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| − | This page contains descriptions of the available proof tactics within the RODIN Platform.
| + | Slides from Steve Wright's presentation "Experiences with a Quite Big Event-b Model", given at the Rodin workshop, Southampton, July 16th 2009. |
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| − | For each tactic, the descriptions is as follows:
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| − | * '''Description''': A high-level description of the tactic. This will be the description appeared in the RODIN Platform preferences.
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| − | * '''Additional details''': (Optional) Details explanation of the tactic.
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| − | * '''ID''': An unique ID associated with the tactic.
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| − | * '''Auto-tactic''': ''No'': the tactic cannot be added as an auto-tactic. ''Yes'': the tactic can be added as an auto-tactic. ''Default'': the tactic is a default auto-tactic.
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| − | * '''Post-tactic''': ''No'': the tactic cannot be added as a post-tactic. ''Yes'': the tactic can be added as a post-tactic. ''Default'': the tactic is a default post-tactic.
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| − | * '''Preference display''': Information on how an application of the tactic is displayed in the auto-tactic preference or the post-tactic preference.
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| − | * '''Interactive''': ''No'': the tactic cannot be invoked interactively. ''Global'': The tactic can be invoked from the Proof Control. ''Goal'': The tactic can be invoked from the goal view. ''Hypothesis'': The tactic can be invoked from the hypothesis view. If the tactic can be invoked interactively (i.e. either ''Global'', ''Goal'' or ''Hypothesis''), more information about how this could be done will be given. Note that since the '''Post-tactics''' can be launched manually, any tactics that can be included in the post-tactic in principle can be invoked interactively via the post-tactic. Here ''No'' only means that there is no separate invocation for this specific tactic.
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| − | * '''Proving interface display''': Example(s) on how an application of this tactic can be seen from the proving interface of the RODIN Platform.
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| − | == True Goal ==
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| − | * '''Description''': Discharges any sequent whose goal is '⊤' (logical true).
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| − | * '''ID''': org.eventb.core.seqprover.trueGoalTac
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| − | * '''Auto-tactic''': ''Default''
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| − | * '''Post-tactic''': ''Default''
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| − | * '''Preference display''': True Goal (Discharge)
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| − | * '''Interactive''': ''No''
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| − | * '''Proving interface display''': ⊤ goal
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| − | [[Image:TrueGoalExp1.png]]
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| − | == False Hypothesis ==
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| − | * '''Description''': Discharges any sequent containing a '⊥' hypothesis
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| − | * '''ID''': org.eventb.core.seqprover.falseHypTac
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| − | * '''Auto-tactic''': ''Default''
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| − | * '''Post-tactic''': ''Default''
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| − | * '''Preference display''': False Hypothesis (Discharge)
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| − | * '''Interactive''': ''No''
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| − | * '''Proving interface display''': ⊥ hyp
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| − | [[Image: FalseHypExp1.png]]
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| − | == Goal in Hypotheses ==
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| − | * '''Description''': Discharges any sequent whose goal is contained in its hypotheses
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| − | * '''ID''': org.eventb.core.seqprover.goalInHypTac
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| − | * '''Auto-tactic''': ''Default''
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| − | * '''Post-tactic''': ''Default''
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| − | * '''Preference display''': Goal in Hypotheses (Discharge)
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| − | * '''Interactive''': ''No''
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| − | * '''Proving interface display''': hyp
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| − | [[Image: GoalInHypExp1.png]]
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| − | == Goal Disjunct in Hypothesis ==
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| − | * '''Description''': Discharges any sequent whose goal is a disjunction and one of whose disjuncts is present in the hypotheses.
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| − | * '''ID''': org.eventb.core.seqprover.goalDisjInHypTac
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| − | * '''Auto-tactic''': ''No''
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| − | * '''Post-tactic''': ''Default''
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| − | * '''Preference display''': Goal Disjunct in Hypotheses (Discharge)
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| − | * '''Interactive''': ''No''
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| − | * '''Proving interface display''': ∨ goal in hyp
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| − | [[Image: GoalDisjInHypExp1.png]]
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| − | == Functional Goal ==
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| − | * '''Description''': Tries to discharge a sequent whose goal states that an expression is a function (i.e. f ∈ T1 ⇸ T2, where T1 and T2 are type expressions).
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| − | * '''Additional details''': The sequent is discharged if there is a hypothesis specifying that f is a function of any kind (i.e. partial function, total function, partial injection, total injection, partial surjection, total surjection, bijection). More information about type expressions in Event-B is in the [[FAQ#What are type expressions in Event-B?|FAQ]] page.
