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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> `(` <term>* `)`
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 terms 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.
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