diff --git a/haskell-experiments/.direnv/nix-profile-.3928.2c3e5ec5df46 b/haskell-experiments/.direnv/nix-profile-.3928.2c3e5ec5df46
deleted file mode 120000
index fb12d3c..0000000
--- a/haskell-experiments/.direnv/nix-profile-.3928.2c3e5ec5df46
+++ /dev/null
@@ -1 +0,0 @@
-/nix/store/10mznhvw5lmlnm4qk4fxkqf05zapc087-ghc-shell-for-haskell-exps-0.1.0.0-0-env
\ No newline at end of file
diff --git a/haskell-experiments/.direnv/nix-profile-.3928.2c3e5ec5df46.rc b/haskell-experiments/.direnv/nix-profile-.3928.2c3e5ec5df46.rc
deleted file mode 100644
index 30a9bb6..0000000
--- a/haskell-experiments/.direnv/nix-profile-.3928.2c3e5ec5df46.rc
+++ /dev/null
@@ -1,2132 +0,0 @@
-unset shellHook
-PATH=${PATH:-}
-nix_saved_PATH="$PATH"
-XDG_DATA_DIRS=${XDG_DATA_DIRS:-}
-nix_saved_XDG_DATA_DIRS="$XDG_DATA_DIRS"
-AR='ar'
-export AR
-AS='as'
-export AS
-BASH='/nix/store/j8645yndikbrvn292zgvyv64xrrmwdcb-bash-5.3p3/bin/bash'
-CC='gcc'
-export CC
-CONFIG_SHELL='/nix/store/j8645yndikbrvn292zgvyv64xrrmwdcb-bash-5.3p3/bin/bash'
-export CONFIG_SHELL
-CXX='g++'
-export CXX
-HOSTTYPE='x86_64'
-HOST_PATH='/nix/store/kpi3v5fl8hlgy5lagjvn6ayq78mla49k-ncurses-6.5/bin:/nix/store/n8f6dc226f3z0yz8b7yh2ksi5gx70mha-numactl-2.0.18/bin:/nix/store/iiishysy5bzkjrawxl4rld1s04qj0k0c-coreutils-9.8/bin:/nix/store/6hcyzg88adcz37hn5pslwb06ck6pnq07-findutils-4.10.0/bin:/nix/store/7ylvy12ylwy8wxya9i2ly8qkhiz7173r-diffutils-3.12/bin:/nix/store/rm3yhwgahfrmshmcrv6cr28x4rz7881s-gnused-4.9/bin:/nix/store/737jwbhw8ji13x9s88z3wpp8pxaqla92-gnugrep-3.12/bin:/nix/store/gh0ijwnyv6csn59yars8z8kxbnd31y8f-gawk-5.3.2/bin:/nix/store/l5ibq1yp8m7jibzgqbmpc46hkcnvv8fq-gnutar-1.35/bin:/nix/store/0hq8fc3ihp7clficpl72lxybfb23qvfc-gzip-1.14/bin:/nix/store/2xq4b1wjl6yklsqs86mf95lg9j8mbxvl-bzip2-1.0.8-bin/bin:/nix/store/bw02qy5hlr6a12p5f2apkk79204n20yh-gnumake-4.4.1/bin:/nix/store/j8645yndikbrvn292zgvyv64xrrmwdcb-bash-5.3p3/bin:/nix/store/mv1hg02434l28cf4vwg4qbrz2h967ms8-patch-2.8/bin:/nix/store/gq3243j1d8y6qgpcrgbbb0vxkbxzs0ix-xz-5.8.1-bin/bin:/nix/store/30k6wlj854gb3rw7ny2rj3fixn8xrx6p-file-5.45/bin'
-export HOST_PATH
-IFS=' 	
-'
-IN_NIX_SHELL='impure'
-export IN_NIX_SHELL
-LANG='en_US.UTF-8'
-export LANG
-LD='ld'
-export LD
-LINENO='76'
-LOCALE_ARCHIVE='/nix/store/64zw8gswdqli6d5jcklisic0f3xgjjdd-glibc-locales-2.40-66/lib/locale/locale-archive'
-export LOCALE_ARCHIVE
-MACHTYPE='x86_64-pc-linux-gnu'
-NIX_BINTOOLS='/nix/store/4dh4138m8gbp56kh63j2pwgsfhf5l8v7-binutils-wrapper-2.44'
-export NIX_BINTOOLS
-NIX_BINTOOLS_WRAPPER_TARGET_HOST_x86_64_unknown_linux_gnu='1'
-export NIX_BINTOOLS_WRAPPER_TARGET_HOST_x86_64_unknown_linux_gnu
-NIX_BUILD_CORES='24'
-export NIX_BUILD_CORES
-NIX_CC='/nix/store/myvv172x2am72534zgn9wx0qp5amq6a8-gcc-wrapper-14.3.0'
-export NIX_CC
-NIX_CC_WRAPPER_TARGET_HOST_x86_64_unknown_linux_gnu='1'
-export NIX_CC_WRAPPER_TARGET_HOST_x86_64_unknown_linux_gnu
-NIX_CFLAGS_COMPILE=' -frandom-seed=10mznhvw5l'
-export NIX_CFLAGS_COMPILE
-NIX_ENFORCE_NO_NATIVE='1'
-export NIX_ENFORCE_NO_NATIVE
-NIX_GHC='/nix/store/v6yy2qmxn5hnxnrrdy2wvddl4ifbksk0-ghc-9.10.3-with-packages/bin/ghc'
-export NIX_GHC
-NIX_GHCPKG='/nix/store/v6yy2qmxn5hnxnrrdy2wvddl4ifbksk0-ghc-9.10.3-with-packages/bin/ghc-pkg'
-export NIX_GHCPKG
-NIX_GHC_DOCDIR='/nix/store/v6yy2qmxn5hnxnrrdy2wvddl4ifbksk0-ghc-9.10.3-with-packages/share/doc/ghc/html'
-export NIX_GHC_DOCDIR
-NIX_GHC_LIBDIR='/nix/store/v6yy2qmxn5hnxnrrdy2wvddl4ifbksk0-ghc-9.10.3-with-packages/lib/ghc-9.10.3/lib'
-export NIX_GHC_LIBDIR
-NIX_HARDENING_ENABLE='bindnow format fortify fortify3 libcxxhardeningextensive libcxxhardeningfast pic relro stackclashprotection stackprotector strictoverflow zerocallusedregs'
-export NIX_HARDENING_ENABLE
