Pattern matching and unification

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Pattern matching and unification??????? -?????

• ??? ???
• ???? ????????
• ????? ??????

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• Men Are all alike.
• IN WHAT WAY.
• They're always bugging us about something or
  another.
• CAN YOU BE MORE SPECIFIC.
• Well, my boyfriend made me come here.
• YOUR BOYFRIEND MADE YOU COME HERE.
• He says I'm depressed much of the time.
• I AM SORRY TO HEAR YOU ARE DEPRESSED.
• It's true. I'm unhappy.
• DO YOU THINK COMING HERE WILL HELP YOU NOT TO
  BE UNHAPPY.
• I need some help, that much is certain.
• WHAT WOULD IT MEAN TO YOU IF YOU GOT SOME
  HELP.
• Perhaps I could learn to get along with my
  mother.
• TELL ME MORE ABOUT YOUR FAMILY.

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?? ?????

• ????? ?? ??? Joseph Weizenbaum 1966
• ????? ?? ???? ?? ???????? ???'?????.
• ????'?????? ?????? ????? ?-nondirective, ?????
  ?????-???? ??????? ?????? ?????? ?????? ??
  ????.
• ????? ?? ????????? ???? ????? pattern-matching
  (????? ??????) ??? ?????? ??????? ???? ????.
• http//www.cit.gu.edu.au/7Eterryd/subjects/intro.
  to.ai/lecture2slide3.html

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?? ??? ?? ?????

• Specification
• 1. Read input.
• 2. Find a pattern matching input.
• 3. Transform input into a response.
• 4. Print response.
• Back to 1

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Pattern matching

• Pattern
• (i need a X)
• Response
• (what would it mean to you if you got a X ?)
• Match symbols with same symbols and variables
  with any symbol.
• Generalization of equal
• (defun pat-match (pattern input)
• "Does pattern match input? Any variable can
  match anything."
• (if (variable-p pattern)
• t
• (if (or (atom pattern) (atom input))
• (eql pattern input)
• (and (pat-match (first pattern) (first
  input))
• (pat-match (rest pattern) (rest
  input))))))

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Representing variables

• use naming convention on symbols.
• Any symbol with name starting with '?'.
• (defun variable-p (x)
• "Is x a variable (a symbol beginning with
  '?')?"
• (and
• (symbolp x)
• (equal
• (char (symbol-name x) 0) \?)))

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Extracting information from the match

• Want to get out the bindings of variables when
  successful.
• How to represent bindings? difficult issue to
  optimize.
• Take advantage of the SUBLIS primitive.
• (sublis
• '((?X . vacation))
• '(what would it mean to you if you got a ?X
  ?))
• (WHAT WOULD IT MEAN TO YOU IF YOU GOT A VACATION
  ?)

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Pattern matching with variables

• (defun pat-match (pattern input)
• "Does pattern match input? BUGGY VERSION."
• (if (variable-p pattern)
• (list (cons pattern input))
• (if (or (atom pattern) (atom input))
• (eql pattern input)
• (append
• (pat-match (first pattern) (first input))
• (pat-match (rest pattern) (rest input))))))
• 4 bugs
• a. (eql pattern input) can return T and append
  will die.
• b. (eql pattern input) can return NIL meaning
  failure, and be
• interpreted as an empty binding
  (semi-predicate problem).
• c. We want the bindings of variables to agree
  (?X ?X) (1 2) fails.
• d. Inefficient to check first and rest when we
  know that first fails.

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Bindings Management

• Need to be more careful about bindings
• a. pass them as parameter to pat-match (pat-match
  pat input bindings)
• b. distinguish between failure and no-bindings.
• New abstraction
• (defconstant fail nil)
• (defconstant no-bindings '((t . t)))
• (defun get-binding (var bindings)
• "Find a (var . value) pair in a binding list."
• (assoc var bindings))
• (defun binding-val (binding)
• "Get the value part of a binding."
• (cdr binding))
• (defun lookup (var bindings)
• "Get the value part (for var) from a binding
  list."
• (binding-val (get-binding var bindings)))
• (defun extend-bindings (var val bindings)
• "Add a (var . value) pair to a binding list."

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A (first) correct version of pat-match with
binding management

• (defun pat-match (pattern input optional
  (bindings no-bindings))
• "Match pattern against input in the context of
  the bindings."
• (cond ((eq bindings fail) fail)
• ((variable-p pattern)
• (match-variable pattern input bindings))
• ((eql pattern input) bindings)
• ((and (consp pattern) (consp input))
• (pat-match (rest pattern) (rest input)
• (pat-match (first pattern)
  (first input) bindings)))
• (t fail)))

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• (defun match-variable (var input bindings)
• "Does VAR match input? Uses (or updates) and
  returns bindings."
• (let ((binding (get-binding var bindings)))
• (cond ((not binding)
• (extend-bindings var input bindings))
• ((equal input (binding-val
  binding))
• bindings)
• (t fail))))
• gt (pat-match '(i need a ?X) '(i need a vacation))
• ((?X . vacation) (t . t))

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Make extend-bindings smarter

• (defun extend-bindings (var val bindings)
• "Add a (var . val) pair to a binding list."
• (cons (var val)
• (if (eq bindings no-bindings) nil
  bindings)))
• gt (pat-match '(1 2 3) '(1 2 3))
• ((t . t))
• gt (pat-match '(?X is ?X) '((2 2) is 4))
• nil
• gt (pat-match '(?X is ?X) '((2 2) is (2 2)))
• ((?X 2 2))