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| − | * '''ID''': org.eventb.core.seqprover.funGoalTac
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| − | * '''Auto-tactic''': ''Default''
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| − | * '''Post-tactic''': ''Default''
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| − | * '''Preference display''': Functional Goal (Discharge)
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| − | * '''Interactive''': ''No''
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| − | * '''Proving interface display''': functional goal
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| − | [[Image:FunctionalGoalExp1.png]]
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| − | == Simplification Rewriter ==
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| − | * '''Description''': Tries to simplify all predicates in a sequent using pre-defined simplification rewriting rules.
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| − | * '''Additional details''': The list of rewriting rules are in the following page [[All Rewrite Rules | http://wiki.event-b.org/index.php/All_Rewrite_Rules]], which are marked as ''Automatic''.
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| − | * '''ID''': org.eventb.core.seqprover.autoRewriteTac
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| − | * '''Auto-tactic''': ''Default''
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| − | * '''Post-tactic''': ''Default''
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| − | * '''Preference display''': Simplification Rewriter (Simplify)
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| − | * '''Interactive''': ''No''
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| − | * '''Proving interface display''': simplification rewrites
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| − | The example below shows the screen-shots of the step before the application of the tactic and the step just after the application of the tactic. There are 3 rewritings have been done as follows.
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| − | <math>
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| − | \begin{array}{rcl}
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| − | a + 0 & \Longrightarrow & a \\
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| − | a = a & \Longrightarrow & \btrue \\
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| − | c * 1 & \Longrightarrow & c \\
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| − | \end{array}
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| − | </math>
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| − | Note that <math>\btrue</math> hypothesis is always ''dropped'' in the RODIN Platform.
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| − | Before [[Image:SimplifcationRewritesExp1.png]]
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| − | After [[Image:SimplifcationRewritesExp2.png]]
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| − | == Type Rewriter ==
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| − | * '''Description''': Simplifies predicates containing type expressions such as E ∈ T to ⊤ and T = ∅ to ⊥.
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| − | * '''Additional details''': More information about type expressions in Event-B is in the [[FAQ#What are type expressions in Event-B?|FAQ]] page.
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| − | * '''ID''': org.eventb.core.seqprover.typeRewriteTac
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| − | * '''Auto-tactic''': ''Default''
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| − | * '''Post-tactic''': ''Default''
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| − | * '''Preference display''': Type Rewriter (Simplify)
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| − | * '''Interactive''': ''No''
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| − | * '''Proving interface display''': type rewrites
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| − | The example below shows the screen-shots of the step before the application of the tactic and the step just after the application of the tactic.
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| − | Before [[Image: TypeRewritesExp1.png]]
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| − | After [[Image: TypeRewritesExp2.png]]
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| − | == Implication Goal ==
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| − | * '''Description''': Simplifies any sequent with an implicative goal by adding the left hand side of the implication to the hypotheses and making its right hand side the new goal.
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| − | * '''ID''': org.eventb.core.seqprover.impGoalTac
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| − | * '''Auto-tactic''': ''No''
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| − | * '''Post-tactic''': ''Default''
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| − | * '''Preference display''': Implicative Goal (Simplify)
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| − | * '''Interactive''': ''Goal''. The <math>\limp</math> symbol in the implicative goal is ''redden''. When the mouse hovers the red symbol, the label of the tactic in the context menu is ''Deduction''.
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| − | [[Image: ImpGoalInteractive1.png]]
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| − | * '''Proving interface display''': ⇒ goal
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| − | The example below shows the screen-shots of the step before the application of the tactic and the step just after the application of the tactic.
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| − | Before [[Image: ImpGoalExp1.png]]
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| − | After [[Image: ImpGoalExp2.png]]
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| − | == For-all Goal ==
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| − | * '''Description''': Simplifies any sequent with a universally quantified goal by freeing all its bound variables.
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| − | * '''ID''': org.eventb.core.seqprover.forallGoalTac
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| − | * '''Auto-tactic''': ''No''
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| − | * '''Post-tactic''': ''Yes''
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| − | * '''Preference display''': For-all Goal (Simplify)
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| − | * '''Interactive''': ''Goal''. The symbol <textcolor=red><math>\forall</math></textcolor> in the universal quantified goal is redden. When the mouse hovers the red symbol, the label of the tactic in the context menu is ''Forall instantiation''.
