dpans/concept-conses.tex

% -*- Mode: TeX -*-

A \newterm{cons} is a compound data \term{object} 
having two components called the \term{car} and the \term{cdr}.

\displaythree{Some defined names relating to conses.}{
car&cons&rplacd\cr
cdr&rplaca&\cr
}

Depending on context, a group of connected \term{conses} can be viewed
in a variety of different ways.  A variety of operations is provided to
support each of these various views.

\beginsubsection{Conses as Trees}

A \newterm{tree} is a binary recursive data structure made up of
\term{conses} and \term{atoms}:
the \term{conses} are themselves also \term{trees}
(sometimes called ``subtrees'' or ``branches''), and the \term{atoms}
are terminal nodes (sometimes called \newterm{leaves}). 
Typically, the \term{leaves} represent data while the branches 
establish some relationship among that data.

\displayfour{Some defined names relating to trees.}{
caaaar&caddar&cdar&nsubst\cr
caaadr&cadddr&cddaar&nsubst-if\cr
caaar&caddr&cddadr&nsubst-if-not\cr
caadar&cadr&cddar&nthcdr\cr
caaddr&cdaaar&cdddar&sublis\cr
caadr&cdaadr&cddddr&subst\cr
caar&cdaar&cdddr&subst-if\cr
cadaar&cdadar&cddr&subst-if-not\cr
cadadr&cdaddr&copy-tree&tree-equal\cr
cadar&cdadr&nsublis&\cr
}

\beginsubsubsection{General Restrictions on Parameters that must be Trees}

\issue{DOTTED-LIST-ARGUMENTS:CLARIFY}
Except as explicitly stated otherwise,
for any \term{standardized} \term{function} that takes a \term{parameter}
that is required to be a \term{tree},
the consequences are undefined
if that \term{tree} is circular.
\endissue{DOTTED-LIST-ARGUMENTS:CLARIFY}

\endsubsubsection%{General Restrictions on Parameters that must be Trees}

\endsubsection%{Conses as Trees}

\beginsubsection{Conses as Lists}

A \newterm{list} is a chain of \term{conses} in which the \term{car} of each
\term{cons} is an \term{element} of the \term{list}, 
and the \term{cdr} of each \term{cons} is either the next
link in the chain or a terminating \term{atom}.  

A \newterm{proper list} is a \term{list} terminated by the \term{empty list}.
The \term{empty list} is a \term{proper list}, but is not a \term{cons}.

An \newterm{improper list} is a \term{list} that is not a \term{proper list};
that is, it is a \term{circular list} or a \term{dotted list}.

A \newterm{dotted list} is a \term{list} that has a terminating \term{atom}
that is not the \term{empty list}.  A \term{non-nil} \term{atom} by itself
is not considered to be a \term{list} of any kind---not even a \term{dotted list}.

A \newterm{circular list} is a chain of \term{conses} that has no termination 
because some \term{cons} in the chain is the \term{cdr} of a later \term{cons}.

\displayfour{Some defined names relating to lists.}{
append&last&nbutlast&rest\cr
butlast&ldiff&nconc&revappend\cr
copy-alist&list&ninth&second\cr
copy-list&list*&nreconc&seventh\cr
eighth&list-length&nth&sixth\cr
endp&make-list&nthcdr&tailp\cr
fifth&member&pop&tenth\cr
first&member-if&push&third\cr
fourth&member-if-not&pushnew&\cr
}
 
\beginsubsubsection{Lists as Association Lists}

An \newterm{association list} is a \term{list} of \term{conses} 
representing an association of \term{keys} with \term{values}, 
where the \term{car} of each \term{cons} is the \term{key} 
and the \term{cdr} is the \term{value} associated with that \term{key}.

\displayfour{Some defined names related to assocation lists.}{
acons&assoc-if&pairlis&rassoc-if\cr
assoc&assoc-if-not&rassoc&rassoc-if-not\cr
}

\endsubsubsection%{Lists as Association Lists}

\beginsubsubsection{Lists as Sets}

\term{Lists} are sometimes viewed as sets by considering their elements
unordered and by assuming there is no duplication of elements.

\displayfour{Some defined names related to sets.}{
adjoin&nset-difference&set-difference&union\cr
intersection&nset-exclusive-or&set-exclusive-or&\cr
nintersection&nunion&subsetp&\cr
}

\endsubsubsection%{Lists as Sets}

\beginsubsubsection{General Restrictions on Parameters that must be Lists}

%Barrett: This forces something like
% 	    \f{(MEMBER X '(X Y . Z))} to detect the \f{( . Z )}
% 	  in safe code even when it would not naturally be reached
% 	  by the search.  We should soften this slightly.
%KMP: Fixed.
Except as explicitly specified otherwise,
any \term{standardized} \term{function} that takes a \term{parameter}
that is required to be a \term{list} should be prepared to signal 
an error \oftype{type-error} if the \term{value} received is a \term{dotted list}.

% Sandra complained that this was only said a few places, 
% and needed to be said more.
% This is a stopgap while we make sure we mean it everywhere.
Except as explicitly specified otherwise,
for any \term{standardized} \term{function} that takes a \term{parameter}
that is required to be a \term{list}, 
the consequences are undefined 
if that \term{list} is \term{circular}.

\endsubsubsection%{General Restrictions on Parameters that must be Lists}

\endsubsection%{Conses as Lists}