Javascript recursiveness

Question

Save, I started reading the book "Javascript Eloquent" and in the chapter on higher order functions I came across the following example of a code that calculates the genes that an individual inherited from the family:

var ANCESTRY_FILE = JSON.stringify([
    {"name": "Carolus Haverbeke", "sex": "m", "born": 1832, "died": 1905, "father": "Carel Haverbeke", "mother": "Maria van Brussel"},
    {"name": "Emma de Milliano", "sex": "f", "born": 1876, "died": 1956, "father": "Petrus de Milliano", "mother": "Sophia van Damme"},
    {"name": "Maria de Rycke", "sex": "f", "born": 1683, "died": 1724, "father": "Frederik de Rycke", "mother": "Laurentia van Vlaenderen"},
    {"name": "Jan van Brussel", "sex": "m", "born": 1714, "died": 1748, "father": "Jacobus van Brussel", "mother": "Joanna van Rooten"},
    {"name": "Philibert Haverbeke", "sex": "m", "born": 1907, "died": 1997, "father": "Emile Haverbeke", "mother": "Emma de Milliano"},
    {"name": "Jan Frans van Brussel", "sex": "m", "born": 1761, "died": 1833, "father": "Jacobus Bernardus van Brussel", "mother":null},
    {"name": "Pauwels van Haverbeke", "sex": "m", "born": 1535, "died": 1582, "father": "N. van Haverbeke", "mother":null},
    {"name": "Clara Aernoudts", "sex": "f", "born": 1918, "died": 2012, "father": "Henry Aernoudts", "mother": "Sidonie Coene"},
    {"name": "Emile Haverbeke", "sex": "m", "born": 1877, "died": 1968, "father": "Carolus Haverbeke", "mother": "Maria Sturm"},
    {"name": "Lieven de Causmaecker", "sex": "m", "born": 1696, "died": 1724, "father": "Carel de Causmaecker", "mother": "Joanna Claes"},
    {"name": "Pieter Haverbeke", "sex": "m", "born": 1602, "died": 1642, "father": "Lieven van Haverbeke", "mother":null},
    {"name": "Livina Haverbeke", "sex": "f", "born": 1692, "died": 1743, "father": "Daniel Haverbeke", "mother": "Joanna de Pape"},
    {"name": "Pieter Bernard Haverbeke", "sex": "m", "born": 1695, "died": 1762, "father": "Willem Haverbeke", "mother": "Petronella Wauters"},
    {"name": "Lieven van Haverbeke", "sex": "m", "born": 1570, "died": 1636, "father": "Pauwels van Haverbeke", "mother": "Lievijne Jans"},
    {"name": "Joanna de Causmaecker", "sex": "f", "born": 1762, "died": 1807, "father": "Bernardus de Causmaecker", "mother":null},
    {"name": "Willem Haverbeke", "sex": "m", "born": 1668, "died": 1731, "father": "Lieven Haverbeke", "mother": "Elisabeth Hercke"},
    {"name": "Pieter Antone Haverbeke", "sex": "m", "born": 1753, "died": 1798, "father": "Jan Francies Haverbeke", "mother": "Petronella de Decker"},
    {"name": "Maria van Brussel", "sex": "f", "born": 1801, "died": 1834, "father": "Jan Frans van Brussel", "mother": "Joanna de Causmaecker"},
    {"name": "Angela Haverbeke", "sex": "f", "born": 1728, "died": 1734, "father": "Pieter Bernard Haverbeke", "mother": "Livina de Vrieze"},
    {"name": "Elisabeth Haverbeke", "sex": "f", "born": 1711, "died": 1754, "father": "Jan Haverbeke", "mother": "Maria de Rycke"},
    {"name": "Lievijne Jans", "sex": "f", "born": 1542, "died": 1582, "father":null, "mother":null},
    {"name": "Bernardus de Causmaecker", "sex": "m", "born": 1721, "died": 1789, "father": "Lieven de Causmaecker", "mother": "Livina Haverbeke"},
    {"name": "Jacoba Lammens", "sex": "f", "born": 1699, "died": 1740, "father": "Lieven Lammens", "mother": "Livina de Vrieze"},
    {"name": "Pieter de Decker", "sex": "m", "born": 1705, "died": 1780, "father": "Joos de Decker", "mother": "Petronella van de Steene"},
    {"name": "Joanna de Pape", "sex": "f", "born": 1654, "died": 1723, "father": "Vincent de Pape", "mother": "Petronella Wauters"},
    {"name": "Daniel Haverbeke", "sex": "m", "born": 1652, "died": 1723, "father": "Lieven Haverbeke", "mother": "Elisabeth Hercke"},
    {"name": "Lieven Haverbeke", "sex": "m", "born": 1631, "died": 1676, "father": "Pieter Haverbeke", "mother": "Anna van Hecke"},
    {"name": "Martina de Pape", "sex": "f", "born": 1666, "died": 1727, "father": "Vincent de Pape", "mother": "Petronella Wauters"},
    {"name": "Jan Francies Haverbeke", "sex": "m", "born": 1725, "died": 1779, "father": "Pieter Bernard Haverbeke", "mother": "Livina de Vrieze"},
    {"name": "Maria Haverbeke", "sex": "m", "born": 1905, "died": 1997, "father": "Emile Haverbeke", "mother": "Emma de Milliano"},
    {"name": "Petronella de Decker", "sex": "f", "born": 1731, "died": 1781, "father": "Pieter de Decker", "mother": "Livina Haverbeke"},
    {"name": "Livina Sierens", "sex": "f", "born": 1761, "died": 1826, "father": "Jan Sierens", "mother": "Maria van Waes"},
    {"name": "Laurentia Haverbeke", "sex": "f", "born": 1710, "died": 1786, "father": "Jan Haverbeke", "mother": "Maria de Rycke"},
    {"name": "Carel Haverbeke", "sex": "m", "born": 1796, "died": 1837, "father": "Pieter Antone Haverbeke", "mother": "Livina Sierens"},
    {"name": "Elisabeth Hercke", "sex": "f", "born": 1632, "died": 1674, "father": "Willem Hercke", "mother": "Margriet de Brabander"},
    {"name": "Jan Haverbeke", "sex": "m", "born": 1671, "died": 1731, "father": "Lieven Haverbeke", "mother": "Elisabeth Hercke"},
    {"name": "Anna van Hecke", "sex": "f", "born": 1607, "died": 1670, "father": "Paschasius van Hecke", "mother": "Martijntken Beelaert"},
    {"name": "Maria Sturm", "sex": "f", "born": 1835, "died": 1917, "father": "Charles Sturm", "mother": "Seraphina Spelier"},
    {"name": "Jacobus Bernardus van Brussel", "sex": "m", "born": 1736, "died": 1809, "father": "Jan van Brussel", "mother": "Elisabeth Haverbeke"}
])

