Commit c557ab8b by Gerwin Klein

merge from afp-2021

 ... ... @@ -44,7 +44,7 @@ default_isabelle_tool() ISABELLE_VERSION="Isabelle$VERSION" ISABELLE_TOOL="$ISABELLE_RELEASES/$ISABELLE_VERSION/bin/isabelle" if [[ "$OSTYPE" == darwin* && ! -x "$ISABELLE_TOOL" ]]; then ISABELLE_TOOL="$ISABELLE_RELEASES/${ISABELLE_VERSION}.app/Isabelle/bin/isabelle" ISABELLE_TOOL="$ISABELLE_RELEASES/${ISABELLE_VERSION}.app/bin/isabelle" fi fi fi ... ...  ... ... @@ -122,7 +122,7 @@ if [ "$1" != "-" ]; then mv $EXPORT.tar.gz$TARS/ echo "Generating HTML for [$@]"$ISABELLE_TOOL afp_build -- -v -c $@ || fail "isabelle afp_build failed on [$@]" $ISABELLE_TOOL afp_build -- -v -c -j 2$@ || fail "isabelle afp_build failed on [$@]" cd$EXPORT/thys for ENTRY in \$@; do ... ...
 ... ... @@ -9676,6 +9676,23 @@ abstract = pi for i>k.

[Formal_Puiseux_Series] title = Formal Puiseux Series author = Manuel Eberl topic = Mathematics/Algebra date = 2021-02-17 notify = eberlm@in.tum.de abstract =

Formal Puiseux series are generalisations of formal power series and formal Laurent series that also allow for fractional exponents. They have the following general form: $\sum_{i=N}^\infty a_{i/d} X^{i/d}$ where N is an integer and d is a positive integer.

This entry defines these series including their basic algebraic properties. Furthermore, it proves the Newton–Puiseux Theorem, namely that the Puiseux series over an algebraically closed field of characteristic 0 are also algebraically closed.

[Gaussian_Integers] title = Gaussian Integers author = Manuel Eberl ... ... @@ -10232,8 +10249,8 @@ author = Jakub Kądziołka topic = Logic/General logic/Logics of knowledge and belief date = 2021-01-30 notify = kuba@kadziolka.net abstract = In a puzzle published by abstract = In a puzzle published by Randall Munroe, perfect logicians forbidden from communicating are stranded on an island, and may only leave once they have figured out their own eye color. We present a method of ... ... @@ -10266,3 +10283,29 @@ abstract = used for the proof of the strong law is a particularly quick and slick one based on ergodic theory, which was formalised by Gouëzel in another AFP entry.

[BTree] title = A Verified Imperative Implementation of B-Trees author = Niels Mündler topic = Computer science/Data structures date = 2021-02-24 notify = n.muendler@tum.de abstract = In this work, we use the interactive theorem prover Isabelle/HOL to verify an imperative implementation of the classical B-tree data structure invented by Bayer and McCreight [ACM 1970]. The implementation supports set membership and insertion queries with efficient binary search for intra-node navigation. This is accomplished by first specifying the structure abstractly in the functional modeling language HOL and proving functional correctness. Using manual refinement, we derive an imperative implementation in Imperative/HOL. We show the validity of this refinement using the separation logic utilities from the Isabelle Refinement Framework . The code can be exported to the programming languages SML and Scala. We examine the runtime of all operations indirectly by reproducing results of the logarithmic relationship between height and the number of nodes. The results are discussed in greater detail in the corresponding Bachelor's Thesis.
 ... ... @@ -20,3 +20,4 @@ 2018 = 2018-08-16 2019 = 2019-06-10 2020 = 2020-04-16 2021 = 2021-02-21