imported>Laurent |
imported>Billaude |
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| − | This page describes the design of a tactic requested here : [https://sourceforge.net/tracker/index.php?func=detail&aid=3306228&group_id=108850&atid=651672 Feature Request #3306228]
| + | #REDIRECT [[Maplet Overriding in Goal]] |
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| − | = Objective =
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| − | Split every goal in the form : <math>f\ovl{\{x\mapsto y\}}\in A\;op_1\;B </math> into two sub-goals if and only if the sequent contains a hypothesis such as <math>f\in A\;op_2\;B</math> :
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| − | :*<math>x\in A</math>
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| − | :*<math>y\in B</math>
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| − | Where <math>op_1</math> denote either a Relation <math>\left(\rel\right)</math>, or a Total Relation <math>\left(\trel\right)</math>, or a Partial Function <math>\left(\pfun\right)</math>, or a Total Function <math>\left(\tfun\right)</math>, and <math>op_2</math> is such as <math>f\in A\;op_2\;B\limp f\in A\;op_1\;B</math>.
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| − | = Design Decision =
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| − | Those two subgoals and the predicate are not equivalent to the goal. Indeed, in the case <math>op_1</math> is a Relation, the goal is equivalent to <math>\{x\}\domsub f\in A\setminus\{x\}\rel B\land x\in A\land y\in B</math>. But this has the drawback of writing three times the expression ''x''. If this expression is big, then it can make the proof rule hard to read.
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| − | But, we know that <math>\left(f\in A\;op_1\;B\right)\limp \left(\{x\}\domsub f\in A\setminus\{x\}\;op_1\;B\right)</math> for all the relation given in Objective. By ensuring that <math>f\in A\;op_2\;B</math> is among the hypotheses of the sequent, we ensure that the first predicate of the conjunction is provable. Indeed, if this check was not done, the proof obligation may be unprovable since there are a loss of informations by writing <math>f\in A\;op_2\;B</math> instead of <math>\{x\}\domsub f\in A\setminus\{x\}\;op_1\;B</math>.
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| − | = Table =
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| − | | |
| − | {| class="wikitable alternance" style="text-align:center; width:80%;"
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| − | |+ <math>f\in A\;op_2\;B\limp f\in A\;op_1 B</math>
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| − | |-
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| − | |<math>op_1\;\backslash\;op_2</math>
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| − | ! scope=col | <math>\rel</math>
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| − | ! scope=col | <math>\trel</math>
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| − | ! scope=col | <math>\srel</math>
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| − | ! scope=col | <math>\strel</math>
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| − | ! scope=col | <math>\pfun</math>
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| − | ! scope=col | <math>\tfun</math>
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| − | ! scope=col | <math>\pinj</math>
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| − | ! scope=col | <math>\tinj</math>
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| − | ! scope=col | <math>\psur</math>
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| − | ! scope=col | <math>\tsur</math>
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| − | ! scope=col | <math>\tbij</math>
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| − | |-
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| − | ! scope=row | <math>\rel</math>
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| − | |<math>\checkmark</math>
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| − | |<math>\checkmark</math>
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| − | |<math>\checkmark</math>
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| − | |<math>\checkmark</math>
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| − | |<math>\checkmark</math>
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| − | |<math>\checkmark</math>
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| − | |<math>\checkmark</math>
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| − | |<math>\checkmark</math>
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| − | |<math>\checkmark</math>
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| − | |<math>\checkmark</math>
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| − | |<math>\checkmark</math>
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| − | |-
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| − | ! scope=row | <math>\trel</math>
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| − | |<math>-</math>
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| − | |<math>\checkmark</math>
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| − | |<math>-</math>
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| − | |<math>\checkmark</math>
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| − | |<math>-</math>
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| − | |<math>\checkmark</math>
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| − | |<math>-</math>
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| − | |<math>\checkmark</math>
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| − | |<math>-</math>
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| − | |<math>\checkmark</math>
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| − | |<math>\checkmark</math>
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| − | |-
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| − | ! scope=row | <math>\srel</math>
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| − | |<math>-</math>
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| − | |<math>-</math>
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| − | |<math>\checkmark</math>
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| − | |<math>\checkmark</math>
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| − | |<math>-</math>
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| − | |<math>-</math>
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| − | |<math>-</math>
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| − | |<math>-</math>
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| − | |<math>\checkmark</math>
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| − | |<math>\checkmark</math>
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| − | |<math>\checkmark</math>
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| − | |-
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| − | ! scope=row | <math>\strel</math>
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| − | |<math>-</math>
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| − | |<math>-</math>
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| − | |<math>-</math>
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| − | |<math>\checkmark</math>
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| − | |<math>-</math>
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| − | |<math>-</math>
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| − | |<math>-</math>
