Programming Style and Technique

1
Programming Style and Technique

• Notes for Ch.8 of Bratko
• For CENG421553 Fall03

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Use
3
Use of Recursion maplist

• Recursion is always used. maplist is an example
  of a higher-order function a function that
  applies to another function
• In the original LISP (McCarthy, 1960)
• ((label maplist
• (lambda (x f)
• (cond ((null x) ( ))
• (t (cons (f (car x))
  (maplist (cdr x) f))))))
• maplist( List, F, NewList) if NewList contains
  the result of applying F to each element of List,
  in order
• The function F the binary relation representing
  the function we want to apply

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maplist II

• Boundary (base) case List
• if List then NewList
• General case List XTail
• To transform a list of the form XTail, do
• transform the item X by F, obtaining New X, and
• transform the list Tail obtaining NewTail
• the whole transformed list if NewXNewTail
• See ch8_1.pl
• Prolog ?recursion ?objects recursive

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• / maplist( List,F,NewList) if NewList contains
  the result of applying
• the function F (represented by a binary relation
  ltdomain,rangegt) to each
• entry of NewList, in order. /
• maplist( ,_,).
• maplist( XTail,F, NewXNewTail) -
• G .. F,X,NewX,
• G, some Prologs require call( G)
  instead of G
• maplist( Tail,F,NewTail).
• / Square function, for example query
• ?- maplist( 2,6,5,square,Squares) /
• square( X,Y) - Y is XX.

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Generalization

• Generalization allows us to use recursion
• Example eight queens
• without generalization, no integer to recur on!
• Define nqueens( Pos,N)
• if N queens are safe in position Pos
• Base case N 0 trivial
• General case N gt 0
• achieve a safe configuration of N-1 queens
• add the remaining queen so that it does attack
• eightqueens( Pos) - nqueens( Pos,8).

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Debugging

• Most Prolog interpreters and compilers use a
  four-port model for goals

foo/n
call
succeed
fail
retry
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Improving Efficiency

• Eight queens, again
• using a more informed initial ordering of queen
  coordinate values helps, as described in the
  comments at the end of ex4_6.pl
• Map coloring
• start with countries that have many neighbors
• Warnsdorffs heuristic for the knights tour

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• A solution template
• template( 1/Y1,2/Y2,3/Y3,4/Y4,5/Y5,6/Y6,7/Y7,8/Y8
  ).
• solution1(S) - template(S), solution(S).
• When computing all solutions, all orders are
  equivalent
• / Original Order member( Y,1,2,3,4,5,6,7,8)
• 4 ?- time(setof(S,solution1(S),L)), length(L,N).
• 171,051 inferences in 0.22 seconds (776387
  Lips) /
• / More informed order member(
  Y,1,3,5,7,2,4,6,1)
• 16 ?- time(setof(S,solution1(S),L)), length(L,N).
• 171,051 inferences in 0.22 seconds (776387
  Lips)
• /
• When computing one solution, the informed order
  is much better
• / More informed order member(
  Y,1,3,5,7,2,4,6,1)
• 18 ?- time(solution1(S)).
• 368 inferences in 0.00 seconds (Infinite Lips)
  /

• Ex 4.6B
• Figure 4.7 Program 1 for the eight queens
  problem.
• solution( BoardPosition) if
• BoardPosition is a list of non-attacking
  queens
• solution( ).
• solution( X/Y Others ) - First queen at
  X/Y, other queens at Others
• solution( Others),
• member( Y,1,2,3,4,5,6,7,8), Order of
  alternatives defined here!
• noattack( X/Y, Others). First queen
  does not attack others
• noattack( _, ). Nothing to
  attack
• noattack( X/Y, X1/Y1 Others ) -
• Y \ Y1, Different
  Y-coordinates
• Y1-Y \ X1-X, Different
  diagonals
• Y1-Y \ X-X1,

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• colors( ).
• colors( Country/ColorRest) -
• colors( Rest),
• member( Color,yellow,blue,red,green),
• not( (member( Country1/Color,Rest),neighbor(
  Country,Country1)) ).
• Note the extra parentheses, to make a
  single conjunctive goal of two
• neighbor( Country,Country1) -
• ngb( Country,Neighbors),
• member( Country1,Neighbors).
• makelist( List) -
• collect( germany,,List).
• collect( ,Closed,Closed). No more candidates
  for closed
• collect( XOpen,Closed,List) -
• member( X,Closed),!, If X has already
  been collected,
• collect( Open,Closed,List). discard it
• collect( XOpen,Closed,List) -

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• Neighbors for the 6 original EU countries
  (Treaty of Rome, 1957)
• Andorra, Monaco, San Marino, and Vatican City
  are not considered
• Only land (bridge and tunnel included) borders
  are considered
• / Reorder the ngb relation so that the country
  that has the largest amount of neighbour will be
  at the top. So start coloring from that, continue
  with its neighbours, then the neighbours of the
  neighbours etc.
• /
• ngb( germany, denmark,poland,czech,austria,switze
  rland,france,luxembourg,belgium,netherlands).
• ngb( netherlands, germany,belgium,france).
• ngb( belgium, netherlands,germany,luxembourg,fran
  ce).
• ngb( france, belgium,luxembourg,germany,switzerla
  nd,italy,spain).
• ngb( luxembourg, belgium,germany,france).
• ngb( italy, france,austria,slovenia).
• ngb( denmark, germany).
• ngb( poland, germany).
• ngb( czech, germany).
• ngb( austria, germany, italy).
• ngb( switzerland, germany,italy,france).
• ngb( spain, france).
• ngb( slovenia, italy).

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Difference Lists

• The difference list L-E contains the elements of
  L that occur before E. E is a suffix of L.
• E.g., a,b,c,d c,d is a,b
• Trick a,b,c,dE E is a,b,c,d!
• Difference lists allow concatenation of lists in
  constant time, as in imperative languages.

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Concatenation and Difference Lists

• Difference lists can be concatenated in constant
  time by using conc_dl
• ?conc_dl(a,bA A, c,dC C, Result)
• unify with conc_dl(X Y, Y Z, X Z)
• X / a,bA
• Y / A
• A / c,dC
• Z / C
• Result / X Z, i.e. Result / a,bA C,
  i.e.
• Result / a,b,c,dC C

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Some Caveats

• While the result of conc_dl has an uninstatiated
  tail, the first argument does not.
• You cannot use it as an argument to conc_dl in
  the same clause.
• Difference lists are powerful but
  counterintuitive. They appear most often in
  procedures that were first implemented with
  conventional lists and then carefully rewritten
  for efficiency Covington, p.183.

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Improveing efficiency by asserting derived facts

• fib and fib2.
• Execution trees
• Page 204
• More difficult but more efficient oneforwardfib