-NIX_LDFLAGS='-rpath /home/felix/projects/pyrites/haskell-experiments/outputs/out/lib  -L/nix/store/kpi3v5fl8hlgy5lagjvn6ayq78mla49k-ncurses-6.5/lib -L/nix/store/c86nvwib4x4w4lkd3qw2aw40a354b6yd-libffi-3.5.2/lib -L/nix/store/v6v4r40nfy7inyr36yckidhi6ngh0k6p-elfutils-0.194/lib -L/nix/store/z658zzyxfc8106bjl5svssvsjvk513yj-gmp-with-cxx-6.3.0/lib -L/nix/store/n8f6dc226f3z0yz8b7yh2ksi5gx70mha-numactl-2.0.18/lib -L/nix/store/kpi3v5fl8hlgy5lagjvn6ayq78mla49k-ncurses-6.5/lib -L/nix/store/c86nvwib4x4w4lkd3qw2aw40a354b6yd-libffi-3.5.2/lib -L/nix/store/v6v4r40nfy7inyr36yckidhi6ngh0k6p-elfutils-0.194/lib -L/nix/store/z658zzyxfc8106bjl5svssvsjvk513yj-gmp-with-cxx-6.3.0/lib -L/nix/store/n8f6dc226f3z0yz8b7yh2ksi5gx70mha-numactl-2.0.18/lib'
-export NIX_LDFLAGS
-NIX_NO_SELF_RPATH='1'
-NIX_STORE='/nix/store'
-export NIX_STORE
-NM='nm'
-export NM
-OBJCOPY='objcopy'
-export OBJCOPY
-OBJDUMP='objdump'
-export OBJDUMP
-OLDPWD=''
-export OLDPWD
-OPTERR='1'
-OSTYPE='linux-gnu'
-PATH='/nix/store/v6yy2qmxn5hnxnrrdy2wvddl4ifbksk0-ghc-9.10.3-with-packages/bin:/nix/store/xpq3c9bhlr1iby8kchf918salbf3zdpj-hspec-discover-2.11.14/bin:/nix/store/pkym0fzf9fn58wbkg41xbsgw83ngv49y-haskell-language-server-2.12.0.0/bin:/nix/store/w0y1r4k85x6a7i65sqmn4gdpb3z73wiv-cabal-install-3.16.0.0/bin:/nix/store/axrdk0z4gwqv9kpql2lgqq42l37m3yd1-patchelf-0.15.2/bin:/nix/store/myvv172x2am72534zgn9wx0qp5amq6a8-gcc-wrapper-14.3.0/bin:/nix/store/m1k4nxs8r0fl0pjxqp5n37vxgms7gdlb-gcc-14.3.0/bin:/nix/store/ijmp8r14ivvzk5r95lwx49bbv089003g-glibc-2.40-66-bin/bin:/nix/store/iiishysy5bzkjrawxl4rld1s04qj0k0c-coreutils-9.8/bin:/nix/store/4dh4138m8gbp56kh63j2pwgsfhf5l8v7-binutils-wrapper-2.44/bin:/nix/store/v9zpzmigqkcjrw1jpf0zjc49y47cm55s-binutils-2.44/bin:/nix/store/kpi3v5fl8hlgy5lagjvn6ayq78mla49k-ncurses-6.5/bin:/nix/store/n8f6dc226f3z0yz8b7yh2ksi5gx70mha-numactl-2.0.18/bin:/nix/store/iiishysy5bzkjrawxl4rld1s04qj0k0c-coreutils-9.8/bin:/nix/store/6hcyzg88adcz37hn5pslwb06ck6pnq07-findutils-4.10.0/bin:/nix/store/7ylvy12ylwy8wxya9i2ly8qkhiz7173r-diffutils-3.12/bin:/nix/store/rm3yhwgahfrmshmcrv6cr28x4rz7881s-gnused-4.9/bin:/nix/store/737jwbhw8ji13x9s88z3wpp8pxaqla92-gnugrep-3.12/bin:/nix/store/gh0ijwnyv6csn59yars8z8kxbnd31y8f-gawk-5.3.2/bin:/nix/store/l5ibq1yp8m7jibzgqbmpc46hkcnvv8fq-gnutar-1.35/bin:/nix/store/0hq8fc3ihp7clficpl72lxybfb23qvfc-gzip-1.14/bin:/nix/store/2xq4b1wjl6yklsqs86mf95lg9j8mbxvl-bzip2-1.0.8-bin/bin:/nix/store/bw02qy5hlr6a12p5f2apkk79204n20yh-gnumake-4.4.1/bin:/nix/store/j8645yndikbrvn292zgvyv64xrrmwdcb-bash-5.3p3/bin:/nix/store/mv1hg02434l28cf4vwg4qbrz2h967ms8-patch-2.8/bin:/nix/store/gq3243j1d8y6qgpcrgbbb0vxkbxzs0ix-xz-5.8.1-bin/bin:/nix/store/30k6wlj854gb3rw7ny2rj3fixn8xrx6p-file-5.45/bin'
-export PATH
-PS4='+ '
-RANLIB='ranlib'
-export RANLIB
-READELF='readelf'
-export READELF
-SHELL='/nix/store/j8645yndikbrvn292zgvyv64xrrmwdcb-bash-5.3p3/bin/bash'
-export SHELL
-SIZE='size'
-export SIZE
-SOURCE_DATE_EPOCH='315532800'
-export SOURCE_DATE_EPOCH
-STRINGS='strings'
-export STRINGS
-STRIP='strip'
-export STRIP
-XDG_DATA_DIRS='/nix/store/v6yy2qmxn5hnxnrrdy2wvddl4ifbksk0-ghc-9.10.3-with-packages/share:/nix/store/w0y1r4k85x6a7i65sqmn4gdpb3z73wiv-cabal-install-3.16.0.0/share:/nix/store/axrdk0z4gwqv9kpql2lgqq42l37m3yd1-patchelf-0.15.2/share'
-export XDG_DATA_DIRS
-__structuredAttrs=''
-export __structuredAttrs
-_substituteStream_has_warned_replace_deprecation='false'
-buildCommandPath='/build/.attr-0l2nkwhif96f51f4amnlf414lhl4rv9vh8iffyp431v6s28gsr90'
-export buildCommandPath
-buildInputs=''
-export buildInputs
-builder='/nix/store/j8645yndikbrvn292zgvyv64xrrmwdcb-bash-5.3p3/bin/bash'
-export builder
-cmakeFlags=''
-export cmakeFlags
-configureFlags=''
-export configureFlags
-defaultBuildInputs=''
