1. Unification algorithm We have seen examples of the use of unification. Now we will see, in detail, one way to implement a unification algorithm which implements structure sharing

2. A data structure to support unification We need a special data structure to allow structure sharing during unification: – each feature structure is represented using two components, a content component and a pointer component. – the representation forms a Directed Acyclic Graph (DAG)

3. Example 1 The DAG representation for a simple feature structure: [Number SG, Person 3] Expand first to: [Content[Number[Content SG, Pointer NULL], Person[Content 3, Pointer NULL]], Pointer NULL] CONTENT POINTER NUMBER PERSON CONTENT POINTER CONTENT POINTER SG NULL 3

4. Example 2 The DAG representation for a simple feature structure: [Number SG] CONTENT POINTER NUMBER CONTENT POINTER SG NULL

5. Example 3 The DAG representation for a simple feature structure: [Person 3] CONTENT POINTER PERSON CONTENT POINTER 3 NULL

6. Algorithm (pg. 423 of text) function Unify(f1, f2) returns fs or failure f1.real  real contents of f1, *(f1.ptr) if ptr != null f2.real  real contents of f2, *(f2.ptr) if ptr != null if (f1.real is null) { f1.ptr  f2; return f2 } else if (f2.real is null) { f2.ptr  f1; return f1 } else if (f1.real == f2.real) {f1.ptr  f2; return f2 } else if (f1.real is complex and f2.real is complex) { f2.ptr  f1 foreach ftr2 in f2.real { ftr1  find/create feature ftr2 in f1.real if Unify(ftr2.value,ftr1.value) fails {return failure} return f1 else return failure

7. Example 4, initial state [Number SG]  [Person 3] CONTENT POINTER NUMBER CONTENT POINTER SG NULL CONTENT POINTER PERSON NULL CONTENT POINTER 3 NULL f2: f1:

8. Example 4, part 2 [Number SG]  [Person 3] (note sharing!) CONTENT POINTER NUMBER CONTENT POINTER SG NULL CONTENT POINTER PERSON CONTENT POINTER 3 NULL

9. Example 4, part 3 [Number SG]  [Person 3] (note sharing!) CONTENT POINTER NUMBER CONTENT POINTER SG NULL CONTENT PERSON CONTENT POINTER 3 NULL PERSON CONTENT POINTER NULL POINTER

10. Another example? We can work through example on page 424 of text if you’d like.