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We will now concentrate on a simple form of the problem which can be solved with topological sorting. This form is not concerned with -versions. From an initial set of packages $S_0$, we would like to -install in addition a new set $A$ of packages obtaining $S_f = S_0 \cup -A$. +versions. Neither do we consider remote repositories. From an initial +set of packages $S_0$, we would like to install in addition a new set +$A$ of packages obtaining $S_f = S_0 \cup A$, for a static set of package +relations. -The only relations considered are of the form: $a$ Depends on $b$, or more -briefly $aDb$. - -The graph of all such simple dependency relations is a digraph $G$. -For each dependency relation $aDb$, there is an edge $a \to b$ in $G$. -Accessing graph $G$ usually requires a database operation and is -therefore expensive. +The only relations considered are of the form: $a$ Depends on $b$, or +more briefly $aDb$. The graph of all such simple dependency relations +is a digraph $G$. For each dependency relation $aDb$, there is an +edge $a \to b$ in $G$. Accessing graph $G$ usually requires a database +operation and is therefore expensive. We now consider the digraph $G_A$ of the minimal set of simple dependency relations which contains all information required to @@ -183,7 +182,7 @@ condition, for instance a program may require a dependency on program may require a dependency on a particular source release. These conditions are local because they can be computed over the elements of system state $S_i$, e.g. package (name, version) pairs. Let us denote this -condition by a predicate $P(b)$ such that $aDb iff P(b)$. The +condition by a predicate $P(b)$ such that $aDb$ iff $P(b)$. The predicate $P$ for the dependency $aDb$ can be stored as edge data for $(u,v)$ on the graph. % thus when we say $P(u,v)$, this means the predicate stored on @@ -200,43 +199,51 @@ $P(v)$. \subsection{Conflicts and COMAR dependencies} -The tags \texttt{Conflicts} and \texttt{Provides} are inherited from -Debian distribution. A conflict between two packages ($a$ conflicts -with $b$) is a symmetric relation that prevents the packages ($a,b$) -from being installed simultaneously. (It is sufficient that only one -direction of the relation is declared, the other direction is -inferred) Provision in the form of $a$ provides $A$ denotes that $a$ -implements a virtual package abstraction $A$. +The tags \texttt{Conflicts} and \texttt{Provides} in PISI are +inherited from Debian distribution. A conflict between two packages +($a$ conflicts with $b$) is a symmetric relation that prevents the +packages $a,b$ from being installed simultaneously (It is +sufficient that only one direction of the relation is declared, the +other direction is inferred). Provision in the form of $a$ provides $A$ +denotes that $a$ implements a virtual package abstraction $A$. In PISI, a package can provide an object of a COMAR Object Model (OM), and is currently the only model of a ``virtual package''. In the following example, let $a_1,a_2,\ldots,a_n$ provide the OM $A$. A package can depend on another package's OM, for instance $b$ comar-depends on -$A$ (or in short form $bDA$). In this case, it is sufficient that only -one of the $a_i$ are installed. To resolve this, the user is asked to -choose from a list of alternatives immediately, since otherwise there -is unavoidable combinatorial explosion (in the form of having to -consider $\Pi_{bDA}num(A)$ graphs in the worst case where $num(A)$ is -the number of alternatives for comar OM $A$; the problem is that there -seems to be no simple solution to solve satisfiability with arbitrary -disjunctions in package dependency, short of a $SAT$ solver). +$A$ (or in short form $bDA$) (Currently, conditions on virtual +dependencies are not supported). In this case, it is sufficient that +only one of the $a_i$ are installed. To resolve this, the user is +asked to choose from a list of alternatives immediately, since +otherwise there is unavoidable combinatorial explosion (in the form of +having to consider $\Pi_{bDA}num(A)$ graphs in the worst case where +$num(A)$ is the number of alternatives for comar OM $A$; the problem +is that there seems to be no simple solution to solve satisfiability +with arbitrary disjunctions in package dependency, short of a $SAT$ +solver). The resolution of conflicts to maintain system consistency condition -$2$ is easier to achieve. This can be always satisfied by disallowing -installation of a package that would violate the condition. In the +$2$ is easier to achieve. This can be satisfied by disallowing +installation of a package that would violate the condition, or +removing currently installed packages which conflict with the newly +installed package and its dependencies. In most package managers, the +second option is confirmed by the user for making it easier. In the install operation, after constructing the partial dependency graph -$G_A$, we merely have to check whether any conflict appears within the +$G_A$, we merely have to check whether any conflict appears among the vertices of $G_A$. If so, then the operation is untenable, since $G_A$ shows the future state of the installed system. Since a conflict is symmetric, it is represented as a bidirectional edge $a \leftrightarrow b$. To distinguish dependencies from conflicts, the edges would have to be -labelled in this case, for instance with 'd' and 'c'. +labelled in this case, for instance with 'd' and 'c'. The removal +option can be implemented by invoking a multi-package remove operation +on the packages in conflict. \subsection{Remove operation} Dependency resolution for remove operation is similar to install. The -only difference is that we remove the packages in the topological order rather -than installing packages in the reverse topological order. +only significant difference is that we remove the packages in the +topological order rather than installing packages in the reverse +topological order. \section{Remote repositories and upgrade operation}