-defaultNativeBuildInputs='/nix/store/axrdk0z4gwqv9kpql2lgqq42l37m3yd1-patchelf-0.15.2 /nix/store/wy55v0yk13h90gcv0fffrisks128ziz1-update-autotools-gnu-config-scripts-hook /nix/store/0y5xmdb7qfvimjwbq7ibg1xdgkgjwqng-no-broken-symlinks.sh /nix/store/cv1d7p48379km6a85h4zp6kr86brh32q-audit-tmpdir.sh /nix/store/85clx3b0xkdf58jn161iy80y5223ilbi-compress-man-pages.sh /nix/store/wgrbkkaldkrlrni33ccvm3b6vbxzb656-make-symlinks-relative.sh /nix/store/5yzw0vhkyszf2d179m0qfkgxmp5wjjx4-move-docs.sh /nix/store/fyaryjvghbkpfnsyw97hb3lyb37s1pd6-move-lib64.sh /nix/store/kd4xwxjpjxi71jkm6ka0np72if9rm3y0-move-sbin.sh /nix/store/pag6l61paj1dc9sv15l7bm5c17xn5kyk-move-systemd-user-units.sh /nix/store/cmzya9irvxzlkh7lfy6i82gbp0saxqj3-multiple-outputs.sh /nix/store/x8c40nfigps493a07sdr2pm5s9j1cdc0-patch-shebangs.sh /nix/store/cickvswrvann041nqxb0rxilc46svw1n-prune-libtool-files.sh /nix/store/xyff06pkhki3qy1ls77w10s0v79c9il0-reproducible-builds.sh /nix/store/z7k98578dfzi6l3hsvbivzm7hfqlk0zc-set-source-date-epoch-to-latest.sh /nix/store/pilsssjjdxvdphlg2h19p0bfx5q0jzkn-strip.sh /nix/store/myvv172x2am72534zgn9wx0qp5amq6a8-gcc-wrapper-14.3.0'
-depsBuildBuild=''
-export depsBuildBuild
-depsBuildBuildPropagated=''
-export depsBuildBuildPropagated
-depsBuildTarget=''
-export depsBuildTarget
-depsBuildTargetPropagated=''
-export depsBuildTargetPropagated
-depsHostHost=''
-export depsHostHost
-depsHostHostPropagated=''
-export depsHostHostPropagated
-depsTargetTarget=''
-export depsTargetTarget
-depsTargetTargetPropagated=''
-export depsTargetTargetPropagated
-doCheck=''
-export doCheck
-doInstallCheck=''
-export doInstallCheck
-dontAddDisableDepTrack='1'
-export dontAddDisableDepTrack
-enableParallelBuilding='1'
-export enableParallelBuilding
-enableParallelChecking='1'
-export enableParallelChecking
-enableParallelInstalling='1'
-export enableParallelInstalling
-declare -a envBuildBuildHooks=()
-declare -a envBuildHostHooks=()
-declare -a envBuildTargetHooks=()
-declare -a envHostHostHooks=('ccWrapper_addCVars' 'bintoolsWrapper_addLDVars' )
-declare -a envHostTargetHooks=('ccWrapper_addCVars' 'bintoolsWrapper_addLDVars' )
-declare -a envTargetTargetHooks=()
-declare -a fixupOutputHooks=('if [ -z "${dontPatchELF-}" ]; then patchELF "$prefix"; fi' 'if [[ -z "${noAuditTmpdir-}" && -e "$prefix" ]]; then auditTmpdir "$prefix"; fi' 'if [ -z "${dontGzipMan-}" ]; then compressManPages "$prefix"; fi' '_moveLib64' '_moveSbin' '_moveSystemdUserUnits' 'patchShebangsAuto' '_pruneLibtoolFiles' '_doStrip' )
-initialPath='/nix/store/iiishysy5bzkjrawxl4rld1s04qj0k0c-coreutils-9.8 /nix/store/6hcyzg88adcz37hn5pslwb06ck6pnq07-findutils-4.10.0 /nix/store/7ylvy12ylwy8wxya9i2ly8qkhiz7173r-diffutils-3.12 /nix/store/rm3yhwgahfrmshmcrv6cr28x4rz7881s-gnused-4.9 /nix/store/737jwbhw8ji13x9s88z3wpp8pxaqla92-gnugrep-3.12 /nix/store/gh0ijwnyv6csn59yars8z8kxbnd31y8f-gawk-5.3.2 /nix/store/l5ibq1yp8m7jibzgqbmpc46hkcnvv8fq-gnutar-1.35 /nix/store/0hq8fc3ihp7clficpl72lxybfb23qvfc-gzip-1.14 /nix/store/2xq4b1wjl6yklsqs86mf95lg9j8mbxvl-bzip2-1.0.8-bin /nix/store/bw02qy5hlr6a12p5f2apkk79204n20yh-gnumake-4.4.1 /nix/store/j8645yndikbrvn292zgvyv64xrrmwdcb-bash-5.3p3 /nix/store/mv1hg02434l28cf4vwg4qbrz2h967ms8-patch-2.8 /nix/store/gq3243j1d8y6qgpcrgbbb0vxkbxzs0ix-xz-5.8.1-bin /nix/store/30k6wlj854gb3rw7ny2rj3fixn8xrx6p-file-5.45'
-mesonFlags=''
-export mesonFlags
-name='ghc-shell-for-haskell-exps-0.1.0.0-0-env'
-export name
-nativeBuildInputs='/nix/store/v6yy2qmxn5hnxnrrdy2wvddl4ifbksk0-ghc-9.10.3-with-packages /nix/store/pkym0fzf9fn58wbkg41xbsgw83ngv49y-haskell-language-server-2.12.0.0 /nix/store/w0y1r4k85x6a7i65sqmn4gdpb3z73wiv-cabal-install-3.16.0.0'
-export nativeBuildInputs
-out='/home/felix/projects/pyrites/haskell-experiments/outputs/out'
-export out
-outputBin='out'
-outputDev='out'
-outputDevdoc='REMOVE'
-outputDevman='out'
-outputDoc='out'
-outputInclude='out'
-outputInfo='out'
-outputLib='out'
-outputMan='out'
-outputs='out'
-export outputs
-passAsFile='buildCommand'
-export passAsFile
-patches=''
-export patches
-pkg='/nix/store/myvv172x2am72534zgn9wx0qp5amq6a8-gcc-wrapper-14.3.0'
-declare -a pkgsBuildBuild=()
