Comp 200 Lecture 11
Family Trees

Fri 08 Feb 2002

Family Trees

(perhaps better called "ancestor trees").
Draw some examples:

?     ?     ?   ?  ?      ?
 \   /       \ /    \    /
'jackie      'mona  'abraham
 (1926)  ?   (1929) (1920)
    \   /       \   /
   'marge      'homer
    (1956)      (1955)
        \      /
         'bart
         (1979)

Note: We don't know the name of Grampa Bouvier, marge's father, but he died in a roller-coaster accident.) (Birthdates fabricated, but names courtesy of springfield nuclear power plant's web site.) We know Abe was an enlisted man in WWII: his squad, the flying hellfish, found a a cache of stolen paintings, and they formed a tontine ("an investment plan in which participants buy shares in a common fund and recevie an annuity, with the entire fund going to the final survivor or to those who survive after a specified time. [Fr., after Lorenzo Tonti (1635-90?), Naples-born French banker]. Source: American Heritage College Dictionary)
Some simpler family trees:

?      ?
 \    /
 'jackie
  (1926)

and

?     ?
 \   /
'jackie   
 (1926)  ?
    \   /
   'marge
   (1958)

What might be considered the simplest possible family tree?

Definition: a FamTree is

(make-unknown), or
(make-child symbol FamTree FamTree number), where the symbol represents a name, the first FamTree is the mother's family tree, the second FamTree is the father's side, and the number is the birthyear.

Note: Be sure to differentiate the two different concepts: "child", which is somebody whose name we know, vs "FamTree", which might be a child or an unknown. We used ? above to denote unknown.

Examples:

(define stone-age -2000000) ;; negative years are BCE (BC)

(make-child 'barney (make-unknown) (make-unknown) (+ stone-age 120))

(make-child 'bam-bam  
            (make-child 'barney (make-unknown) (make-unknown) (+ stone-age 120))
            (make-child 'betty  (make-unknown) (make-unknown) (+ stone-age 125))
            (+ stone-age 150))

(make-unknown)

?     ?     ?   ?    ?     ?
 \   /       \ /      \   /
'jackie      'mona  'abraham
 (1926)  ?   (1929) (1903)
    \   /       \   /
   'marge      'homer
    (1958)      (1959)
        \      /
         'bart
         (1983)

(make-child 'bart 
            (make-child 'marge 
                        (make-child 'jackie (make-unknown) (make-unknown) 1926)
                        (make-unknown)
                        1958)
            (make-child 'homer 
                        (make-child 'abraham (make-unknown) (make-unknown) 1903)
                        (make-child 'mona    (make-unknown) (make-unknown) 1929)
                        1959)
            1983)

Aside: In Computer Science, trees of this pattern are called binary trees. Can you guess why?

Looking for a parallel to lists:

purpose list functions tree functions (provided to you)

terminal values empty unknown

build one out of smaller parts cons: any, list --> list make-child: symbol, FamTree, FamTree, number --> child

select parts of a compound item

`first`	:	`cons`	`-->`	any
`rest`	:	`cons`	`-->`	list

`child-name`	:	`child`	`-->`	symbol
`child-ma`	:	`child`	`-->`	FamTree
`child-pa`	:	`child`	`-->`	FamTree
`child-birthyear`	:	`child`	`-->`	number

recognizers (predicate functions)

`list?`	:	any	`-->`	boolean
`empty?`	:	any	`-->`	boolean
`cons?`	:	any	`-->`	boolean

`FamTree?`	:	any	`-->`	boolean
`unknown?`	:	any	`-->`	boolean
`child?`	:	any	`-->`	boolean

We will define them. In the above table, I distinguish between structure values and the functions that create those structures. For instance, make-unknown and make-child describe the functions used to create an unknown structure and a child structure, respectively. In the data definition, we used make-X along with the structure parameters (variables), to talk about the structures themselves, not the functions that create them. This is a bit confusing to understand at first.

Currently, these functions aren't built-in to DrScheme. We will define them ourseleves. We represent FamTrees using structures.

#|
  We will define the following Family Tree functions: 
  make-child, child-name, child-ma, child-pa, child-birthyear,
  child?, unknown?, and FamTree? 
|#

;;remember, this structure definition will define the following functions:
;;  make-child, child-ma, child-pa, child-birthyear, child?
(define-struct child (name ma pa birthyear))

;;and this defines make-unknown and unknown?
(define-struct unknown ())

(define (FamTree? exp)
    (or (unkown? exp) (child? exp)))

Comp 200 Lecture 11 Family Trees

Fri 08 Feb 2002

Family Trees

Comp 200 Lecture 11
Family Trees