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| − | [[Image: ForallGoalInteractive1.png]]
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| − | * '''Proving interface display''': ∀ goal (frees ''list-of-bounded-identifiers'')
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| − | Before [[Image: ForallGoalExp1.png]]
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| − | After [[Image: ForallGoalExp2.png]]
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| − | == Exists Hypothesis ==
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| − | * '''Description''': TODO
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| − | * '''ID''': TODO
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| − | * '''Display''': TODO
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| − | * '''Auto-tactic''': TODO
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| − | * '''Post-tactic''': TODO
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| − | * '''Interactive''': TODO
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| − | * '''Example''': TODO
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| − | == Find Contradictory Hypothesis ==
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| − | * '''Description''': TODO
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| − | * '''ID''': TODO
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| − | * '''Display''': TODO
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| − | * '''Auto-tactic''': TODO
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| − | * '''Post-tactic''': TODO
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| − | * '''Interactive''': TODO
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| − | * '''Example''': TODO
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| − | == Use Equality Hypothesis ==
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| − | * '''Description''': TODO
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| − | * '''ID''': TODO
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| − | * '''Display''': TODO
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| − | * '''Auto-tactic''': TODO
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| − | * '''Post-tactic''': TODO
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| − | * '''Interactive''': TODO
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| − | * '''Example''': TODO
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| − | == Shrink Implicative Hypothesis ==
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| − | * '''Description''': TODO
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| − | * '''ID''': TODO
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| − | * '''Display''': TODO
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| − | * '''Auto-tactic''': TODO
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| − | * '''Post-tactic''': TODO
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| − | * '''Interactive''': TODO
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| − | * '''Example''': TODO
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| − | == Shrink Enumerated Set ==
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| − | * '''Description''': TODO
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| − | * '''ID''': TODO
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| − | * '''Display''': TODO
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| − | * '''Auto-tactic''': TODO
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| − | * '''Post-tactic''': TODO
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| − | * '''Interactive''': TODO
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| − | * '''Example''': TODO
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| − | == Implicative Hypothesis with Conjunctive RHS ==
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| − | * '''Description''': TODO
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| − | * '''ID''': TODO
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| − | * '''Display''': TODO
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| − | * '''Auto-tactic''': TODO
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| − | * '''Post-tactic''': TODO
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| − | * '''Interactive''': TODO
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| − | * '''Example''': TODO
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| − | == Implicative Hypothesis with Disjunctive LHS ==
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| − | * '''Description''': TODO
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| − | * '''ID''': TODO
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| − | * '''Display''': TODO
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| − | * '''Auto-tactic''': TODO
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| − | * '''Post-tactic''': TODO
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| − | * '''Interactive''': TODO
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| − | * '''Example''': TODO
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| − | == Conjunctive Goal ==
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| − | * '''Description''': TODO
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| − | * '''ID''': TODO
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| − | * '''Display''': TODO
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| − | * '''Auto-tactic''': TODO
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| − | * '''Post-tactic''': TODO
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| − | * '''Interactive''': TODO
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| − | * '''Example''': TODO
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| − | == Clarify Goal ==
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| − | * '''Description''': TODO
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| − | * '''ID''': TODO
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| − | * '''Display''': TODO
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| − | * '''Auto-tactic''': TODO
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| − | * '''Post-tactic''': TODO
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| − | * '''Interactive''': TODO
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| − | * '''Example''': TODO
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| − | == Functional Overriding in Goal ==
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| − | * '''Description''': TODO
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| − | * '''ID''': TODO
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| − | * '''Display''': TODO
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| − | * '''Auto-tactic''': TODO
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| − | * '''Post-tactic''': TODO
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| − | * '''Interactive''': TODO
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| − | * '''Example''': TODO
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| − | == Functional Overriding in Hypothesis ==
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| − | * '''Description''': TODO
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| − | * '''ID''': TODO
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| − | * '''Display''': TODO
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| − | * '''Auto-tactic''': TODO
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| − | * '''Post-tactic''': TODO
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| − | * '''Interactive''': TODO
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| − | * '''Example''': TODO
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| − | == Partition Rewriter ==
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| − | * '''Description''': TODO
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| − | * '''ID''': TODO
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| − | * '''Display''': TODO
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| − | * '''Auto-tactic''': TODO
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| − | * '''Post-tactic''': TODO
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| − | * '''Interactive''': TODO
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| − | * '''Example''': TODO
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| − | == One-Point Rule in Goal ==
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| − | * '''Description''': TODO
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| − | * '''ID''': TODO
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| − | * '''Display''': TODO
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| − | * '''Auto-tactic''': TODO
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| − | * '''Post-tactic''': TODO
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| − | * '''Interactive''': TODO