-declare -a pkgsBuildHost=('/nix/store/v6yy2qmxn5hnxnrrdy2wvddl4ifbksk0-ghc-9.10.3-with-packages' '/nix/store/3if09zz5yh2xp06k74df4ffllcq242v4-hspec-core-2.11.14' '/nix/store/15kpl1k04j2734jpxxn3822yj0l40j4n-ansi-terminal-1.1.3' '/nix/store/hg3dyhm276hkzqbp6grcaryq9db8yiq0-ansi-terminal-types-1.1.3' '/nix/store/86g9qx4iixnzfl2pn14mgfhjrc7ys3bp-colour-2.3.6' '/nix/store/l7wqc6ylsgxnryqq6adxy33f887yff38-call-stack-0.4.0' '/nix/store/8ca4l9p89fnj897pqkhqz8grgv67al3n-haskell-lexer-1.2.1' '/nix/store/y7zpz5zp7sr8fyb8g03hrp1h2nvyg6wl-hspec-expectations-0.8.4' '/nix/store/djlag105fka13zx06xk909grhzzd8sl4-HUnit-1.6.2.0' '/nix/store/vbgfxw3pjdq8k1w71wc0lf7ylp2c85ya-QuickCheck-2.15.0.1' '/nix/store/zpskiivq0xq3k45dcr697fgm2vkydcn1-random-1.2.1.3' '/nix/store/fpk42za9sgq0a2x3waizix007wq2s7m4-splitmix-0.1.3.1' '/nix/store/hq5260px20y1ym58rr8a0w1hfc31gkjd-quickcheck-io-0.2.0' '/nix/store/5l29zzwfq7qkya578zcsbqzm6vqpllrw-tf-random-0.5' '/nix/store/x87fdsm1a9ggy746dlsa21g1qysj0p2x-primitive-0.9.1.0' '/nix/store/xpq3c9bhlr1iby8kchf918salbf3zdpj-hspec-discover-2.11.14' '/nix/store/pkym0fzf9fn58wbkg41xbsgw83ngv49y-haskell-language-server-2.12.0.0' '/nix/store/w0y1r4k85x6a7i65sqmn4gdpb3z73wiv-cabal-install-3.16.0.0' '/nix/store/axrdk0z4gwqv9kpql2lgqq42l37m3yd1-patchelf-0.15.2' '/nix/store/wy55v0yk13h90gcv0fffrisks128ziz1-update-autotools-gnu-config-scripts-hook' '/nix/store/0y5xmdb7qfvimjwbq7ibg1xdgkgjwqng-no-broken-symlinks.sh' '/nix/store/cv1d7p48379km6a85h4zp6kr86brh32q-audit-tmpdir.sh' '/nix/store/85clx3b0xkdf58jn161iy80y5223ilbi-compress-man-pages.sh' '/nix/store/wgrbkkaldkrlrni33ccvm3b6vbxzb656-make-symlinks-relative.sh' '/nix/store/5yzw0vhkyszf2d179m0qfkgxmp5wjjx4-move-docs.sh' '/nix/store/fyaryjvghbkpfnsyw97hb3lyb37s1pd6-move-lib64.sh' '/nix/store/kd4xwxjpjxi71jkm6ka0np72if9rm3y0-move-sbin.sh' '/nix/store/pag6l61paj1dc9sv15l7bm5c17xn5kyk-move-systemd-user-units.sh' '/nix/store/cmzya9irvxzlkh7lfy6i82gbp0saxqj3-multiple-outputs.sh' '/nix/store/x8c40nfigps493a07sdr2pm5s9j1cdc0-patch-shebangs.sh' '/nix/store/cickvswrvann041nqxb0rxilc46svw1n-prune-libtool-files.sh' '/nix/store/xyff06pkhki3qy1ls77w10s0v79c9il0-reproducible-builds.sh' '/nix/store/z7k98578dfzi6l3hsvbivzm7hfqlk0zc-set-source-date-epoch-to-latest.sh' '/nix/store/pilsssjjdxvdphlg2h19p0bfx5q0jzkn-strip.sh' '/nix/store/myvv172x2am72534zgn9wx0qp5amq6a8-gcc-wrapper-14.3.0' '/nix/store/4dh4138m8gbp56kh63j2pwgsfhf5l8v7-binutils-wrapper-2.44' )
-declare -a pkgsBuildTarget=()
-declare -a pkgsHostHost=('/nix/store/kpi3v5fl8hlgy5lagjvn6ayq78mla49k-ncurses-6.5' '/nix/store/c86nvwib4x4w4lkd3qw2aw40a354b6yd-libffi-3.5.2' '/nix/store/v6v4r40nfy7inyr36yckidhi6ngh0k6p-elfutils-0.194' '/nix/store/z658zzyxfc8106bjl5svssvsjvk513yj-gmp-with-cxx-6.3.0' '/nix/store/n8f6dc226f3z0yz8b7yh2ksi5gx70mha-numactl-2.0.18' )
-declare -a pkgsHostTarget=()
-declare -a pkgsTargetTarget=()
-declare -a postFixupHooks=('noBrokenSymlinksInAllOutputs' '_makeSymlinksRelativeInAllOutputs' '_multioutPropagateDev' )
-declare -a postUnpackHooks=('_updateSourceDateEpochFromSourceRoot' )
-declare -a preConfigureHooks=('_multioutConfig' )
-preConfigurePhases=' updateAutotoolsGnuConfigScriptsPhase'
-declare -a preFixupHooks=('_moveToShare' '_multioutDocs' '_multioutDevs' )
-prefix='/home/felix/projects/pyrites/haskell-experiments/outputs/out'
-declare -a propagatedBuildDepFiles=('propagated-build-build-deps' 'propagated-native-build-inputs' 'propagated-build-target-deps' )
-propagatedBuildInputs=''
-export propagatedBuildInputs
-declare -a propagatedHostDepFiles=('propagated-host-host-deps' 'propagated-build-inputs' )
-propagatedNativeBuildInputs=''
-export propagatedNativeBuildInputs
-declare -a propagatedTargetDepFiles=('propagated-target-target-deps' )
-shell='/nix/store/j8645yndikbrvn292zgvyv64xrrmwdcb-bash-5.3p3/bin/bash'
-export shell
-shellHook='unset TEMP TMP TEMPDIR TMPDIR'
-export shellHook
-stdenv='/nix/store/45wimpzmh2rkgagv1r42q9v73cpdfr58-stdenv-linux'
-export stdenv
-strictDeps=''
-export strictDeps
-system='x86_64-linux'
-export system
-declare -a unpackCmdHooks=('_defaultUnpack' )
