Proof Manager: Difference between revisions
imported>Son No edit summary |
imported>Son No edit summary |
||
Line 1: | Line 1: | ||
The Proof Manager is responsible for constructing proofs and maintaining existing proofs associated with proof obligations. | The Proof Manager is responsible for constructing proofs and maintaining existing proofs associated with proof obligations. | ||
Proof obligations are generated by the proof obligation generator and have the form of ''sequents''. | |||
For this, the Proof Manager architecture is separated into two parts: ''extensible'' part and ''static'' part. The extensible part is responsible for generating individual proof rules. The static part is responsible for putting proof rules together to construct and manage proofs. We call components that generate valid proof rules ''reasoners''. | For this, the Proof Manager architecture is separated into two parts: ''extensible'' part and ''static'' part. The extensible part is responsible for generating individual proof rules. The static part is responsible for putting proof rules together to construct and manage proofs. We call components that generate valid proof rules ''reasoners''. | ||
Line 7: | Line 9: | ||
By applying the generated proof rules by different reasoner, the Proof Manager builds a (partial) proof for an proof obligation by constructing ''proof trees''. | By applying the generated proof rules by different reasoner, the Proof Manager builds a (partial) proof for an proof obligation by constructing ''proof trees''. | ||
== | == Sequents == | ||
Sequents are of the following form | |||
'''H |- G''' | '''H |- G''' | ||
where '''H''' is the set of hypotheses (predicates) and '''G''' is the goal ( | where '''H''' is the set of hypotheses (predicates) and '''G''' is the goal (a predicate in the mathematical language). | ||
== Reasoners == | == Reasoners == |
Revision as of 13:38, 10 September 2008
The Proof Manager is responsible for constructing proofs and maintaining existing proofs associated with proof obligations.
Proof obligations are generated by the proof obligation generator and have the form of sequents.
For this, the Proof Manager architecture is separated into two parts: extensible part and static part. The extensible part is responsible for generating individual proof rules. The static part is responsible for putting proof rules together to construct and manage proofs. We call components that generate valid proof rules reasoners.
The basic reasoning capabilities of the Proof Manager can be extended by adding new reasoners. A reasoner may implement a decision procedure for automated proof, or a derived rule schema for interactive proof.
By applying the generated proof rules by different reasoner, the Proof Manager builds a (partial) proof for an proof obligation by constructing proof trees.
Sequents
Sequents are of the following form
H |- G
where H is the set of hypotheses (predicates) and G is the goal (a predicate in the mathematical language).
Reasoners
Reasoners are responsible for generating proof rules. The input of a reasoner is:
1. A sequent.
2. Optional input (e.g. a predicate in the case of the Cut Rule).
The output of the reasoner (in case of successful) is a proof rule. This proof rule is trusted by the Proof Manager to built the proof.
An important point about reasoners is that the internal workings of them are not visible to the other part of the Proof Manager. It is only required that they satisfy the following requirements:
a. Logically Valid A generated proof rule must be valid (i.e. can be derived) in the mathematical logic.
b. Replayable A reasoner must work deterministically, i.e. given the same input, a reasoner must generate the same proof rule every time.