# The IDENT statement

## Purpose:

This statement is a rule, which defines an identity on a concept. It is syntactic sugar for specifying a set of relations that identify atoms in a specific concept. For example, if relations pi and rho determine an atom of concept T uniquely, you can write:

IDENT "T uniqueness" :  T (pi, rho)


As the IDENT statement defines a rule, it can be in the same places as any other RULE.

## Syntax

IDENT (<label> :)? <Concept> ( <expression>* )


where:

• <label> is the name of the rule. It can be a single word or a string (enclosed by double brackets). It is followed by a colon (:) to distinguish the label from the concept that follows.
• <Concept> is the name of the Concept for atoms of which the rule specifies an identity
• Between brackets are expressions whose source concept must be <Concept>. This is enforced by the type system.

## Informal Semantics

IDENT "Rule Name" : C (e1, e2, ...)


translates into the following rule:

  RULE "Rule Name":  {e1}<>{e1}~ /\ {e2}<>{e2}~ /\ ... |- I[C]


Note that

• in case everyeis both univalent and total, e<>e~ equals e;e~, and the rule is equivalent to:
   RULE "Rule Name":  {e1};{e1}~ /\ {e2};{e2}~ /\ ... |- I[C]

• in case every e is univalent but not total, you should use the IDENT statement (or the rule that it implements), because that also works when an e is not populated.