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--- sav08:lecture26 [2008/05/28 05:40]
vkuncak
+++ sav08:lecture26 [2008/11/14 20:39]
vkuncak
@@ Line 27: / Line 27: @@
   * Peter B. Andrews: An Introduction to Mathematical Logic and Type theory: To Truth through Proof, Springer 2002 (Chapter 5: Type Theory)
   * [[http://imps.mcmaster.ca/doc/seven-virtues.pdf|The Seven Virtues of Simple Type Theory]]
 ===== LCF Theorem Proving Approach =====
@@ Line 40: / Line 37: @@
 [[Proof and Code Generation in LCF Systems]]
+[[http://afp.sourceforge.net/entries/BinarySearchTree.shtml|Binary Search Trees Example]]
 Further reading:
@@ Line 47: / Line 46: @@
   * Logic and Computation: Interactive Proof with Cambridge LCF
-===== Overview of Interactive Provers =====
+===== Some Interactive Provers =====
+[[http://hol.sourceforge.net/|HOL]] - use directly ML
+[[http://www.cl.cam.ac.uk/~jrh13/hol-light/|HOL Light]] - compact version, written in OCaml
+[[http://www.cl.cam.ac.uk/research/hvg/Isabelle/|Isabelle]] - popular, ML part largely hidden
+[[http://pvs.csl.sri.com/|PVS]] - automation through decision procedures
-HOL, Isabelle
+[[http://coq.inria.fr/|Coq]] - was less automated, now catching up; more complex logic
-PVS - decision procedures
+[[http://www.cs.cornell.edu/Info/Projects/Nuprl/|NuPRL]] - more complex type theory, constructive mathematics
-Coq, NuPRL - more complex type theory, constructive mathematics
+[[http://www.cs.utexas.edu/~moore/acl2/|ACL2]] - emphasis on executable functions, quantifier-free statements, automated induction, pioneering industrial-scale case studies
-ACL2 - emphasis on executable functions, quantifier-free statements, automated induction, pioneering industrial-scale case studies
+===== Example Results in Isabell =====
+<code>NipkowETAL06FlyspeckI,
+Paulson03ConsistencyAxiomChoiceIsabelle,
+PaulsonGrabczewski96MechanizingSetTheory,
+Berghofer07FirstOrderLogicAccordingtoFitting
+</code>