3.Ancestor relation

1
3.Ancestor relation
2
3. Predicate proof in CafeOBJ
3
Family Tree
4
Skolem Functions

• A Skolem function f is used to construct a new
  value that depends on the universally quantified
  variable. For example
• (?x)(?y)loves(x,y)
• Becomes
• (?x)loves(x,f(x))
• In this case, f(x) specifies the person that x
  loves
• In general

5
Using Skolem constant to remove ?

• The existential quantifier (?) says that some
  object exists. When we remove the existential
  quantifier we are giving the object a name. It
  is safe to move from ?X dog(x) to
  dog(aSkolemDog) .

6
No Skolem Function in CafeOBJ

• In the example below we can have variables on
  the RHS that do not appear on the LHS. This is
  not the case with ordinary reduction (red
  command).
• ceq e1 sister(X,Y) true
• if female(X) and
• parent(Z,X) and
• parent(Z,Y) .

7
Skolem Function in CafeOBJ

• If we want to use reduction the we cannot have a
  variable on the RHS that does not appear on the
  LHS. Compare this slide with the previous one.
• ceq e1 sister(X,Y) true
• if female(X) and
• parent(parentOf(Y),X) and parent(parentOf(Y),Y) .

8
Recursion
9
Recursion