SOCRATES : A sequence of notes is composed using the prior method with propositions, which can be written as part of a logical formula. Given �The mushrooms are planted, therefore the mushrooms are watered� and �The mushrooms are watered, therefore the mushrooms grow�, what is the conclusion?
LUCIAN : �The mushrooms are planted, therefore the mushrooms grow�.
SOCRATES : Suppose �The mushrooms are planted� represents the first note, �C�, �the mushrooms are watered� represents the second note, �B�, and �the mushrooms grow� represents the third note, �C�. What are the changes in whether the note goes up or down?
LUCIAN : The music goes down from �C� to �B�, (represented as '-') then up from �B� to �C� (represented as '+').
SOCRATES : What are the minima and maxima in this music?
LUCIAN : �C� is a maximum, �B� is a minimum and �C� is a maximum. If there is a change in whether the music goes up or down, then the note just before the change is the maxima or minima, respectively.
%% ?- find_minima_and_maxima([+,+,-,-], [c, d, e, d, c], Music).
%% Music = [c, e, c] ;
%% find_minima_and_maxima(Changes,Music1,Music2).
%% Changes - List of +'s or -'s, indicating whether a note should
%% go up or down from the last one, respectively.
%% Music1 - List of notes
%% Music2 - List of notes which are minima and maxima of Music1
find_minima_and_maxima([Change1|Changes],[Note1,Note2|Music1],Music2) :-
find_minima_and_maxima1(Changes,Music1,Change1,Note2,[Note1],Music2).
%% find_minima_and_maxima1(Changes,Music1,Change,Note2,Note1,Music2).
%% Changes - as for find_minima_and_maxima/3
%% Music1 - rest of music
%% Change - '+' - go up a note
%% '-' - go down a note
%% Note2 - second note
%% Note1 - first note
%% Music2 - list of notes
find_minima_and_maxima1([],[],_,Note1,Music1,Music2) :-
append(Music1,[Note1],Music2).
find_minima_and_maxima1([Change1|Changes],[Note1|Music1],Change1,_,Music2,Music3) :-
find_minima_and_maxima1(Changes,Music1,Change1,Note1,Music2,Music3).
find_minima_and_maxima1([Change1|Changes],[Note1|Music1],Change2,Note2,Music2,Music3) :-
not(Change1=Change2), append(Music2,[Note2],Music4),
find_minima_and_maxima1(Changes,Music1,Change1,Note1,Music4,Music3).