Using ProB with Atelier B: Difference between revisions

As of version 1.3, ProB contains a much improved parser which tries be compliant with Atelier B as much as possible.

Atelier B Plugin

There is also a plugin for Atelier B for use with the standalone Tcl/Tk Version on Atelier B projects. With this you can animate and model check B machines directly from within the IDE of Atelier-B.

Atelier B also enables to use ProB as a prover/disprover in the interactive proof window. For this you need to set the ProB_Path resource to point to probcli (command-line version of ProB).

Differences with Atelier B

Extra Features of ProB

• Identifiers: ProB also allows identifiers consisting of a single letter. ProB also accepts enumerated set elements to be used as identifiers.

• Lexing: The Atelier-B parser (bcomp) reports a lexical error (illegal token |-) if the vertical bar (|) of a lambda abstraction is followed directly by the minus sign.

• Typing:
  • ProB makes use of a unification-based type inference algorithm. As such, typing information can not only flow from left-to-right inside a formula, but also from right-to-left. For example, it is sufficient to type xx<:yy & yy<:NAT instead of typing both xx and yy in ProB.
  • Similar to Rodin, ProB extracts typing information from all predicates. As such, it is sufficient to write xx/:{1,2} to assign a type to xx.
  • the fields of records are normalized (sorted); hence the predicate rec(a:0,b:1) = rec(b:y,a:x) is correctly typed for ProB.

• DEFINITIONS: the definitions and its arguments are checked by ProB. We believe this to be an important feature for a formal method language. However, as such, every DEFINITION must be either a predicate, an expression or a substitution. You cannot use, for example, lists of identifiers as a definition. Also, for the moment, the arguments to DEFINITIONS have to be expressions. Finally, when replacing DEFINITIONS the associativity is not changed. E.g., with PLUS(x,y) == x+y, the expression PLUS(2,3)*10 will evaluate to 50 (and not to 32 as with Atelier-B).

• for a LET substitution, Atelier-B does not allow introduced identifiers to be used in the right-hand side of equations; ProB allows LET x,y BE x=2 & y=x*x IN ... END if the preference ALLOW_COMPLEX_LETS is set to TRUE.

• ProB allows WHILE loops and sequential composition in abstract machines

• ProB now allows the IF-THEN-ELSE for expressions and predicates: IF x<0 THEN -x ELSE x END

• ProB now allows LET constructs for expressions and predicates

• ProB allows btrue and bfalse as predicates.

• ProB allows to use the Event-B relation operators <<->, <->>, <<->>

• ProB allows escape codes (\n, \', \", see above) and supports UTF-8 characters in strings, and ProB allows multi-line string literals written using three apostrophes (string)

• ProB allows WHILE loops and sequential composition in abstract machines

Differences

• for ProB the order of fields in a record is not relevant (internally the fields are sorted), Atelier-B reports a type error if the order of the name of the fields changes

• Well-definedness: ProB will try to check if your predicates are well-defined during animation or model checking. For this ProB assumes (similar to Rodin) a stricter left-to-right definition of well-definedness than Atelier B.

Limitations

• Parsing: ProB will require parentheses around the comma, the relational composition, and parallel product operators. For example, you cannot write r2=rel;rel. You need to write r2=(rel;rel). This allows ProB to distinguish the relational composition from the sequential composition (or other uses of the semicolon).
• Similarly, tuples without parentheses are not supported; write (a,b,c) instead of a,b,c

• Unsupported Operators:
  • Trees and binary trees: most but not all tree operators (mirror, infix) are supported yet. These operators may disappear in future version of Atelier B and may also disappear from ProB.
  • VALUES: This clause of the IMPLEMENTATION machines is not yet fully supported;

• There are also some general limitations wrt refinements. See Current Limitations#Multiple Machines and Refinements for more details.