Uninterpreted function
An uninterpreted function[1] is one that has no other property than its name and arity. They are often used together with equality in formal reasoning, especially using computers.
Example
An array can be specified the following axiom:
- select(store(a,i,v),j)=(if i=j then v else select(a,j))
This axiom can be used to deduce
- select(store(store(a,1,-1),2,-2),1)
- = select(store(a,1,-1))
- = -1
Note that this reasoning did not use any 'definition' for the functions select and store. All that is known is the axiom.
References
- ^ Bryant, Lahiri, Seshia (2002) "Modeling and verifying systems using a logic of counter arithmetic with lambda expressions and uninterpreted functions". Computer Aided Verification 2404/2002, 106–122.