-_activatePkgs ()
-{
- 
-    local hostOffset targetOffset;
-    local pkg;
-    for hostOffset in "${allPlatOffsets[@]}";
-    do
-        local pkgsVar="${pkgAccumVarVars[hostOffset + 1]}";
-        for targetOffset in "${allPlatOffsets[@]}";
-        do
-            (( hostOffset <= targetOffset )) || continue;
-            local pkgsRef="${pkgsVar}[$targetOffset - $hostOffset]";
-            local pkgsSlice="${!pkgsRef}[@]";
-            for pkg in ${!pkgsSlice+"${!pkgsSlice}"};
-            do
-                activatePackage "$pkg" "$hostOffset" "$targetOffset";
-            done;
-        done;
-    done
-}
-_addRpathPrefix ()
-{
- 
-    if [ "${NIX_NO_SELF_RPATH:-0}" != 1 ]; then
-        export NIX_LDFLAGS="-rpath $1/lib ${NIX_LDFLAGS-}";
-    fi
-}
-_addToEnv ()
-{
- 
-    local depHostOffset depTargetOffset;
-    local pkg;
-    for depHostOffset in "${allPlatOffsets[@]}";
-    do
-        local hookVar="${pkgHookVarVars[depHostOffset + 1]}";
-        local pkgsVar="${pkgAccumVarVars[depHostOffset + 1]}";
-        for depTargetOffset in "${allPlatOffsets[@]}";
-        do
-            (( depHostOffset <= depTargetOffset )) || continue;
-            local hookRef="${hookVar}[$depTargetOffset - $depHostOffset]";
-            if [[ -z "${strictDeps-}" ]]; then
-                local visitedPkgs="";
-                for pkg in "${pkgsBuildBuild[@]}" "${pkgsBuildHost[@]}" "${pkgsBuildTarget[@]}" "${pkgsHostHost[@]}" "${pkgsHostTarget[@]}" "${pkgsTargetTarget[@]}";
-                do
-                    if [[ "$visitedPkgs" = *"$pkg"* ]]; then
-                        continue;
-                    fi;
-                    runHook "${!hookRef}" "$pkg";
-                    visitedPkgs+=" $pkg";
-                done;
-            else
-                local pkgsRef="${pkgsVar}[$depTargetOffset - $depHostOffset]";
-                local pkgsSlice="${!pkgsRef}[@]";
-                for pkg in ${!pkgsSlice+"${!pkgsSlice}"};
-                do
-                    runHook "${!hookRef}" "$pkg";
-                done;
-            fi;
-        done;
-    done
-}
-_allFlags ()
-{
- 
-    export system pname name version;
-    while IFS='' read -r varName; do
-        nixTalkativeLog "@${varName}@ -> ${!varName}";
-        args+=("--subst-var" "$varName");
-    done < <(awk 'BEGIN { for (v in ENVIRON) if (v ~ /^[a-z][a-zA-Z0-9_]*$/) print v }')
-}
-_assignFirst ()
-{
- 
-    local varName="$1";
-    local _var;
-    local REMOVE=REMOVE;
-    shift;
-    for _var in "$@";
-    do
-        if [ -n "${!_var-}" ]; then
-            eval "${varName}"="${_var}";
-            return;
-        fi;
-    done;
-    echo;
-    echo "error: _assignFirst: could not find a non-empty variable whose name to assign to ${varName}.";
-    echo "       The following variables were all unset or empty:";
-    echo "           $*";
-    if [ -z "${out:-}" ]; then
-        echo '       If you do not want an "out" output in your derivation, make sure to define';
-        echo '       the other specific required outputs. This can be achieved by picking one';
-        echo "       of the above as an output.";
-        echo '       You do not have to remove "out" if you want to have a different default';
-        echo '       output, because the first output is taken as a default.';
-        echo;
-    fi;
-    return 1
-}
-_callImplicitHook ()
-{
- 
-    local def="$1";
-    local hookName="$2";
-    if declare -F "$hookName" > /dev/null; then
-        nixTalkativeLog "calling implicit '$hookName' function hook";
-        "$hookName";
-    else
-        if type -p "$hookName" > /dev/null; then
-            nixTalkativeLog "sourcing implicit '$hookName' script hook";
-            source "$hookName";
-        else
-            if [ -n "${!hookName:-}" ]; then
-                nixTalkativeLog "evaling implicit '$hookName' string hook";
