[isabelle-dev] Partial functions

[Roger H.]

Hallo,


i want to create a datatype that allows me to write functions from a nat subset to another nat subset.
for example i wanna be able to write: 


definition f: {1,2,3} => {4,5} 
                     1 -->4,  2-->4, 3-->5


or another one:     


definition g : {6,8} => {2,3,4}
                     


So the thing i want to somehow parametrize is  "which subset of the nat im using each time as domain and range" ,


I thought about creating a new datatype :    'a nat 
The problem with this is that 'a  is instantiated with datatypes, and not sets like {1,2,3}.


Following solutions are bad:


1.  Everytime i want declare a new function, i have to declare by "typedef" the nat subsets i want as domain and range




2.  definition f :  "nat => nat" where
       "f x = (if x : {1,2,3} then ....  else undefined)


This second approach is bad, cause i dont want the domain to be decided as late as the second line of the declaration, cause after this i want to be able to program a selector "domain f"
that returns me the domain of f, thats why i want the domain of f to be somehow incapsulated (parametrized) in the first line "f: nat =>nat " so that i can use it later.
            


What would you do in this situation?       


Many thanks!




 		 	   		   		 	   		  
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