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| − | * '''Example''': TODO
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| − | == One-Point Rule in Hypothesis ==
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| − | * '''Description''': TODO
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| − | * '''ID''': TODO
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| − | * '''Display''': TODO
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| − | * '''Auto-tactic''': TODO
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| − | * '''Post-tactic''': TODO
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| − | * '''Interactive''': TODO
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| − | * '''Example''': TODO
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| − | == Bounded Goal with Finite Hypothesis ==
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| − | * '''Description''': TODO
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| − | * '''ID''': TODO
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| − | * '''Display''': TODO
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| − | * '''Auto-tactic''': TODO
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| − | * '''Post-tactic''': TODO
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| − | * '''Interactive''': TODO
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| − | * '''Example''': TODO
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| − | == Falsify Goal ==
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| − | == conjI ==
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| − | == allI ==
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| − | == exI ==
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| − | == Remove Negation ==
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| − | == Review ==
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| − | == Proof by cases ==
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| − | == Add Hypothesis ==
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| − | == Abstract Expression ==
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| − | == Automatic Prover ==
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| − | == Post tactic ==
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| − | == Lasoo ==
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| − | == Back Tracking ==
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| − | == Prune ==
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| − | == Search Hypothesis ==
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| − | == Cache Hypothesis ==
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| − | == Previous ==
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| − | == Next ==
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| − | == Information ==
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| − | == Falsify Hypothesis ==
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| − | == Modus Ponens ==
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| − | == conjE ==
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| − | == disjE ==
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| − | == allE ==
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| − | == exE ==
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| − | == eq1 ==
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| − | == Double Implication Hypothesis ==
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| − | == cont Implication Hypothesis ==
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| − | == Functional Overriding ==
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| − | == Equality ==
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| − | == Modus Tollens ==
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| − | == Remove Membership ==
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| − | == Remove Inclusion ==
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| − | == Remove Strict-Inclusion ==
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| − | == Inclusion Set Minus Right ==
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| − | == Remove Inclusion Universal ==
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| − | == Implication Introduction ==
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| − | == Disjunction to Implication ==
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| − | == Forall Modus Ponens ==
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| − | == Next Pending Sub-goal ==
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| − | == Next Reviewed Sub-goal ==
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| − | == impAndHyp ==
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| − | == impAndGoal ==
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| − | == impOrHyp ==
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| − | == impOrGoal ==
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| − | == relImgUnionRight ==
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| − | == relImgUnionLeft ==
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| − | == Set Equality ==
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| − | == Equivalent ==
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| − | == Functional Intersection Image ==
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| − | == Functional Set Minus Image ==
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| − | == Functional Singleton Image ==
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| − | == Converse Relation ==
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| − | == Domain Distribution to the Left ==
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| − | == Domain Distribution to the Right ==
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| − | == Range Distribution to the Left ==
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| − | == Range Distribution to the Right ==
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| − | == Set Minus ==
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| − | == Conjunction and Disjunction Distribution ==
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| − | == Union Conjunction Distribution ==
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| − | == compUnionDist ==
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| − | == Domain/Range Union Distribution ==
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| − | == Relational Overriding ==
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| − | == Composition Image ==
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| − | == Domain Composition ==
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| − | == Range Composition ==
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| − | == Functional Composition Image ==
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| − | == Finite Set in Goal ==
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| − | == Finite Intersection in Goal ==
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| − | == Finite Set Minus in Goal ==
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| − | == Finite Relation in Goal ==
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| − | == Finite Relation Image in Goal ==
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| − | == Finite Domain in Goal ==
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| − | == Finite Range in Goal ==
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| − | == Finite Function in Goal ==
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| − | == Finite Function Converse in Goal ==
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| − | == Finite Functional Relational Image in Goal ==
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| − | | |
| − | == Finite Functional Range in Goal ==
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| − | | |
| − | == Finite Functional Domain in Goal ==
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| − | | |
| − | == Finite Minimum in Goal ==
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| − | | |
| − | == Finite Maximum in Goal ==
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| − | | |
| − | == Finite Negative in Goal ==
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| − | | |
| − | == Finite Positive in Goal ==
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| − | | |
| − | == Cardinality Comparison in Goal ==
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| − | | |
| − | == Cardinality Up to ==
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| − | | |
| − | == Partition Rewrite ==
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| − | | |
| − | == Arithmetic Rewrite ==
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| − | | |
| − | == Total Domain in Hypothesis / Goal ==
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