- let's apply it once to one neutron and 10 U235 atoms:
        fission-uranium-235 (|n> + 10|U: 235>)
            2|n> + 9|U: 235> + |Xe: 140> + |Sr: 94>

        -- let's apply it 50 times to one neutron and 100 U235 atoms:
        fission-uranium-235^50 (|n> + 100|U: 235>)
            173|n> + 50|U: 235> + 10|Cs: 137> + 10|Rb: 96> + 12|La: 143> + 12|Br: 90> + 10|Ba: 141> + 10|Kr: 92> + 7|Xe: 140> + 7|Sr: 94> + 7|I: 131> + 7|Y: 89>


        -- finally, let's define some operators to change a person's state:
        -- open-can, eat-food, go-to-sleep:
        open-can (*) #=> drop transform(|closed can>, |open can>) |__self>
        eat-food (*) #=> drop transform(|open can> + |hungry>, |empty can> + |not hungry>) |__self>
        go-to-sleep (*) #=> drop transform(|tired>, |asleep>) |__self>

        -- now define my current state:
        current-state |me> => |closed can> + |hungry> + |tired>

        -- now let's use them step by step:
        open-can current-state |me>
            |hungry> + |tired> + |open can>

        eat-food open-can current-state |me>
            |tired> + |empty can> + |not hungry>

        go-to-sleep eat-food open-can current-state |me>
            |empty can> + |not hungry> + |asleep>

        -- note that you can't successfully eat-food before you open-can:
        eat-food current-state |me>
            |closed can> + |hungry> + |tired>

    see also: