I need to define a recursive ML function composition that accepts two relations and returns the composition of the two relations. I need to use the thhisIsTheImageOf and createRelationFromImage function in my definition of composition.
Here is the code that is needed to be used to define the composition
fun thisIsTheImageOf(e,[])=[] |thisIsTheImageOf(e,(a,b)::xs) = if e=a then b::thisIsTheImageOf(e,xs) else thisIsTheImageOf(e,xs);
Here are the datatype, value, and tested inputs for the thisIsTheImageOf function
datatype city =Vancouver|LosAngeles|Mexico|Minneapolis|Omaha |KansasCity|Denver|StLouis|Memphis|Chicago |NewOrleans|Cinncinati|Pittsburgh|Montreal|NewYork; datatype rivers =Missouri|Platte|NPlatte|SPlatte|Arkansas|Canadian |Kansas|Mississippi|Tennessee|Ohio|Allegheny|Monongahela; val isOnRiver=[(Denver,Platte),(Omaha,Missouri),(Omaha,Platte),(KansasCity,Missouri),(KansasCity,Kansas),(Minneapolis,Mississippi),(StLouis,Mississippi),(StLouis,Mi vssouri),(Memphis,Mississippi),(NewOrleans,Mississippi),(Cinncinati,Ohio),(Pittsburgh,Ohio),(Pittsburgh,Allegheny),(Pittsburgh,Monongahela)]; val flowsInto=[(Platte,Missouri),(Kansas,Missouri),(Missouri,Mississippi),(Allegheny,Ohio),(Monongahela,Ohio),(Tennessee,Ohio),(NPlatte,Platte),(SPlatte,Platte),(Ohio,Mississippi)]; thisIsTheImageOf(Pittsburgh, isOnRiver);thisIsTheImageOf(Mississippi, flowsInto);thisIsTheImageOf(Cinncinati, isOnRiver); fun createRelationFromImage(e,[])=[] createRelationFromImage(e,x::xs)= (e,x)::createRelationFromImage(e,xs);`` Here are tested inputs for the createRelationFromImage function
createRelationFromImage("Cincinnati",["New York", "Boston", "Dallas"]);
These two functions were created as a separate function but I am supposed to use the two functions to make a recursive function of composition.
I know the composition function mathematically and here is what I put as to help me see what I need to do
fun composition( i, r)x=i(r(x));
however, I am stuck on going further when trying to implement the two functions.
fun composition([],_ )=[]
| composition((a,b)::rest,relation)=
let
fun thisIsTheImageOf(e,[])=[]
|thisIsTheImageOf(e,(a,b)::xs) =
if e=a
then b::thisIsTheImageOf(e,xs)
else thisIsTheImageOf(e,xs);
fun createRelationFromImage(e,[])=[]
| createRelationFromImage(e,x::xs)= (e,x)::createRelationFromImage(e,xs);
in
createRelationFromImage(a, (thisIsTheImageOf(b, relation)))@ composition(rest, relation)
end;