Automated Deduction - A Basis For Applications Volume I Foundations - Calculi And Methods Volume Ii Systems And Implementation Techniques Volume Iii Applications (applied Logic Series) (volume 2)
by Wolfgang Bibel /
2010 / English / DjVu
3.9 MB Download
1. BASIC CONCEPTS OF INTERACTIVE THEOREM PROVING Interactive
Theorem Proving ultimately aims at the construction of powerful
reasoning tools that let us (computer scientists) prove things we
cannot prove without the tools, and the tools cannot prove without
us. Interaction typi cally is needed, for example, to direct and
control the reasoning, to speculate or generalize strategic lemmas,
and sometimes simply because the conjec ture to be proved does not
hold. In software verification, for example, correct versions of
specifications and programs typically are obtained only after a
number of failed proof attempts and subsequent error corrections.
Different interactive theorem provers may actually look quite
different: They may support different logics (first-or
higher-order, logics of programs, type theory etc.), may be generic
or special-purpose tools, or may be tar geted to different
applications. Nevertheless, they share common concepts and
paradigms (e.g. architectural design, tactics, tactical reasoning
etc.). The aim of this chapter is to describe the common concepts,
design principles, and basic requirements of interactive theorem
provers, and to explore the band width of variations. Having a
'person in the loop', strongly influences the design of the proof
tool: proofs must remain comprehensible, - proof rules must be
high-level and human-oriented, - persistent proof presentation and
visualization becomes very important.
1. BASIC CONCEPTS OF INTERACTIVE THEOREM PROVING Interactive
Theorem Proving ultimately aims at the construction of powerful
reasoning tools that let us (computer scientists) prove things we
cannot prove without the tools, and the tools cannot prove without
us. Interaction typi cally is needed, for example, to direct and
control the reasoning, to speculate or generalize strategic lemmas,
and sometimes simply because the conjec ture to be proved does not
hold. In software verification, for example, correct versions of
specifications and programs typically are obtained only after a
number of failed proof attempts and subsequent error corrections.
Different interactive theorem provers may actually look quite
different: They may support different logics (first-or
higher-order, logics of programs, type theory etc.), may be generic
or special-purpose tools, or may be tar geted to different
applications. Nevertheless, they share common concepts and
paradigms (e.g. architectural design, tactics, tactical reasoning
etc.). The aim of this chapter is to describe the common concepts,
design principles, and basic requirements of interactive theorem
provers, and to explore the band width of variations. Having a
'person in the loop', strongly influences the design of the proof
tool: proofs must remain comprehensible, - proof rules must be
high-level and human-oriented, - persistent proof presentation and
visualization becomes very important.