-                eval "${!hookName}";
-            else
-                return "$def";
-            fi;
-        fi;
-    fi
-}
-_defaultUnpack ()
-{
- 
-    local fn="$1";
-    local destination;
-    if [ -d "$fn" ]; then
-        destination="$(stripHash "$fn")";
-        if [ -e "$destination" ]; then
-            echo "Cannot copy $fn to $destination: destination already exists!";
-            echo "Did you specify two \"srcs\" with the same \"name\"?";
-            return 1;
-        fi;
-        cp -r --preserve=timestamps --reflink=auto -- "$fn" "$destination";
-    else
-        case "$fn" in 
-            *.tar.xz | *.tar.lzma | *.txz)
-                ( XZ_OPT="--threads=$NIX_BUILD_CORES" xz -d < "$fn";
-                true ) | tar xf - --mode=+w --warning=no-timestamp
-            ;;
-            *.tar | *.tar.* | *.tgz | *.tbz2 | *.tbz)
-                tar xf "$fn" --mode=+w --warning=no-timestamp
-            ;;
-            *)
-                return 1
-            ;;
-        esac;
-    fi
-}
-_doStrip ()
-{
- 
-    local -ra flags=(dontStripHost dontStripTarget);
-    local -ra debugDirs=(stripDebugList stripDebugListTarget);
-    local -ra allDirs=(stripAllList stripAllListTarget);
-    local -ra stripCmds=(STRIP STRIP_FOR_TARGET);
-    local -ra ranlibCmds=(RANLIB RANLIB_FOR_TARGET);
-    stripDebugList=${stripDebugList[*]:-lib lib32 lib64 libexec bin sbin Applications Library/Frameworks};
-    stripDebugListTarget=${stripDebugListTarget[*]:-};
-    stripAllList=${stripAllList[*]:-};
-    stripAllListTarget=${stripAllListTarget[*]:-};
-    local i;
-    for i in ${!stripCmds[@]};
-    do
-        local -n flag="${flags[$i]}";
-        local -n debugDirList="${debugDirs[$i]}";
-        local -n allDirList="${allDirs[$i]}";
-        local -n stripCmd="${stripCmds[$i]}";
-        local -n ranlibCmd="${ranlibCmds[$i]}";
-        if [[ -n "${dontStrip-}" || -n "${flag-}" ]] || ! type -f "${stripCmd-}" 2> /dev/null 1>&2; then
-            continue;
-        fi;
-        stripDirs "$stripCmd" "$ranlibCmd" "$debugDirList" "${stripDebugFlags[*]:--S -p}";
-        stripDirs "$stripCmd" "$ranlibCmd" "$allDirList" "${stripAllFlags[*]:--s -p}";
-    done
-}
-_eval ()
-{
- 
-    if declare -F "$1" > /dev/null 2>&1; then
-        "$@";
-    else
-        eval "$1";
-    fi
-}
-_logHook ()
-{
- 
-    if [[ -z ${NIX_LOG_FD-} ]]; then
-        return;
-    fi;
-    local hookKind="$1";
-    local hookExpr="$2";
-    shift 2;
-    if declare -F "$hookExpr" > /dev/null 2>&1; then
-        nixTalkativeLog "calling '$hookKind' function hook '$hookExpr'" "$@";
-    else
-        if type -p "$hookExpr" > /dev/null; then
-            nixTalkativeLog "sourcing '$hookKind' script hook '$hookExpr'";
-        else
-            if [[ "$hookExpr" != "_callImplicitHook"* ]]; then
-                local exprToOutput;
-                if [[ ${NIX_DEBUG:-0} -ge 5 ]]; then
-                    exprToOutput="$hookExpr";
-                else
-                    local hookExprLine;
-                    while IFS= read -r hookExprLine; do
-                        hookExprLine="${hookExprLine#"${hookExprLine%%[![:space:]]*}"}";
-                        if [[ -n "$hookExprLine" ]]; then
-                            exprToOutput+="$hookExprLine\\n ";
-                        fi;
-                    done <<< "$hookExpr";
-                    exprToOutput="${exprToOutput%%\\n }";
-                fi;
-                nixTalkativeLog "evaling '$hookKind' string hook '$exprToOutput'";
-            fi;
-        fi;
-    fi
-}
-_makeSymlinksRelative ()
-{
- 
-    local symlinkTarget;
-    if [ "${dontRewriteSymlinks-}" ] || [ ! -e "$prefix" ]; then
-        return;
-    fi;
-    while IFS= read -r -d '' f; do
-        symlinkTarget=$(readlink "$f");
-        if [[ "$symlinkTarget"/ != "$prefix"/* ]]; then
-            continue;
