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Automated Mathematical Induction (Paperback, Softcover reprint of the original 1st ed. 1996)
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Automated Mathematical Induction (Paperback, Softcover reprint of the original 1st ed. 1996)
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It has been shown how the common structure that defines a family of
proofs can be expressed as a proof plan [5]. This common structure
can be exploited in the search for particular proofs. A proof plan
has two complementary components: a proof method and a proof
tactic. By prescribing the structure of a proof at the level of
primitive inferences, a tactic [11] provides the guarantee part of
the proof. In contrast, a method provides a more declarative
explanation of the proof by means of preconditions. Each method has
associated effects. The execution of the effects simulates the
application of the corresponding tactic. Theorem proving in the
proof planning framework is a two-phase process: 1. Tactic
construction is by a process of method composition: Given a goal,
an applicable method is selected. The applicability of a method is
determined by evaluating the method's preconditions. The method
effects are then used to calculate subgoals. This process is
applied recursively until no more subgoals remain. Because of the
one-to-one correspondence between methods and tactics, the output
from this process is a composite tactic tailored to the given goal.
2. Tactic execution generates a proof in the object-level logic.
Note that no search is involved in the execution of the tactic. All
the search is taken care of during the planning process. The real
benefits of having separate planning and execution phases become
appar ent when a proof attempt fails.
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