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In this last PyParsing subsection we will create a parser for a DSL for expressing formulas in rst-order logic This has the most complex BNF of all the examples in the chapter, and the implementation requires us to handle operators, including their precedences and associativities, something we have not needed to do so far There is no handcrafted version of this parser once we have reached this level of complexity it is better to use a parser generator But in addition to the PyParsing version shown here, in the following section s last subsection there is an equivalent PLY parser for comparison Here are a few examples of the kind of rst-order logical formulas that we want to be able to parse:

From any array type SC[] to any array type TC[], provided that SC and TC are reference types and there is a narrowing conversion from SC to TC

To modify an existing attribute in the directory, construct an LDAPAttribute with the new values and then create an LDAPModification using the constant

a = b forall x: a = b exists y: a -> b ~ true | true & true -> forall x: exists y: true (forall x: exists y: true) -> true & ~ true -> true true & forall x: x = x true & (forall x: x = x) forall x: x = x & true (forall x: x = x) & true

Such conversions require a test at run time to nd out whether the actual reference value is a legitimate value of the new type If not, then a ClassCastException is thrown

562

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does not exist or contains no values If the attribute is multivalued, a replace will replace all values with the new values The section on multivalued attributes later in this chapter discusses how to modify a single value within a multivalued attribute The following snippet of code modi es the telephone number for an entry, replacing all preexisting values, if any

517 Boxing Conversion Boxing conversion converts values of primitive type to corresponding values of reference type Speci cally, the following 8 conversion are called the boxing conversions: From type boolean to type Boolean From type byte to type Byte From type char to type Character From type short to type Short From type int to type Integer From type long to type Long From type float to type Float From type double to type Double

We have opted to use ASCII characters rather than the proper logical operator symbols, to avoid any distraction from the parser itself So, we have used forall for , exists for , -> for (implies), | for (logical OR), & for (logical AND), and ~ for (logical NOT) Since Python strings are Unicode it would be easy to use the real symbols or we could adapt the parser to accept both the ASCII forms shown here and the real symbols In the formulas shown here, the parentheses make a difference in the last two formulas so those formulas are different but not for the two above them (those starting with true), which are the same despite the parentheses Naturally, the parser must get these details right One surprising aspect of rst-order logic is that not (~) has a lower precedence than equals (=), so ~ a = b is actually ~ (a = b) This is why logicians usually put a space after ~ A BNF for our rst-order logic DSL is given in Figure 1415 For the sake of clarity the BNF does not include any explicit mention of whitespace (no \n or \s* elements), but we will assume that whitespace is allowed between all terminals and nonterminals Although our subset of BNF syntax has no provision for expressing precedence or associativity, we have added comments to indicate associativities for the

LDAPAttribute attr = new LDAPAttribute( "telephoneNumber", "650-555-1212"); LDAPModification mod = new LDAPModification( LDAPModificationREPLACE, attr ); try { ldmodify( theDN, mod ); } catch ( LDAPException e ) { }

At run time, boxing conversion proceeds as follows:

FORMULA ::= ('forall' | 'exists') SYMBOL ':' FORMULA | FORMULA '->' FORMULA # right associative | FORMULA '|' FORMULA # left associative | FORMULA '&' FORMULA # left associative | '~' FORMULA | '(' FORMULA ')' | TERM '=' TERM | 'true' | 'false' TERM ::= SYMBOL | SYMBOL '(' TERM_LIST ')' TERM_LIST ::= TERM | TERM ',' TERM_LIST SYMBOL ::= [a-zA-Z]\w*

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