Changes

where <math>W\!</math> and <math>W'\!</math> are augmented strings or sentential forms of specified types that depend on the style of the grammar that is being sought, are variously known as ''characterizations'', ''covering rules'', ''productions'', ''rewrite rules'', ''subsumptions'', ''transformations'', or ''typing rules''.  These are collected together into a set <math>\mathfrak{K}</math> that serves to complete the definition of the formal grammar in question.

where <math>W\!</math> and <math>W'\!</math> are augmented strings or sentential forms of specified types that depend on the style of the grammar that is being sought, are variously known as ''characterizations'', ''covering rules'', ''productions'', ''rewrite rules'', ''subsumptions'', ''transformations'', or ''typing rules''.  These are collected together into a set <math>\mathfrak{K}</math> that serves to complete the definition of the formal grammar in question.

Correlative with the use of this notation, an expression of the form <math>T <: S,\!</math> read to say that <math>T\!</math> is covered by <math>S,\!</math> can be interpreted to say that <math>T\!</math> is of the type <math>S.\!</math> Depending on the context, this can be taken in either one of two ways:

Correlative with the use of this notation, an expression of the

form "T <: S", read as "T is covered by S", can be interpreted

as saying that T is of the type S.  Depending on the context,

this can be taken in either one of two ways:

1.  Treating "T" as a string variable, it means

# Treating <math>T\!</math> as a string variable, it means that the individual string <math>T\!</math> is typed as <math>S.\!</math>

    that the individual string T is typed as S.

# Treating <math>T\!</math> as a type name, it means that any instance of the type <math>T\!</math> also falls under the type <math>S.\!</math>

In accordance with these interpretations, an expression of the form <math>t <: T\!</math> can be read in all of the ways that one typically reads an expression of the form <math>t : T.\!</math>

 

In accordance with these interpretations, an expression like "t <: T" can be

read in all of the ways that one typically reads an expression like "t : T".

There are several abuses of notation that commonly tolerated in the use

There are several abuses of notation that commonly tolerated in the use

of covering relations.  The worst offense is that of allowing symbols to

of covering relations.  The worst offense is that of allowing symbols to