Predicate Variables Extension

The aim of this extension is to allow defining proof rules for the Rule Based Prover using meta-variables as predicate placeholders.

For example, one will then be able to write a proof rule involving P and Q directly by using such naming letters.

For technical reasons (predicates and expressions are distinct syntactic categories), predicate meta-variables are distinguished by a leading symbol '$'. For one given predicate, one wanting to refer to this predicate as P, will write in one's proof rules meta-variable '$P'. The symbol '?' could be originally chosen to define meta-variables but this revealed to be confusing due to the use of the symbol '?' in CSP. The choice of the symbol '$' seems to solve such kind of issue.

Plan to implement this extension in the API

• A. extend the lexer
• B. extend the parser
• C. extend the AST
• D. modify visitors, rewriters, filters, etc. according to this extension
• E. implement new AST tests

Implementation details

For B, clients (plug-in contributers) will be allowed to select the mode they want to work with. Thus, will coexist 2 parsing modes one taking into account predicate variables and the other, the current one, which parses predicates or expressions without predicate variables.

- the current one available in the current API (FormulaFactory),

 public IParseResult parsePredicate(String formula, LanguageVersion version,Object origin)
 public IParseResult parseExpression(String formula, LanguageVersion version,Object origin)

- a specific one providing the support for predicate variables.

 public IParseResult parsePredicatePattern(String formula, LanguageVersion version,Object origin)
 public IParseResult parseExpressionPattern(String formula, LanguageVersion version,Object origin)

For C, the class 'PredicateVariable' will be added as a new predicate class. In class Formula, two methods are added

public PredicateVariable[] getPredicateVariables()
public boolean hasPredicateVariables()

Further verifications to carry out

A verification will follow implementation, in order to check that no side-effect is introduced by this extension. The typical unwanted side-effet is that a predicate meta-variable creep into code that was not designed to cope with it.

This verification will be done as follows: Check each occurrence of the typeCheck(), isTypeChecked() or even isWellFormed() methods applied to an AST node. If this call occurs just after a parsePredicate() or parseExpression() call, then there is no risk of introducing a predicate meta-variable (as it would be ruled out by the parser). In all other cases (especially when receiving an AST object coming from an external reasoner), a check must be added to ensure that the AST tree that is type-checked is also free of predicate meta-variable.