-        fi;
-        if [ ! -e "$symlinkTarget" ]; then
-            echo "the symlink $f is broken, it points to $symlinkTarget (which is missing)";
-        fi;
-        echo "rewriting symlink $f to be relative to $prefix";
-        ln -snrf "$symlinkTarget" "$f";
-    done < <(find $prefix -type l -print0)
-}
-_makeSymlinksRelativeInAllOutputs ()
-{
- 
-    local output;
-    for output in $(getAllOutputNames);
-    do
-        prefix="${!output}" _makeSymlinksRelative;
-    done
-}
-_moveLib64 ()
-{
- 
-    if [ "${dontMoveLib64-}" = 1 ]; then
-        return;
-    fi;
-    if [ ! -e "$prefix/lib64" -o -L "$prefix/lib64" ]; then
-        return;
-    fi;
-    echo "moving $prefix/lib64/* to $prefix/lib";
-    mkdir -p $prefix/lib;
-    shopt -s dotglob;
-    for i in $prefix/lib64/*;
-    do
-        mv --no-clobber "$i" $prefix/lib;
-    done;
-    shopt -u dotglob;
-    rmdir $prefix/lib64;
-    ln -s lib $prefix/lib64
-}
-_moveSbin ()
-{
- 
-    if [ "${dontMoveSbin-}" = 1 ]; then
-        return;
-    fi;
-    if [ ! -e "$prefix/sbin" -o -L "$prefix/sbin" ]; then
-        return;
-    fi;
-    echo "moving $prefix/sbin/* to $prefix/bin";
-    mkdir -p $prefix/bin;
-    shopt -s dotglob;
-    for i in $prefix/sbin/*;
-    do
-        mv "$i" $prefix/bin;
-    done;
-    shopt -u dotglob;
-    rmdir $prefix/sbin;
-    ln -s bin $prefix/sbin
-}
-_moveSystemdUserUnits ()
-{
- 
-    if [ "${dontMoveSystemdUserUnits:-0}" = 1 ]; then
-        return;
-    fi;
-    if [ ! -e "${prefix:?}/lib/systemd/user" ]; then
-        return;
-    fi;
-    local source="$prefix/lib/systemd/user";
-    local target="$prefix/share/systemd/user";
-    echo "moving $source/* to $target";
-    mkdir -p "$target";
-    ( shopt -s dotglob;
-    for i in "$source"/*;
-    do
-        mv "$i" "$target";
-    done );
-    rmdir "$source";
-    ln -s "$target" "$source"
-}
-_moveToShare ()
-{
- 
-    if [ -n "$__structuredAttrs" ]; then
-        if [ -z "${forceShare-}" ]; then
-            forceShare=(man doc info);
-        fi;
-    else
-        forceShare=(${forceShare:-man doc info});
-    fi;
-    if [[ -z "$out" ]]; then
-        return;
-    fi;
-    for d in "${forceShare[@]}";
-    do
-        if [ -d "$out/$d" ]; then
-            if [ -d "$out/share/$d" ]; then
-                echo "both $d/ and share/$d/ exist!";
-            else
-                echo "moving $out/$d to $out/share/$d";
-                mkdir -p $out/share;
-                mv $out/$d $out/share/;
-            fi;
-        fi;
-    done
-}
-_multioutConfig ()
-{
- 
-    if [ "$(getAllOutputNames)" = "out" ] || [ -z "${setOutputFlags-1}" ]; then
-        return;
-    fi;
-    if [ -z "${shareDocName:-}" ]; then
-        local confScript="${configureScript:-}";
-        if [ -z "$confScript" ] && [ -x ./configure ]; then
-            confScript=./configure;
-        fi;
-        if [ -f "$confScript" ]; then
-            local shareDocName="$(sed -n "s/^PACKAGE_TARNAME='\(.*\)'$/\1/p" < "$confScript")";
-        fi;
-        if [ -z "$shareDocName" ] || echo "$shareDocName" | grep -q '[^a-zA-Z0-9_-]'; then
-            shareDocName="$(echo "$name" | sed 's/-[^a-zA-Z].*//')";
-        fi;
-    fi;
-    prependToVar configureFlags --bindir="${!outputBin}"/bin --sbindir="${!outputBin}"/sbin --includedir="${!outputInclude}"/include --mandir="${!outputMan}"/share/man --infodir="${!outputInfo}"/share/info --docdir="${!outputDoc}"/share/doc/"${shareDocName}" --libdir="${!outputLib}"/lib --libexecdir="${!outputLib}"/libexec --localedir="${!outputLib}"/share/locale;
-    prependToVar installFlags pkgconfigdir="${!outputDev}"/lib/pkgconfig m4datadir="${!outputDev}"/share/aclocal aclocaldir="${!outputDev}"/share/aclocal
-}
-_multioutDevs ()
-{
- 
-    if [ "$(getAllOutputNames)" = "out" ] || [ -z "${moveToDev-1}" ]; then
-        return;
-    fi;
-    moveToOutput include "${!outputInclude}";