var ancestry = JSON.parse(ANCESTRY_FILE);

var byName = {};

ancestry.forEach(function(person){
    byName[person.name] = person;
});

function reduceAncestors(person, f, defaultValue){
    function valueFor(person){
        if(person == null){
            return defaultValue;
        } else {
            return f(person, valueFor(byName[person.mother]), valueFor(byName[person.father]))
        }
    }
    return valueFor(person);
}

function sharedDNA(person, fromFather, fromMother){
    if(person.name == "Pauwels van Haverbeke")
        return 1
    else
        return (fromFather + fromMother) / 2
}

var ph = byName["Philibert Haverbeke"];
console.log(reduceAncestors(ph, sharedDNA, 0) / 4);

If you look at the "valueFor" function, it is a recursive function that returns to the "f" function that references "sharedDNA". The question is those two variables of the function "sharedDNA" to "fromFather" and "fromMother" these two variables appear within the function with values like 1, 0.5, 0.125

fromFather = 0.5
fromMother = 0

But the "f" function returns a parent object and not a decimal number

return f(person, valueFor(byName[person.mother]), valueFor(byName[person.father]))

I don’t understand how "sharedDNA" gets those decimal numbers. If anyone understood and can help I really appreciate.

Answer 1

"f" returns a parent or mother object

No, the father and mother’s objects are passed as arguments for valueFor, whose results are passed as arguments to f. Note the parentheses (I put some extra spaces to facilitate the visualization):

return f ( person, valueFor(byName[person.mother]), valueFor(byName[person.father]) )
         ^    ^    ^                                ^                               ^
         |    |    |                                |                               |__ parênteses que encerra a lista de argumentos de f
         |    |    |                                |
         |    |    |                                |__ terceiro argumento de f
         |    |    |
         |    |    |__ segundo argumento de f
         |    |
         |    |__ primeiro argumento de f
         |
         |__ parênteses que inicia a lista de argumentos de f

That is to say, f takes 3 arguments: the person, the outworking of valueFor(byName[person.mother]) (which is a number) and the outworking of valueFor(byName[person.father]) (which is another number). Objects referring to the father and mother are passed to valueFor, not to f. What f receives is the outworking of valueFor.

And valueFor will always return a number, as there comes a time when a person no longer has a parent registered in the array (then person.mother and person.father will be null) and it will return zero (which is the defaultValue that we indicate when calling reduceAncestors). And when he has a father and a mother, he returns the value of f, passing the result of valueFor of their parents (and to calculate the values of father and mother, he calls recursively in their ancestors). That is, in the end valueFor always returns a number.