author  clasohm 
Thu, 25 Nov 1993 14:32:54 +0100  
changeset 150  919a03a587eb 
parent 141  a133921366cb 
child 152  37025f8608a6 
permissions  rwrr 
104  1 
\contentsline {chapter}{\numberline {1}Introduction}{1} 
2 
\contentsline {section}{\numberline {1.1}Basic interaction with Isabelle}{1} 

3 
\contentsline {section}{\numberline {1.2}Ending a session}{2} 

4 
\contentsline {section}{\numberline {1.3}Reading files of proofs and theories}{2} 

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\contentsline {section}{\numberline {1.4}Printing of terms and theorems}{3} 
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\contentsline {subsection}{Printing limits}{3} 
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\contentsline {subsection}{Printing of metalevel hypotheses}{3} 

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\contentsline {subsection}{Printing of types and sorts}{3} 
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\contentsline {subsection}{$\eta $contraction before printing}{4} 
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\contentsline {section}{\numberline {1.5}Displaying exceptions as error messages}{4} 
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\contentsline {section}{\numberline {1.6}Shell scripts}{5} 
104  12 
\contentsline {chapter}{\numberline {2}Proof Management: The Subgoal Module}{6} 
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\contentsline {section}{\numberline {2.1}Basic commands}{6} 

14 
\contentsline {subsection}{Starting a backward proof}{6} 

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\contentsline {subsection}{Applying a tactic}{7} 

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\contentsline {subsection}{Extracting the proved theorem}{8} 

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\contentsline {subsection}{Undoing and backtracking}{8} 

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\contentsline {subsection}{Printing the proof state}{9} 

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\contentsline {subsection}{Timing}{9} 

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\contentsline {section}{\numberline {2.2}Shortcuts for applying tactics}{9} 

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\contentsline {subsection}{Refining a given subgoal}{9} 

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\contentsline {subsubsection}{Resolution with a list of theorems}{9} 

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\contentsline {subsection}{Scanning shortcuts}{10} 

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\contentsline {subsubsection}{Proof by assumption and resolution}{10} 

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\contentsline {subsubsection}{Resolution with a list of theorems}{10} 

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\contentsline {subsection}{Other shortcuts}{10} 

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\contentsline {section}{\numberline {2.3}Advanced features}{11} 

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\contentsline {subsection}{Executing batch proofs}{11} 

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\contentsline {subsection}{Managing multiple proofs}{11} 

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\contentsline {subsubsection}{The stack of proof states}{12} 

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\contentsline {subsubsection}{Saving and restoring proof states}{12} 

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\contentsline {subsection}{Debugging and inspecting}{12} 

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\contentsline {subsubsection}{Reading and printing terms}{13} 

34 
\contentsline {subsubsection}{Inspecting the proof state}{13} 

35 
\contentsline {subsubsection}{Filtering lists of rules}{13} 

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\contentsline {chapter}{\numberline {3}Tactics}{14} 

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\contentsline {section}{\numberline {3.1}Resolution and assumption tactics}{14} 

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\contentsline {subsection}{Resolution tactics}{14} 

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\contentsline {subsection}{Assumption tactics}{15} 

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\contentsline {subsection}{Matching tactics}{15} 

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\contentsline {subsection}{Resolution with instantiation}{15} 

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\contentsline {section}{\numberline {3.2}Other basic tactics}{16} 

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\contentsline {subsection}{Definitions and metalevel rewriting}{16} 

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\contentsline {subsection}{Tactic shortcuts}{17} 

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\contentsline {subsection}{Inserting premises and facts}{17} 

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\contentsline {subsection}{Theorems useful with tactics}{18} 

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\contentsline {section}{\numberline {3.3}Obscure tactics}{18} 

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\contentsline {subsection}{Tidying the proof state}{18} 

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\contentsline {subsection}{Renaming parameters in a goal}{18} 

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\contentsline {subsection}{Composition: resolution without lifting}{19} 

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\contentsline {section}{\numberline {3.4}Managing lots of rules}{19} 

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\contentsline {subsection}{Combined resolution and elimresolution}{20} 

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\contentsline {subsection}{Discrimination nets for fast resolution}{20} 

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\contentsline {section}{\numberline {3.5}Programming tools for proof strategies}{21} 

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\contentsline {subsection}{Operations on type {\ptt tactic}}{22} 

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\contentsline {subsection}{Tracing}{22} 

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\contentsline {subsection}{Sequences}{23} 

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\contentsline {subsubsection}{Basic operations on sequences}{23} 

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\contentsline {subsubsection}{Converting between sequences and lists}{23} 

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\contentsline {subsubsection}{Combining sequences}{23} 

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\contentsline {chapter}{\numberline {4}Tacticals}{25} 

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\contentsline {section}{\numberline {4.1}The basic tacticals}{25} 

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\contentsline {subsection}{Joining two tactics}{25} 

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\contentsline {subsection}{Joining a list of tactics}{25} 

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\contentsline {subsection}{Repetition tacticals}{26} 

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\contentsline {subsection}{Identities for tacticals}{26} 

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\contentsline {section}{\numberline {4.2}Control and search tacticals}{27} 

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\contentsline {subsection}{Filtering a tactic's results}{27} 

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\contentsline {subsection}{Depthfirst search}{28} 

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\contentsline {subsection}{Other search strategies}{28} 

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\contentsline {subsection}{Auxiliary tacticals for searching}{29} 

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\contentsline {subsection}{Predicates and functions useful for searching}{29} 

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\contentsline {section}{\numberline {4.3}Tacticals for subgoal numbering}{29} 

