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Funcons-beta : Objects.cbs | PLAIN | PDF

Objects

\[\begin{align*} [ \ \KEY{Datatype} \quad & \NAMEREF{objects} \\ \KEY{Funcon} \quad & \NAMEREF{object} \\ \KEY{Funcon} \quad & \NAMEREF{object-identity} \\ \KEY{Funcon} \quad & \NAMEREF{object-class-name} \\ \KEY{Funcon} \quad & \NAMEREF{object-feature-map} \\ \KEY{Funcon} \quad & \NAMEREF{object-subobject-sequence} \\ \KEY{Funcon} \quad & \NAMEREF{object-tree} \\ \KEY{Funcon} \quad & \NAMEREF{object-single-inheritance-feature-map} \ ] \end{align*}\] \[\begin{align*} \KEY{Datatype} \quad \NAMEDECL{objects} \ ::= \ & \NAMEDECL{object}( \_ : \NAMEHYPER{../../../Computations/Normal}{Generating}{atoms}, \_ : \NAMEHYPER{../../../Computations/Normal}{Binding}{identifiers}, \_ : \NAMEHYPER{../../../Computations/Normal}{Binding}{environments}, \_ : \NAMEREF{objects}\STAR) \end{align*}\]

\(\SHADE{\NAMEREF{object} ( \VAR{A}, \VAR{C}, \VAR{Env}, \VAR{O}\STAR )}\) is an object:

  • distinguished by an atom \(\SHADE{\VAR{A}}\),
  • of a class named \(\SHADE{\VAR{C}}\),
  • with an environment \(\SHADE{\VAR{Env}}\) with the features of the object, and
  • a sequence \(\SHADE{\VAR{O}\STAR}\) of subobjects of the direct superclasses of \(\SHADE{\VAR{C}}\). \(\SHADE{\NAMEREF{object} ( \VAR{A}, \VAR{C}, \VAR{Env} )}\) is an object of a base class. \(\SHADE{\NAMEREF{object} ( \VAR{A}, \VAR{C}, \VAR{Env}, \VAR{O}' )}\) is an object of a class with a single superclass. With multiple inheritance, subobjects due to repeated inheritance of the same class may be shared.

Implementations of objects generally represent an object as a vector of fields, and use pointers and offsets for efficient access to individual fields. The representation of objects used in this specification is independent of such implementation concerns.

\[\begin{align*} \KEY{Funcon} \quad & \NAMEDECL{object-identity}( \_ : \NAMEREF{objects}) : \TO \NAMEHYPER{../../../Computations/Normal}{Generating}{atoms} \\ \KEY{Rule} \quad & \NAMEREF{object-identity} \\&\quad \NAMEREF{object} ( \VAR{A} : \NAMEHYPER{../../../Computations/Normal}{Generating}{atoms}, \_ : \NAMEHYPER{../../../Computations/Normal}{Binding}{identifiers}, \_ : \NAMEHYPER{../../../Computations/Normal}{Binding}{environments}, \_\STAR : \NAMEREF{objects}\STAR ) \leadsto \\&\quad \VAR{A} \end{align*}\] \[\begin{align*} \KEY{Funcon} \quad & \NAMEDECL{object-class-name}( \_ : \NAMEREF{objects}) : \TO \NAMEHYPER{../../../Computations/Normal}{Binding}{identifiers} \\ \KEY{Rule} \quad & \NAMEREF{object-class-name} \\&\quad \NAMEREF{object} ( \_ : \NAMEHYPER{../../../Computations/Normal}{Generating}{atoms}, \VAR{C} : \NAMEHYPER{../../../Computations/Normal}{Binding}{identifiers}, \_ : \NAMEHYPER{../../../Computations/Normal}{Binding}{environments}, \_\STAR : \NAMEREF{objects}\STAR ) \leadsto \\&\quad \VAR{C} \end{align*}\] \[\begin{align*} \KEY{Funcon} \quad & \NAMEDECL{object-feature-map}( \_ : \NAMEREF{objects}) : \TO \NAMEHYPER{../../../Computations/Normal}{Binding}{environments} \\ \KEY{Rule} \quad & \NAMEREF{object-feature-map} \\&\quad \NAMEREF{object} ( \_ : \NAMEHYPER{../../../Computations/Normal}{Generating}{atoms}, \_ : \NAMEHYPER{../../../Computations/Normal}{Binding}{identifiers}, \VAR{Env} : \NAMEHYPER{../../../Computations/Normal}{Binding}{environments}, \_\STAR : \NAMEREF{objects}\STAR ) \leadsto \\&\quad \VAR{Env} \end{align*}\] \[\begin{align*} \KEY{Funcon} \quad & \NAMEDECL{object-subobject-sequence}( \_ : \NAMEREF{objects}) : \TO \NAMEREF{objects}\STAR \\ \KEY{Rule} \quad & \NAMEREF{object-subobject-sequence} \\&\quad \NAMEREF{object} ( \_ : \NAMEHYPER{../../../Computations/Normal}{Generating}{atoms}, \_ : \NAMEHYPER{../../../Computations/Normal}{Binding}{identifiers}, \_ : \NAMEHYPER{../../../Computations/Normal}{Binding}{environments}, \VAR{O}\STAR : \NAMEREF{objects}\STAR ) \leadsto \\&\quad \VAR{O}\STAR \end{align*}\] \[\begin{align*} \KEY{Funcon} \quad & \NAMEDECL{object-tree}( \_ : \NAMEREF{objects}) : \TO \NAMEHYPER{../.}{Trees}{trees} ( \NAMEREF{objects} ) \end{align*}\]

\(\SHADE{\NAMEREF{object-tree} \ \VAR{O}}\) forms a tree where the branches are the object trees for the direct subobjects of \(\SHADE{\VAR{O}}\).

\[\begin{align*} \KEY{Rule} \quad & \NAMEREF{object-tree} ( \VAR{O} : \NAMEREF{objects} ) \leadsto \\&\quad \NAMEHYPER{../.}{Trees}{tree} ( \\&\quad\quad \VAR{O}, \\&\quad\quad \NAMEHYPER{../../../Computations/Normal}{Giving}{interleave-map} ( \\&\quad\quad\quad \NAMEREF{object-tree} \ \NAMEHYPER{../../../Computations/Normal}{Giving}{given}, \\&\quad\quad\quad \NAMEREF{object-subobject-sequence} \ \VAR{O} ) ) \end{align*}\] \[\begin{align*} \KEY{Funcon} \quad & \NAMEDECL{object-single-inheritance-feature-map}( \VAR{O} : \NAMEREF{objects}) : \TO \NAMEHYPER{../../../Computations/Normal}{Binding}{environments} \\&\quad \leadsto \NAMEHYPER{../.}{Maps}{map-override} \ \NAMEHYPER{../../../Computations/Normal}{Giving}{left-to-right-map} ( \\&\quad\quad\quad\quad \NAMEREF{object-feature-map} \ \NAMEHYPER{../../../Computations/Normal}{Giving}{given}, \\&\quad\quad\quad\quad \NAMEHYPER{../.}{Trees}{single-branching-sequence} \ \NAMEREF{object-tree} \ \VAR{O} ) \end{align*}\]

For multiple inheritance, different resolution orders can be specified by using difference linearisations of the object tree.

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