Provides a set implementation for machine CSP sets. This relies heavily on the type checking and assumes in many places that the sets being operated on are suitable for the opertion in question.

We cannot just use the built in set implementation as FDR assumes in several places that infinite sets are allowed.

- data ValueSet
- = Integers
- | Processes
- | IntSetFrom Int

- emptySet :: ValueSet
- fromList :: [Value] -> ValueSet
- toList :: ValueSet -> [Value]
- compareValueSets :: ValueSet -> ValueSet -> Maybe Ordering
- member :: Value -> ValueSet -> Bool
- card :: ValueSet -> Integer
- empty :: ValueSet -> Bool
- union :: ValueSet -> ValueSet -> ValueSet
- unions :: [ValueSet] -> ValueSet
- intersection :: ValueSet -> ValueSet -> ValueSet
- intersections :: [ValueSet] -> ValueSet
- difference :: ValueSet -> ValueSet -> ValueSet
- cartesianProduct :: ([Value] -> Value) -> [ValueSet] -> ValueSet
- powerset :: ValueSet -> ValueSet
- allSequences :: ValueSet -> ValueSet
- singletonValue :: ValueSet -> Maybe Value
- valueSetToEventSet :: ValueSet -> Set Event

# Construction

Integers | Set of all integers |

Processes | Set of all processes |

IntSetFrom Int | The infinite set of integers starting at lb. |

# Basic Functions

compareValueSets :: ValueSet -> ValueSet -> Maybe OrderingSource

Compares two value sets using subseteq (as per the specification).

card :: ValueSet -> IntegerSource

The cardinality of the set. Throws an error if the set is infinite.

union :: ValueSet -> ValueSet -> ValueSetSource

Union two sets throwing an error if it cannot be done in a way that will terminate.

intersection :: ValueSet -> ValueSet -> ValueSetSource

Intersects two sets throwing an error if it cannot be done in a way that will terminate.

intersections :: [ValueSet] -> ValueSetSource

Replicated intersection.

difference :: ValueSet -> ValueSet -> ValueSetSource

# Derived functions

cartesianProduct :: ([Value] -> Value) -> [ValueSet] -> ValueSetSource

Produces a ValueSet of the carteisan product of several ValueSets,
using `vc`

to convert each sequence of values into a single value.

allSequences :: ValueSet -> ValueSetSource

Returns the set of all sequences over the input set. This is infinite so we use a CompositeSet.

# Specialised Functions

singletonValue :: ValueSet -> Maybe ValueSource

Returns the value iff the set contains one item only.