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Segment pattern matching

• - Similar to kleene-star notation in regular
  expressions want to match
• any number of elements in a list.
• - Choose a syntax to write segment variables (?
  ?var)
• (defun segment-pattern-p (pattern)
• (and (consp pattern) (starts-with (first
  pattern) '?)))
• gt (pat-match '((? ?x) is (? ?p) ?) '(1 2 3
  is 5 2 ?))
• ((?x 1 2 3) (?p 5 2))
• (defun pat-match (pattern input optional
  (bindings no-bindings))
• "Match pattern against input in the context of
  the bindings."
• (cond ((eq bindings fail) fail)
• ((variable-p pattern)
• (match-variable pattern input bindings))
• ((eql pattern input) bindings)
• ((segment-pattern-p pattern)
  
• (segment-pattern-match pattern input
  bindings))
• ((and (consp pattern) (consp input))

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Segment Pattern Matching and backtracking

• How far should segment pattern match?
• Assume segment pattern is followed by a non
  variable C
• (pattern starts with ((? ?p) C p2...))
• Look for first occurrence of C in input index
  pos. (... C i2 ...)
• If not found, fail.
• Else match up to pos and check that (rest input)
  matches (rest pattern)
• b2 (pat-match (p2...) (r2 ...))
• If b2 succeeds -gt succeed and extend with binding
  ?p.
• Else? Maybe need to bind ?p to a longer segment.
• gt (pat-match '((? ?p) is a (? ?x)) '(what he is
  is a fool))
• ((?p what he is) (?x fool))

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• (defun segment-match (pattern input bindings
  optional (start 0))
• "Match segment pattern ((? var) . pat) against
  input."
• (let ((var (second (first pattern)))
• (pat (rest pattern)))
• (if (null pat)
• (match-variable var input bindings)
• assume pat starts with a constant
• (let ((pos (position (first pat) input
  start start test 'equal)))
• (if (null pos)fail
• (let ((b2 (pat-match pat (subseq input
  pos) bindings)))
• If this one failed, try a longer
  segment
• Else check that the variables
  match
• (if (eq b2 fail)
• (segment-match pattern input
  bindings
• ( pos 1))
• (match-variable var (subseq input 0
  pos) b2))))))))

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A bug in segment-match!

• gt (pat-match
• '((? ?x) a b (? ?x))
• '(1 2 a b a b 1 2 a b)) --gt NIL!
• (defun segment-match (pattern input bindings
  optional (start 0))
• "Match segment pattern ((? var) . pat) against
  input."
• (let ((var (second (first pattern)))
• (pat (rest pattern)))
• (if (null pat)
• (match-variable var input bindings)
• assume pat starts with a constant
• (let ((pos (position (first pat) input
  start start test 'equal)))
• (if (null pos)
• fail
• (let ((b2 (pat-match pat (subseq input
  pos)
• (match-variable
  var (subseq input 0 pos)
• 
  bindings))))
• If this one failed, try a longer
  segment
• (if (eq b2 fail)

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ELIZA A Rule-based translator

• (defun rule-pattern (rule) (first rule))
• (defun rule-responses (rule) (rest rule))
• Rule example
• ((? ?x) I want (? ?y))
• (What would it mean if you got ?y)
• (Why do you want ?y)
• (Suppose you got ?y soon))
• If pattern matches, select one of the answers
  randomly.

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How to handle a set of rules?

• Several rules match, what to do?
• - Option 1 accept the first matching rule.
• - Option 2 choose one rule randomly among the
  matching rules.
• - Option 3 combine the responses from several
  matching rules.
• Use option 1.

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• (defparameter eliza-rules
• '((((? ?x) hello (? ?y))
• (How do you do. Please state you problem.))
• (((? ?x) I want (? ?y))
• (What would it mean if you got ?y)
• (Why do you want ?y)
• (Suppose you got ?y soon))
• (((? ?x) if (? ?y))
• (Do you really think it is likely that ?y)
• (Do you wish that ?y)
• (What do you think about ?y)
• (Really -- if ?y))))

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A rule-based interpreter

• (defun eliza ()
• "Respond to user input using pattern matching
  rules."
• (loop
• (print 'elizagt)
• (write (flatten (use-eliza-rules (read)))
  pretty t)))
• (defun use-eliza-rules (input)
• "Find some rul with which to transform the
  input."
• (some '(lambda (rule)
• (let ((result (pat-match
  (rule-pattern rule) input)))
• (if (not (eq result fail))
• (sublis (switch-viewpoint result)
• (random-elt
  (rule-responses rule))))))
• eliza-rules))

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• (defun switch-viewpoint (words)
• "Change I to you and vice-versa, and so on."
• (sublis '((I . you) (you . I) (me . you) (am .
  are)) words))
• aux functions
• (defun flatten (the-list)
• "Append together elements or lists in the-list"
• (mappend 'mklist the-list))
• (defun mklist (x)
• "Return x if it is a list, otherwise (x)"
• (if (listp x) x (list x)))
• (defun random-elt (choices)
• (elt choices (random (length choices))))

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• What Eliza Can't Do
• In a word anything. 
• ELIZA defines the major areas of AI in terms of
  what she can't do and doesn't know.
• She doesn't know anything Knowledge
  Representation (KR) She can't reason  Reasoning
  She can't plan Planning She can't learn
  Machine Learning She doesn't understand natural
  language Natural Language Processing (NLP)