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Define negation element evaluation #751

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143 changes: 74 additions & 69 deletions shacl12-rules/index.html
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Original file line number Diff line number Diff line change
Expand Up @@ -110,17 +110,16 @@
}

.algorithm {
/*
/* <pre> written as CSS
font-family: monospace;
font-size: 16px
white-space: pre;
*/
color: #444;
}
</style>


</head>

<body>
<section id="abstract">
<p>This document describes Shapes Constraint Language (SHACL) Rules.</p>
Expand Down Expand Up @@ -806,19 +805,16 @@ <h4>Evaluation of an Expression</h4>
<p class=ednote>Sketch</p>

<pre class="algorithm">

Let F(arg1, arg2, ...) be an expression.
where arg1, arg2 are RDF terms.
@@

Let [x/<var>μ</var>] be
if x is an RDF term, then [x/row] is x
if x is a variable, then [x/row] is <var>μ</var>(x)
## By well-formedness, it is an error if x is not in the row.

eval(F(expr1, expr2 ...), row) = F(eval(expr1, row), eval(expr2, row), ...)
...
eval(FF(expr1, expr2) , row) = ... things that are not functions like `IF`
@@ Reference SPARQL expression evaluation <a data-cite="SPARQL12-QUERY/#expression-evaluation">EXPR</a>
@@ Reference SPARQL EBV <a data-cite="SPARQL12-QUERY/#expression-evaluation">EXPR</a>

define evalFunction(F, <var>μ</var>):
Let [x/<var>μ</var>] be
if x is an RDF term, then [x/row] is x
if x is a variable, then [x/row] is <var>μ</var>(x)
## By well-formedness, it is an error if x is not in the row.
eval(F(expr1, expr2 ...), row) = F(eval(expr1, row), eval(expr2, row), ...)
eval(FF(expr1, expr2) , row) = ... things that are not functions like `IF`
</pre>
</section>

Expand All @@ -833,66 +829,76 @@ <h4>Evaluation of a Rule</h4>

<pre class="algorithm">
let R be a well-formed rule.

let rule R = (H, B) where
H is the sequence of triple templates in the head
B is the sequence of triple patterns, condition expressions,
B is the sequence of triple patterns,
condition expressions, negation elements,
and assignments in the body

let R : map variable to RDF term as a set of pairs (variable, RDF term)
# Solution sequence of one solution that does not map any variables.
let SEQ0: Solution sequence = { <var>μ</var><sub>0</sub> }

## Solution sequence of one solution that does not map any variables.
## (This is the join identity)

let SEQ: Solution sequence = { <var>μ</var><sub>0</sub> }
let G = <a>evaluation graph</a>

# Start::

Replace each blank node in B with a fresh
variable that does not occur in the rule body.

# Evaluate rule body

for each rule element rElt in B
if rElt is a triple pattern TP:
X = graphMatch(G, TP)
SEQ1 = {}
for each <var>μ</var><sub>1</sub> in X:
for each <var>μ</var><sub>2</sub> in SEQ:
if compatible(<var>μ</var><sub>1</sub>, <var>μ</var><sub>2</sub>)
<var>μ</var><sub>3</sub> = merge(<var>μ</var>1, <var>μ</var><sub>2</sub>)
add <var>μ</var><sub>3</sub> to SEQ1
endfor
endif

if rElt is a condition expression F:
SEQ1 = {}
for each solution <var>μ</var> in SEQ:
## EBV = Effective boolean value.
## TODO: Eval errors.
if ( EBV(eval(<var>μ</var>, F)) is true )
add <var>μ</var> to SEQ1
endif
endfor
endif

if rElt is an assignment(V, expr)
SEQ1 = {}
for each solution S in SEQ:
let x = eval(expr, S)
add(V, x) to S
add S to SEQ1
endfor
endif

if SEQ1 is empty
SEQ = {}
exit
endif

SEQ = SEQ1

endfor
# This function returns a sequence of solutions
define evalRuleElements(B, SEQ, G):

for each rule element rElt in B:

if rElt is a triple pattern TP:
X = graphMatch(G, TP)
SEQ1 = {}
for each <var>μ</var><sub>1</sub> in X:
for each <var>μ</var><sub>2</sub> in SEQ:
if compatible(<var>μ</var><sub>1</sub>, <var>μ</var><sub>2</sub>)
<var>μ</var><sub>3</sub> = merge(<var>μ</var>1, <var>μ</var><sub>2</sub>)
add <var>μ</var><sub>3</sub> to SEQ1
endfor
endif

if rElt is a condition expression with expression F:
SEQ1 = {}
for each solution <var>μ</var> in SEQ:
if evalFunction(F, <var>μ</var>) is <var>true<var>:
add <var>μ</var> to SEQ1
endif
endfor
endif

if rElt is a negation expression with body elements N:
SEQ1 = {}
for each solution <var>μ</var> in SEQ:
S = sequence{ <var>μ</var> }
NEG = evalRuleElements(N, S, G)
if NEG is empty
add <var>μ</var> to SEQ1
endif
endfor
endif

if rElt is an assignment with variable V and expression expr
SEQ1 = {}
for each solution S in SEQ:
let x = eval(expr, S)
add(V, x) to S
add S to SEQ1
endfor
endif

if SEQ1 is empty
SEQ = {}
return SEQ
endif

SEQ = SEQ1
endfor

return SEQ
enddefine

let SEQ = evalRuleElements(B, SEQ0, G)

# Evaluate rule head
let H = empty set
Expand All @@ -905,7 +911,6 @@ <h4>Evaluation of a Rule</h4>
endfor

result eval(R, G) is H

</pre>
<p>Note that `H` may contain triples that are also in the data graph.</p>
</section>
Expand Down