# Informal Summary of Action Notation

##### Actions| Yielders| Data
• The systematic informal description of action notation summarizes Action Notation, and gives further details. It is intended for reference.

• To make it self-contained, it starts by repeating most of the introduction to the concepts of actions, data, and yielders given in Semantic Entities.

Action Notation
Actions are essentially dynamic, computational entities. The performance of an action directly represents information processing behaviour and reflects the gradual, step-wise nature of computation. Items of data are, in contrast, essentially static, mathematical entities, representing pieces of information, e.g., particular numbers. Of course actions are `mathematical' too, in the sense that they are abstract, formally-defined entities, analogous to abstract machines defined in automata theory. A yielder represents an unevaluated item of data, whose value depends on the current information, i.e., the previously-computed and input values that are available to the performance of the enclosing action. For example, a yielder might always evaluate to the datum currently stored in a particular cell, which could change during the performance of an action.

## Actions

##### Actions| Yielders| Data

A performance of an action, which may be part of an enclosing action, either:
• completes, corresponding to normal termination (the performance of the enclosing action proceeds normally); or

• escapes, corresponding to exceptional termination (parts of the enclosing action are skipped until the escape is trapped); or

• fails, corresponding to abandoning the performance of an action (the enclosing action performs an alternative action, if there is one, otherwise it fails too); or

• diverges, corresponding to nontermination (the enclosing action also diverges).

Actions can be used to represent the semantics of programs: action performances correspond to possible program behaviours. Furthermore, actions can represent the (perhaps indirect) contribution that parts of programs, such as statements and expressions, make to the semantics of entire programs.
An action may be nondeterministic, having different possible performances for the same initial information. Nondeterminism represents implementation-dependence, where the behaviour of a program (or the contribution of a part of it) may vary between different implementations---or even between different instants of time on the same implementation. Note that nondeterminism does not imply actual randomness: each implementation of a nondeterministic behaviour may be absolutely deterministic.
The information processed by action performance may be classified according to how far it tends to be propagated, as follows:

• transient: tuples of data, corresponding to intermediate results;

• scoped: bindings of tokens to data, corresponding to symbol tables;

• stable: data stored in cells, corresponding to the values assigned to variables;

• permanent: data communicated between distributed actions.

Transient information is made available to an action for immediate use. Scoped information, in contrast, may generally be referred to throughout an entire action, although it may also be hidden temporarily. Stable information can be changed, but not hidden, in the action, and it persists until explicitly destroyed. Permanent information cannot even be changed, merely augmented.
When an action is performed, transient information is given only on completion or escape, and scoped information is produced only on completion. In contrast, changes to stable information and extensions to permanent information are made during action performance, and are unaffected by subsequent divergence, failure, or escape.
The different kinds of information give rise to so-called facets of actions, focusing on the processing of at most one kind of information at a time:

• the basic facet, processing independently of information (control flows);

• the functional facet, processing transient information (actions are given and give data);

• the declarative facet, processing scoped information (actions receive and produce bindings);

• the imperative facet, processing stable information (actions reserve and unreserve cells of storage, and change the data stored in cells); and

• the communicative facet, processing permanent information (actions send messages, receive messages in buffers, and offer contracts to em agents).

These facets of actions are independent. For instance, changing the data stored in a cell---or even unreserving the cell---does not affect any bindings. There are, however, some directive actions, which process a mixture of scoped and stable information, so as to provide finite representations of self-referential bindings. There are also some hybrid primitive actions and combinators, which involve more than one kind of information at once, such as an action that both reserves a cell of storage and gives it as transient data.
The notation for specifying actions consists of action primitives, which may involve yielders, and action combinators, which operate on one or two subactions. See Section D.9.3 for an explanation of the notation for specifying sorts of actions.

## Yielders

##### Actions| Yielders| Data

Yielders are entities that can be evaluated to yield data during action performance. The data yielded may depend on the current information, i.e., the given transients, the received bindings, and the current state of the storage and buffer. In fact action notation provides primitive yielders that evaluate to compound data (tuples, maps, lists) representing entire slices of the current information, such as the current state of storage. Evaluation cannot affect the current information.
Compound yielders can be formed by the application of data operations to yielders. The data yielded by evaluating a compound yielder are the result of applying the operation to the data yielded by evaluating the operands. For instance, one can form the sum of two number yielders. Items of data are a special case of data yielders, and always yield themselves when evaluated. See Section D.9.4 for an explanation of the notation for specifying sorts of yielders.

## Data

##### Actions| Yielders| Data

The information processed by actions consists of items of data, organized in structures that give access to the individual items. Data can include various familiar mathematical entities, such as truth-values, numbers, characters, strings, lists, sets, and maps. It can also include entities such as tokens, cells, and agents, used for accessing other items, and some compound entities with data components, such as messages and contracts.
Actions themselves are not data, but they can be incorporated in so-called abstractions, which are data, and subsequently enacted back into actions. (Abstraction and enaction are a special case of so-called reification and reflection.) New kinds of data can be introduced ad hoc, for representing special pieces of information.

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[Created by Jin Jin Yi and Ana Carla Santos. Last modified at 21 Dec 1997 by Ana Carla]