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   Re: A bunch of components, but no mandated organization - reasonable?

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"Roger L. Costello" <costello@mitre.org> wrote in message 
200501121345.j0CDj1v18371@smtp-bedford-dr.mitre.org">news:200501121345.j0CDj1v18371@smtp-bedford-dr.mitre.org...
> Hi Folks,
>
> Suppose that:
>
> 1. There exist a collection of "components", and each component is
> well-defined and understood.
>
> 2. There does NOT exist any rules which specify how the components should 
> be
> assembled.
>
> If I assemble some of the components into a certain structure, and send 
> the
> structure to you, will you be able to understand my structure?

The question is very generic. There are cases where the answer is positive.

Take FXSL:

  -  Most of the functions and operators don't know about the existence of 
other functions.

  -  Most/all functions can be combined in any arbitrary ways (that only 
must satisfy type rules) through functional composition

  - The result is easily understood, even in some more complicated cases

An example:

  f:map(f:flip(f:round-half-to-even(f:sqrt(2, 0.000001))), 0 to 13)

It is not too difficult to conclude that this evaluates to a list of 
numbers, each of which is a rounding of sqrt(2) (with precision of 0.000001) 
and the respective number of digits after the decimal point (from o to 13 
digits after the decimal point).

So, one is not surprised to see the following result:
1
1.4
1.41
1.414
1.4142
1.41421
1.414214
1.4142136
1.41421356
1.414213562
1.4142135624
1.41421356237
1.414213562375
1.4142135623747

So, there are systems (any system with support for higher-order functions), 
where it is possible to combine components in almost arbitrary ways and this 
is "by design".


Cheers,
Dimitre Novatchev


>
> Let me be a bit more concrete.  Suppose that:
>
> 1. There exist a collection of information components, and each 
> information
> component is well-defined and understood.  Some examples of information
> components might include - a missile information component (this component
> provides information about a missile, such as its direction, speed, 
> warhead
> type, etc), an aircraft information component (this component provides
> information about an aircraft, such as its altitude, wingspan, speed, 
> etc).
>
> 2. There does NOT exist any rules which specify how the information
> components should be assembled.  In other words, there is no grammar which
> dictates how the components must be bound together.
>
> If I assemble some of the information components into a certain structure,
> and send the structure to you, will you be able to understand my 
> information
> structure?
>
> Can information be transmitted in a world where the building blocks are
> understood, but no grammar exists?
>
> Is a grammar necessary for information transfer?
>
> Let me give a simple example.  Suppose that:
>
> 1. There exists these three components - A, B, C.  And everyone knows the
> meaning of each component.
>
> 2. There are no rules that specify how A, B, or C should be organized, nor
> the number of occurrences of each.
>
> Suppose that I create this message: AACABBAC.  And I send it to you.  Will
> you be able to understand my message?
>
> Consider the English language.  Suppose that:
>
> 1. The English language was just comprised of a bunch of words (and each
> word is understood), ...
>
> 2. ... but there was no English grammar.
>
> If I compose a sentence using these words, will you be able to understand 
> my
> sentence?
>
> Consider XML Schemas.  Suppose that:
>
> 1. An XML Schema declares a bunch of independent elements (i.e., 
> components)
> and each component is understood.  For example, here's a Book component:
>
> <xsd:element name="Book">
>    <xsd:complexType>
>         <xsd:all>
>            <xsd:element name="Title" type="xsd:string"/>
>            <xsd:element name="Author" type="xsd:string"/>
>            <xsd:element name="Date" type="xsd:date"/>
>            <xsd:element name="ISBN" type="xsd:string"/>
>            <xsd:element name="Publisher" type="xsd:string"/>
>        </xsd:all>
>    </xsd:complexType>
> </xsd:element>
>
> Here's a BookCover component:
>
> <xsd:element name="BookCover">
>    <xsd:complexType>
>         <xsd:choice>
>            <xsd:element name="Hardcover"><xsd:complexType/></xsd:element>
>            <xsd:element name="Softcover"><xsd:complexType/></xsd:element>
>        </xsd:choice>
>    </xsd:complexType>
> </xsd:element>
>
> Everyone understands the meaning of each component in the Schema.
>
> 2. But there is no declaration tying the components together, e.g., there 
> is
> no overarching element declaration that relates the Book component with 
> the
> BookCover component.
>
> If I create an XML instance document using the components and send the
> instance document to you, will you be able to understand my data?
>
> /Roger
>
>
>
>
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