Section6.18

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## 6.18 Example: A Database

This example shows how you can use Axiom to organize a database of lineage data and then query the database for relationships.

The database is entered as ``assertions'' that are really pieces of a function definition.

children("albert") == ["albertJr","richard","diane"]
Type: Void

Each piece children(x)==y means ``the children of x are y''.

children("richard") == ["douglas","daniel","susan"]
Type: Void

This family tree thus spans four generations.

children("douglas") == ["dougie","valerie"]
Type: Void

Say ``no one else has children.''

children(x) == []
Type: Void

We need some functions for computing lineage. Start with childOf.

childOf(x,y) == member?(x,children(y))
Type: Void

To find the parentOf someone, you have to scan the database of people applying children.

parentOf(x) ==
for y in people repeat
(if childOf(x,y) then return y)
"unknown"
Type: Void

And a grandparent of x is just a parent of a parent of x.

grandParentOf(x) == parentOf parentOf x
Type: Void

The grandchildren of x are the people y such that x is a grandparent of y.

grandchildren(x) == [y for y in people | grandParentOf(y) = x]
Type: Void

Suppose you want to make a list of all great-grandparents. Well, a great-grandparent is a grandparent of a person who has children.

greatGrandParents == [x for x in people |
reduce(_or,
[not empty? children(y) for y in grandchildren(x)],false)]
Type: Void

Define descendants to include the parent as well.

descendants(x) ==
kids := children(x)
null kids => [x]
concat(x,reduce(concat,[descendants(y)
for y in kids],[]))
Type: Void

Finally, we need a list of people. Since all people are descendants of ``albert'', let's say so.

people == descendants "albert"
Type: Void

We have used ``=='' to define the database and some functions to query the database. But no computation is done until we ask for some information. Then, once and for all, the functions are analyzed and compiled to machine code for run-time efficiency. Notice that no types are given anywhere in this example. They are not needed.

Who are the grandchildren of ``richard''?

grandchildren "richard"
Compiling function children with type String -> List String
Compiling function descendants with type String -> List String
Compiling body of rule people to compute value of type List String
Compiling function childOf with type (String,String) -> Boolean
Compiling function parentOf with type String -> String
Compiling function grandParentOf with type String -> String
Compiling function grandchildren with type String -> List String

["dougie","valerie"]

Type: List String

Who are the great-grandparents?

greatGrandParents
Compiling body of rule greatGrandParents to compute value of
type List String

["albert"]

Type: List String
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