Basic Action Notation

complete | escape | fail | commit | diverge | unfold | unfolding A | indivisibly A
A₁ and A₂ | A₁ or A₂ | A₁ and then A₂ | A₁ trap A₂

• All primitive basic actions:
  
  
  • Give no transients, except for escape.
    
    
  • Produce no bindings.
    
    
  • Make no changes to storage.
    
    
  • do not communicate.
    
    
  • Redirect no bindings.
    
    
  
  
• All basic action combinators are:
  
  
  • Functionally conducting (see the basic action A₁andA₂), except for A₁trapA₂, which is functionally composing (see the functional action A₁thenA₂.
    
    
  • declaratively conducting (see the basic action A₁andA₂).
    
    
• complete: a primitive basic action. Represents normal termination. Unit for A₁andA₂, as well as for A₁and thenA₂.
  
  
  • Indivisible. Always completes.
    
    
• escape: a primitive basic action. Represents abnormal termination. Unit for A₁trapA₂.
  
  
  • Indivisible. Always escapes.
    
    
  • Gives any given transients.
    
    
• fail: a primitive basic action. Represents abortion of the current alternative. Unit for A₁orA₂.
  
  
  • Indivisible. Always fails.
    
    
  Example
  
  
• commit: a primitive basic action. Represents commitment to the current alternative, cutting away other current alternatives.
  
  
  • Indivisible. Always commits and completes.
    
    
  Example
  
  
  
• diverge: a basic action. Represents nontermination.
  
  
  • Always diverges.
    
    
  Example
  
  
  
• unfold: a dummy action, standing for the innermost enclosing unfolding.
  
  
• unfolding A: Represents the (in general, infinite) action formed by continually substituting A for unfold. (To avoid singularities in pathological cases, substitute complete and then A, rather than just A.)
  
  
  • Performs A, but whenever the dummy action unfold is reached, A is performed in place of unfold.
    
    
• indivisibly A: a basic combination of action A. Represents that the steps of performing A are not interleaved with those of other actions performed by the same agent. Also ensures that the performance of A cannot be interrupted by an escape or failure occurring outside A. For use only when A cannot diverge.
  
  
  • Indivisible: A is performed as a single step.
    
    
• A₁ or A₂: a basic combination of actions A₁ or A₂. Represents implementation-dependent choice; specializes to deterministic choice when one or the other of A₁, A₂ must fail.
  
  
  • Performs either A₁orA₂. When the performed alternative fails without committing, it is ignored and the other alternative is performed instead.
    
    
  • All the transients given to the combination of A₁, A₂ are given to the performed alternative. On normal or abnormal termination, all the transients given by the performed alternative are given by the combined action.
    
    
  • All the bindings received by the combination of A₁, A₂ are received by the performed alternative. On normal termination, all the bindings produced by the performed alternative are produced by the combined action.
    
    
• A₁ and A₂: a basic combination of actions A₁, A₂. Represents implementation-dependent order of performance of indivisible subactions, specializing to independent performance when there is no interference between A₁ and A₂.
  
  
  • Basically interleaving: Performs both A₁, A₂, with arbitrary interleaving of their indivisible steps. An escape or a failure causes any remaining parts of the subactions to be skipped.
    
    
  • Functionally conducting: The transients given to the combination of A₁, A₂ is given to both A₁, A₂. On normal termination, all the transients given by A₁, A₂ is collected and given by the combined action---if both give one or more items of transients, these are tupled in the given order. On escape, only the transients given by the escape is given by the combined action.
    
    
  • declaratively conducting: The bindings received by the combination of A₁, A₂ are received by both A₁, A₂. On normal termination, all the bindings produced by A₁, A₂ are collected and produced by the combined action---provided that the bindings are all for distinct tokens, otherwise the combined action fails.
    
    
• A₁ and then A₂: a basic combination of actions A₁, A₂. Represents dependency on normal termination.
  
  
  • Basically (normal) sequencing: Performs A₁ first. If A₁ completes, performs A₂.
    
    
• A₁ trap A₂: a basic action combination. Represents recovery from abnormal termination.
  
  
  • Performs A₁ first. If A₁ escapes, performs A₂.
    
    
  • Functionally composing (see the functional action A₁thenA₂ in Section d.2.1).
    
    
• action: the sort of all actions.
  

  Actions | Yielders | Data

  
  

the d yielded by Y | yielder

• the d yielded by Y: a yielder, where d is a sort of data and Y is a yielder. When Y yields an individual, it yields that individual, provided that the individual is included in the sort, otherwise it yields nothing.
  
  
• Every data-operation (i.e., operation specified for arguments included in data) is extended to arguments of sort yielder. The application of a data operation to yielders yields whatever is yielded by applying the data operation to the data yielded by the arguments. For instance, sum(Y₁, Y₂) yields the numerical sum of whatever Y₁andY₂ yield.
  
  
• yielder:the sort of all yielders.
  

  Actions | Yielders | Data

  
  

datum | data | a d