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\contentsline {subsection}{Restricting a tactic to one subgoal}{30} 

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\contentsline {subsection}{Scanning for a subgoal by number}{31} 

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\contentsline {subsection}{Joining tactic functions}{32} 

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\contentsline {subsection}{Applying a list of tactics to 1}{32} 

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\contentsline {chapter}{\numberline {5}Theorems and Forward Proof}{33} 

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\contentsline {section}{\numberline {5.1}Basic operations on theorems}{33} 

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\contentsline {subsection}{Prettyprinting a theorem}{33} 

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\contentsline {subsubsection}{Toplevel commands}{33} 

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\contentsline {subsubsection}{Operations for programming}{34} 

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\contentsline {subsection}{Forwards proof: joining rules by resolution}{34} 

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\contentsline {subsection}{Expanding definitions in theorems}{35} 

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\contentsline {subsection}{Instantiating a theorem}{35} 

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\contentsline {subsection}{Miscellaneous forward rules}{35} 

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\contentsline {subsection}{Taking a theorem apart}{36} 

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\contentsline {subsection}{Tracing flags for unification}{36} 

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\contentsline {section}{\numberline {5.2}Primitive metalevel inference rules}{37} 

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\contentsline {subsection}{Propositional rules}{38} 

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\contentsline {subsubsection}{Assumption}{38} 

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\contentsline {subsubsection}{Implication}{38} 

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\contentsline {subsubsection}{Logical equivalence (equality)}{39} 

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\contentsline {subsection}{Equality rules}{39} 

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\contentsline {subsection}{The $\lambda $conversion rules}{39} 

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\contentsline {subsection}{Universal quantifier rules}{40} 

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\contentsline {subsubsection}{Forall introduction}{40} 

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\contentsline {subsubsection}{Forall elimination}{40} 

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\contentsline {subsubsection}{Instantiation of unknowns}{41} 

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\contentsline {subsection}{Freezing/thawing type variables}{41} 

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\contentsline {section}{\numberline {5.3}Derived rules for goaldirected proof}{41} 

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\contentsline {subsection}{Proof by assumption}{41} 

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\contentsline {subsection}{Resolution}{41} 

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\contentsline {subsection}{Composition: resolution without lifting}{42} 

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\contentsline {subsection}{Other metarules}{42} 

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\contentsline {chapter}{\numberline {6}Theories, Terms and Types}{44} 

107 
\contentsline {section}{\numberline {6.1}Defining Theories}{44} 

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\contentsline {subsection}{Classes and types}{47} 
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\contentsline {section}{\numberline {6.2}Loading Theories}{47} 
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\contentsline {subsection}{Reading a new theory}{47} 
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\contentsline {subsection}{Filenames and paths}{48} 
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\contentsline {subsection}{Reloading a theory}{48} 
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\contentsline {subsection}{Pseudo theories}{48} 
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\contentsline {subsection}{Removing a theory}{49} 
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\contentsline {subsection}{Using Poly/{\psc ml}}{49} 
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\contentsline {section}{\numberline {6.3}Basic operations on theories}{49} 
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\contentsline {subsection}{Extracting an axiom from a theory}{49} 
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\contentsline {subsection}{Building a theory}{50} 
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\contentsline {subsection}{Inspecting a theory}{51} 
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\contentsline {section}{\numberline {6.4}Terms}{52} 
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\contentsline {section}{\numberline {6.5}Certified terms}{53} 
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\contentsline {subsection}{Printing terms}{53} 
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\contentsline {subsection}{Making and inspecting certified terms}{53} 
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\contentsline {section}{\numberline {6.6}Types}{54} 
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\contentsline {section}{\numberline {6.7}Certified types}{54} 
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\contentsline {subsection}{Printing types}{54} 
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\contentsline {subsection}{Making and inspecting certified types}{54} 
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\contentsline {chapter}{\numberline {7}Substitution Tactics}{56} 
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\contentsline {section}{\numberline {7.1}Simple substitution}{56} 
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\contentsline {section}{\numberline {7.2}Substitution in the hypotheses}{57} 
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\contentsline {section}{\numberline {7.3}Setting up {\ptt hyp_subst_tac}}{57} 
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\contentsline {chapter}{\numberline {8}Simplification}{60} 
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\contentsline {section}{\numberline {8.1}Simplification sets}{60} 
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\contentsline {subsection}{Rewrite rules}{60} 
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\contentsline {subsection}{Congruence rules}{61} 
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\contentsline {subsection}{The subgoaler}{61} 
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\contentsline {subsection}{The solver}{62} 
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\contentsline {subsection}{The looper}{62} 
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\contentsline {section}{\numberline {8.2}The simplification tactics}{63} 
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\contentsline {section}{\numberline {8.3}Example: using the simplifier}{64} 
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\contentsline {chapter}{\numberline {9}The classical theorem prover}{67} 
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\contentsline {section}{\numberline {9.1}The sequent calculus}{67} 
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\contentsline {section}{\numberline {9.2}Simulating sequents by natural deduction}{68} 
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\contentsline {section}{\numberline {9.3}Extra rules for the sequent calculus}{69} 
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\contentsline {section}{\numberline {9.4}Classical rule sets}{70} 
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\contentsline {section}{\numberline {9.5}The classical tactics}{71} 
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\contentsline {subsection}{Singlestep tactics}{72} 
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\contentsline {subsection}{The automatic tactics}{72} 
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\contentsline {subsection}{Other useful tactics}{72} 
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\contentsline {subsection}{Creating swapped rules}{73} 
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\contentsline {section}{\numberline {9.6}Setting up the classical prover}{73} 