Unification algorithm

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

SG
CONTENT
NULL
NUMBER
POINTER
PERSON
CONTENT
3
POINTER
NULL
NULL
4
Example 2

• The DAG representation for a simple feature
  structure Number SG

SG
CONTENT
NULL
NUMBER
POINTER
NULL
5
Example 3

• The DAG representation for a simple feature
  structure Person 3

3
CONTENT
NULL
PERSON
POINTER
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

SG
CONTENT
NULL
NUMBER
POINTER
f1
NULL
CONTENT
3
PERSON
POINTER
NULL
f2
NULL
8
Example 4, part 2

• Number SG ? Person 3 (note sharing!)

SG
CONTENT
NULL
NUMBER
POINTER
CONTENT
POINTER
NULL
CONTENT
3
PERSON
POINTER
POINTER
NULL
CONTENT
9
Example 4, part 3

• Number SG ? Person 3 (note sharing!)

SG
CONTENT
NULL
NUMBER
POINTER
CONTENT
PERSON
CONTENT
NULL
POINTER
POINTER
NULL
CONTENT
3
PERSON
POINTER
POINTER
NULL
CONTENT
10
Another example?

• We can work through example on page 424 of text
  if youd like.