The following predicates are used in the puzzle solutions.
- 1 Higher-order Predicates
- 2 Lists
- 3 Arithmetic
- 4 Character Input/Output
unique_solution( +Goal )
holds when Goal has one ground solution. Operationally, Goal
may produce several solutions, ("don't care" non-deterministically), but
they must all be identical (
unique_solution( Goal ) :- findall( Goal, Goal, [Solution|Solutions] ), same_solution( Solutions, Solution ), Solution = Goal. same_solution( , _Solution ). same_solution( [Solution0|Solutions], Solution ) :- Solution0 == Solution, same_solution( Solutions, Solution ).
forall( +Enumerator, +Test )
is true if Enumerator and Test are goals and Test holds everywhere that Enumerator does. NB: forall/2 does not instantiate arguments further.
forall( Enumerator, Test ) :- \+ (call(Enumerator), \+ call(Test)).
count_solutions( +Goal, ?Count )
is true if Count is the number of solutions for Goal. The solutions might not be distinct.
count_solutions/2 enumerates the possible solutions to Goal but does not instantiate Goal's arguments further.
count_solutions( Goal, Count ) :- findall( x, Goal, Xs ), length( Xs, Count ).
member( ?Element, ?List )
holds when Element is a member of List.
member( H, [H|_] ). member( H, [_|T] ) :- member( H, T ).
select( ?Element, ?List0, ?List1 )
is true if List1 is equal to List0 with Element removed.
select( H, [H|T], T ). select( Element, [H|T0], [H|T1] ) :- select( Element, T0, T1 ).
memberchk( +Element, +List )
succeeds (once) if Element is a member of List.
memberchk( Element, List ) :- member( Element, List ), !.
append( ?Front, ?Back, ?List )
succeeds if Front, Back and List are all lists and List is the concatenation of Front and Back.
append( , L, L ). append( [H|T], L, [H|L1] ) :- append( T, L, L1 ).
length( ?List, ?N )
succeeds if N is the length of List.
length( List, N ) :- len1( List, 0, N ). len1( , N, N ). len1( [_H|T], N0, N ) :- N1 is N0+1, len1( T, N1, N ).
between( +Lower, +Upper, ?Index )
is true if Lower =< Index =< Upper. Two valid cases are possible:
- Index is already instantiated to an integer, so the checks on order are applied (test).
- Index is a logical variable: a series of alternative solutions may be generated as the monotonic sequence of values between Lower and Upper (non-deterministic generator).
between( Lower, Upper, Index ) :- integer( Lower ), integer( Upper ), Lower =< Upper, ( integer( Index ) -> % Case 1: "test" Index >= Lower, Index =< Upper ; var( Index ) -> % Case 2: "generate". generate_between( Lower, Upper, Index ) ). generate_between( Lower, Upper, Index ) :- ( Lower =:= Upper -> Index = Lower ; Index = Lower ; Next is Lower + 1, Next =< Upper, generate_between( Next, Upper, Index ) ).
sum( +List, ?Sum )
holds when the List of numbers sum to Sum.
sum( [H|T], Sum ) :- sum1( T, H, Sum ). sum1( , Sum, Sum ). sum1( [H|T], Sum0, Sum ):- Sum1 is Sum0 + H, sum1( T, Sum1, Sum ).
put_chars( +Chars )
if Chars is a (possibly empty) list of character codes and the corresponding characters are written to the current output stream.
put_chars(  ). put_chars( [Char|Chars] ) :- put( Char ), put_chars( Chars ).
get_chars( ?Chars )
if Chars is a (possibly empty) list of character codes read from the current input stream.
get_chars( Input ) :- get0( Char ), ( Char > -1 -> Input = [Char|Chars], get_chars( Chars ) ; otherwise -> Input =  ).
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