Thank you, Roger.
I suppose my confusion is that Schematron
expresses a set of constraints on a given (static) file.
I didn't realize we were talking about live processing.
Forgive my use of the bandwidth to backtrack on this topic.
. . . . . Ken
At 2022-05-01 17:38 +0000, Roger L Costello wrote:
>Hi Ken,
>
>What is an invariant?
>
>I will first give an example of an invariant and then a definition.
>
>Example: Suppose you are working on a very old
>computer that does not support integer division.
>You are writing a program that, among other
>things, needs to divide x by y. Your program
>wants the quotient q and the remainder r. For
>example, if x = 7 and y = 2, then q = 3 and r =
>1 (two goes into seven three times with a remainder of one).
>
>One way to solve this division problem is
>through repeated subtraction. Store a copy of x
>into t ("t" for temp). Keep subtracting y from t until t is less than y.
>
>So there is a loop. Before the loop q is
>initialized to zero and each time through the
>loop q is incremented by 1. When the loop is
>completed q has the quotient and whatever remains in t is the remainder r.
>
>Here's the cool thing: every time the loop is
>executed this expression must hold true:
>
> x = q * y + t
>
>Further, that expression must hold true before
>the loop is executed, at the start of the loop,
>at the end of the loop, and after the loop.
>
>So we can pepper the code with this assertion:
>
> assert(x = q * y + t)
>
>At any point, if the assertion fails, then there is a bug in the code.
>
>In XSLT the assertion would be expressed as:
>
> <xsl:assert test="$x = $q * $y + $t" />
>
>The expression (the relation) that must always
>hold true is called an "invariant."
>
>Definition: an invariant is an
>expression/relation that must hold true throughout the course of processing.
>
>How do invariants differ from constraints?
>
>An XML Schema specifies a set of constraints. We
>may write an XML Schema for the input data and
>validate the input against the XML Schema. That
>is a static, before run-time, check on the input
>data. During processing the input data likely
>will be changed, twisted, contorted, and no longer conform to the XML Schema.
>
>So the constraints expressed in an XML Schema
>are static constraints. The constraint/relation
>expressed by an invariant is a dynamic constraint/relation.
>
>At least, that's how I think of it. I hope
>others will correct any errors I may have made and add additional insights.
>
>/Roger
>
>
>-----Original Message-----
>From: G. Ken Holman <>
>Sent: Sunday, May 1, 2022 9:45 AM
>To: Rick Jelliffe <>; xml-dev <>
>Subject: Re: [xml-dev] Are there invariants in XML processing?
>
>Forgive me, but I'm trying to understand the use
>of the noun "invariant". This is the first I've
>seen it used, and it is being bandied about.
>Rick's post using it extensively is dated 2016,
>so I feel very much out of the loop.
>
>Is an invariant any different than a constraint?
>
>Does the use of this noun come from another
>discipline where the use is common?
>
>When does it help the listener/reader to use the
>noun "invariant" rather than "constraint" or some other word?
>
>Thanks for your patience with my questions ... I'm just curious.
>
>. . . . . Ken
>
>At 2022-05-01 14:08 +1000, Rick Jelliffe wrote:
> >For a Schematron introduction to this, including
> >document invariants (fixed and co-occurrence)
> >and input/output invariants, and round-trip
> >invariants, see Six Kinds of Validation using
> >Schematron at
> ><https://www.schematron.com/document/279.html>h
> ttps://www.schematron.com/document/279.html
> >
> >For people interest in the practical theory of
> >invariants, Bertam Meyers' work on Design by
> >Contact still is a great place to start: he
> >couches it in functional terms of pre-condition,
> >invariant, post-condition, which I think is
> >more systematic than just "invariants".
> >
> >For the example, the Schematron IO validation
> >(output to input) might be (roughly)
> >
> ><sch:pattern
> >id="publicMilitaryIndicator-nullTransform" documents="'input.xml'">
> >
> >Â Â Â <sch:rule context="publicMilitaryIndicator">
> >Â Â Â Â Â Â Â <sch:let
> >name="matching-output" value="myFunc:findMatchingRow(., 'output.xml')" />
> >Â Â Â Â Â Â
> >Â Â Â Â Â Â Â <sch:assert test="TYPE =
> >'A' or TYPE = 'B' or TYPE = 'C'"
> >role="pre-condition" >Every
> >publicMilitaryIndicator input should have a
> >TYPEÂ with value A, b, or C (i.e., Civil, Joint, Military)</sch:assert>
> >
> >Â Â Â Â Â Â Â Â Â <sch:assert
> >test="$matching-output/TYPE = 'A' orÂ
> >$matching-output/TYPE = 'B' orÂ
> >$matching-output/TYPE = 'C'"
> >role="post-condition" >Every
> >publicMilitaryIndicator output should have a
> >TYPEÂ with value A, b, or C (i.e., Civil, Joint, Military)</sch:assert>
> >
> >Â Â Â Â Â Â Â Â <sch:assert
> >test="$matching-output" role="invariant">Every
> >input publicMilitaryIndicator should have a matching output</sch:assert>
> >
> >Â Â Â Â Â Â Â Â Â <sch:assert
> >test="$matching-output/TYPE= ./TYPE"
> >role="invariant" >Every input
> >publicMilitaryIndicator TYPE value should be
> >carried through to the output</sch:assert>
> >
> ></sch:rule></sch:pattern>
> >
> >Rick
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