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| − | |<math>-</math>
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| − | |<math>-</math>
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| − | |<math>\checkmark</math>
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| − | |<math>\checkmark</math>
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| − | |-
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| − | ! scope=row | <math>\pfun</math>
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| − | |<math>-</math>
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| − | |<math>-</math>
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| − | |<math>-</math>
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| − | |<math>-</math>
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| − | |<math>\checkmark</math>
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| − | |<math>\checkmark</math>
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| − | |<math>\checkmark</math>
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| − | |<math>\checkmark</math>
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| − | |<math>\checkmark</math>
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| − | |<math>\checkmark</math>
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| − | |<math>\checkmark</math>
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| − | |-
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| − | ! scope=row | <math>\tfun</math>
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| − | |<math>-</math>
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| − | |<math>-</math>
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| − | |<math>-</math>
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| − | |<math>-</math>
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| − | |<math>-</math>
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| − | |<math>\checkmark</math>
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| − | |<math>-</math>
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| − | |<math>\checkmark</math>
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| − | |<math>-</math>
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| − | |<math>\checkmark</math>
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| − | |<math>\checkmark</math>
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| − | |-
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| − | ! scope=row | <math>\pinj</math>
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| − | |<math>-</math>
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| − | |<math>-</math>
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| − | |<math>-</math>
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| − | |<math>-</math>
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| − | |<math>-</math>
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| − | |<math>-</math>
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| − | |<math>\checkmark</math>
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| − | |<math>\checkmark</math>
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| − | |<math>-</math>
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| − | |<math>-</math>
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| − | |<math>\checkmark</math>
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| − | |-
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| − | ! scope=row | <math>\tinj</math>
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| − | |<math>-</math>
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| − | |<math>-</math>
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| − | |<math>-</math>
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| − | |<math>-</math>
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| − | |<math>-</math>
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| − | |<math>-</math>
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| − | |<math>-</math>
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| − | |<math>\checkmark</math>
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| − | |<math>-</math>
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| − | |<math>-</math>
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| − | |<math>\checkmark</math>
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| − | |-
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| − | ! scope=row | <math>\psur</math>
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| − | |<math>-</math>
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| − | |<math>-</math>
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| − | |<math>-</math>
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| − | |<math>-</math>
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| − | |<math>-</math>
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| − | |<math>-</math>
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| − | |<math>-</math>
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| − | |<math>-</math>
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| − | |<math>\checkmark</math>
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| − | |<math>\checkmark</math>
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| − | |<math>\checkmark</math>
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| − | |-
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| − | ! scope=row | <math>\tsur</math>
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| − | |<math>-</math>
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| − | |<math>-</math>
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| − | |<math>-</math>
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| − | |<math>-</math>
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| − | |<math>-</math>
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| − | |<math>-</math>
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| − | |<math>-</math>
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| − | |<math>-</math>
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| − | |<math>-</math>
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| − | |<math>\checkmark</math>
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| − | |<math>\checkmark</math>
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| − | |-
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| − | ! scope=row | <math>\tbij</math>
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| − | |<math>-</math>
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| − | |<math>-</math>
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| − | |<math>-</math>
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| − | |<math>-</math>
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| − | |<math>-</math>
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| − | |<math>-</math>
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| − | |<math>-</math>
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| − | |<math>-</math>
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| − | |<math>-</math>
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| − | |<math>-</math>
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| − | |<math>\checkmark</math>
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| − | |-
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| − | |}
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| − | [[Category:Design]] | |
