REACH language

The language REACH is used for specifying reachability properties. This approach has the following advantages:

• Custom properties can be easily and concisely specified
• The user does not have to modify the model in any way, in particular the model does not have to be translated into an input language of some model checker.
• Almost any reachability analyser can be used as the back-end.

• true, false
• integers
• strings (e.g. “Hello”)
• events, conditions, places, transitions, signals – cannot be directly specified, but returned by some operators, like C, E, P, T, S, etc.

Built of English letters, digits and '_', not starting with a digit, case sensitive.

• fail string – creates a special failure expression to report errors; has a complicated semantics
• $ event or $ condition or $ place or $ signal – Interpreted on the configuration C to be reached: returns true iff the event is in C, or the condition is in Cut(C), or the place is in Mark(C), or the signal is 1 in Code(C)
• @ event or @ transition or @ signal – Interpreted on the configuration C to be reached: returns true iff C enables event/transition/signal
• signal ' – Interpreted on the configuration C to be reached: returns true iff the next state of signal is high in the final state of C; equivalent to ($ signal ^ @ signal)
• C number – Finds a condition by number
• E number – Finds an event by number
• P name or P number – Finds a place by name or number
• T name or T number – Finds a transition by name or number
• S name or S number – Finds a signal by name or number
• PP regular_expression – Finds a set of places whose names match the given regular expression
• TT regular_expression – Finds a set of transitions whose names match the given regular expression
• SS regular_expression – Finds a set of signals whose names match the given regular expression
• # event or # condition or # place or # transition or # signal – Returns the number of a condition, event, place, transition or signal
• name place or name transition or name signal – Returns the name of a place, transition or signal
• string expression – Returns a string representation of the argument
• downclose event or downclose set_of_events – Downcloses an event or a set thereof, returning a set of events
• trig event – Computes the set of triggers of an event, returning a set of events
• is_init event or is_init condition or is_init place or is_init transition or is_init signal – Checks if a condition/place is initially marked, or an event/transition/signal is initially enabled
• is_cutoff event – Checks if an event is cut-off
• is_input signal – Checks if a signal is an input
• is_output signal – Checks if a signal is an output
• is_internal signal – Checks if a signal is internal
• is_dummy signal – Checks if a signal is dummy
• is_local signal – Checks if a signal is local
• is_plus event or is_plus transition – Checks if an STG event or transition has a sign '+'
• is_minus event or is_minus transition – Checks if an STG event or transition has a sign '-'
• ~ bool – Boolean negation
• - number – Unary minus
• pre event or pre condition or pre place or pre transition or pre set_of_events or pre set_of_conditions or pre set_of_places or pre set_of_transitions – Preset of a node or set of nodes
• post event or post condition or post place or post transition or post set_of_events or post set_of_conditions or post set_of_places or post set_of_transitions – Postset of a node or set of nodes
• cond place or cond set_of_places – Set of conditions corresponding to a place or a place set
• evs transition or evs signal or evs set_of_transitions or evs set_of_signals – Set of events corresponding to a transition, a signal, a transition set or a signal set
• pls condition or pls set_of_conditions – Place corresponding to a condition, or place set corresponding to a condition set
• tran event or tran set_of_events or tran signal or tran set_of_signals – Transition corresponding to an event, or transition set corresponding to an event set, a signal or a signal set
• sig event or sig transition or sig set_of_events or sig set_of_ transitions – Signal corresponding to an event or a transition, or signal set corresponding to event set or an transition set
• card set – Set cardinality

• &, |, ^, →, ↔ – Boolean AND, OR, XOR, implication, and equivalence
• +, -, *, /, % – Numerical operators as usual
• =, != – Equality and non-equality for non-Booleans, as long as the argument types agree; for Booleans use ↔ and ^ instead
• <, ⇐, >, >= – Numerical comparisons and set inclusion
• + – String concatenation
• +, *, \ – Set union, intersection, and difference
• element in set – Set membership

• string[number..number] – Returns a substring of a string
• condition ? expression : expression – Conditional expression, like in C/C++

• threshold[number](bool, bool, …, bool) – Multi-operand threshold operator; if [number] is dropped, 2 is assumed
• {expression, expression, …, expression} – Constructs a set out of several expressions of the same type; an empty set cannot be constructed in this way, as its type cannot be determined

Below the “s.t.” clause is optional:

• forall var in set s.t. predicate {expression} – Constructs an AND-expression by filtering and transforming elements of the given set
• exists var in set s.t. predicate {expression} – Constructs an OR-expression by filtering and transforming elements of the given set
• xorsum var in set s.t. predicate {expression} – Constructs an XOR-expression by filtering and transforming elements of the given set
• threshold[number] var in set s.t. predicate {expression} – Constructs a threshold operator by filtering and transforming elements of the given set; if [number] is dropped, 2 is assumed
• gather var in set s.t. predicate {expression} – Constructs a set by filtering and transforming elements of the given set

• let var=value { expression } – Creates a name with a fixed value and scope