-    moveToOutput lib/pkgconfig "${!outputDev}";
-    moveToOutput share/pkgconfig "${!outputDev}";
-    moveToOutput lib/cmake "${!outputDev}";
-    moveToOutput share/aclocal "${!outputDev}";
-    for f in "${!outputDev}"/{lib,share}/pkgconfig/*.pc;
-    do
-        echo "Patching '$f' includedir to output ${!outputInclude}";
-        sed -i "/^includedir=/s,=\${prefix},=${!outputInclude}," "$f";
-    done
-}
-_multioutDocs ()
-{
- 
-    local REMOVE=REMOVE;
-    moveToOutput share/info "${!outputInfo}";
-    moveToOutput share/doc "${!outputDoc}";
-    moveToOutput share/gtk-doc "${!outputDevdoc}";
-    moveToOutput share/devhelp/books "${!outputDevdoc}";
-    moveToOutput share/man "${!outputMan}";
-    moveToOutput share/man/man3 "${!outputDevman}"
-}
-_multioutPropagateDev ()
-{
- 
-    if [ "$(getAllOutputNames)" = "out" ]; then
-        return;
-    fi;
-    local outputFirst;
-    for outputFirst in $(getAllOutputNames);
-    do
-        break;
-    done;
-    local propagaterOutput="$outputDev";
-    if [ -z "$propagaterOutput" ]; then
-        propagaterOutput="$outputFirst";
-    fi;
-    if [ -z "${propagatedBuildOutputs+1}" ]; then
-        local po_dirty="$outputBin $outputInclude $outputLib";
-        set +o pipefail;
-        propagatedBuildOutputs=`echo "$po_dirty"             | tr -s ' ' '\n' | grep -v -F "$propagaterOutput"             | sort -u | tr '\n' ' ' `;
-        set -o pipefail;
-    fi;
-    if [ -z "$propagatedBuildOutputs" ]; then
-        return;
-    fi;
-    mkdir -p "${!propagaterOutput}"/nix-support;
-    for output in $propagatedBuildOutputs;
-    do
-        echo -n " ${!output}" >> "${!propagaterOutput}"/nix-support/propagated-build-inputs;
-    done
-}
-_nixLogWithLevel ()
-{
- 
-    [[ -z ${NIX_LOG_FD-} || ${NIX_DEBUG:-0} -lt ${1:?} ]] && return 0;
-    local logLevel;
-    case "${1:?}" in 
-        0)
-            logLevel=ERROR
-        ;;
-        1)
-            logLevel=WARN
-        ;;
-        2)
-            logLevel=NOTICE
-        ;;
-        3)
-            logLevel=INFO
-        ;;
-        4)
-            logLevel=TALKATIVE
-        ;;
-        5)
-            logLevel=CHATTY
-        ;;
-        6)
-            logLevel=DEBUG
-        ;;
-        7)
-            logLevel=VOMIT
-        ;;
-        *)
-            echo "_nixLogWithLevel: called with invalid log level: ${1:?}" >&"$NIX_LOG_FD";
-            return 1
-        ;;
-    esac;
-    local callerName="${FUNCNAME[2]}";
-    if [[ $callerName == "_callImplicitHook" ]]; then
-        callerName="${hookName:?}";
-    fi;
-    printf "%s: %s: %s\n" "$logLevel" "$callerName" "${2:?}" >&"$NIX_LOG_FD"
-}
-_overrideFirst ()
-{
- 
-    if [ -z "${!1-}" ]; then
-        _assignFirst "$@";
-    fi
-}
-_pruneLibtoolFiles ()
-{
- 
-    if [ "${dontPruneLibtoolFiles-}" ] || [ ! -e "$prefix" ]; then
-        return;
-    fi;
-    find "$prefix" -type f -name '*.la' -exec grep -q '^# Generated by .*libtool' {} \; -exec grep -q "^old_library=''" {} \; -exec sed -i {} -e "/^dependency_libs='[^']/ c dependency_libs='' #pruned" \;
-}
-_updateSourceDateEpochFromSourceRoot ()
-{
- 
-    if [ -n "$sourceRoot" ]; then
-        updateSourceDateEpoch "$sourceRoot";
-    fi
-}
-activatePackage ()
-{
- 
-    local pkg="$1";
-    local -r hostOffset="$2";
-    local -r targetOffset="$3";
-    (( hostOffset <= targetOffset )) || exit 1;
-    if [ -f "$pkg" ]; then
-        nixTalkativeLog "sourcing setup hook '$pkg'";
-        source "$pkg";
-    fi;
-    if [[ -z "${strictDeps-}" || "$hostOffset" -le -1 ]]; then
-        addToSearchPath _PATH "$pkg/bin";
-    fi;
-    if (( hostOffset <= -1 )); then
-        addToSearchPath _XDG_DATA_DIRS "$pkg/share";
-    fi;
-    if [[ "$hostOffset" -eq 0 && -d "$pkg/bin" ]]; then
-        addToSearchPath _HOST_PATH "$pkg/bin";
-    fi;
-    if [[ -f "$pkg/nix-support/setup-hook" ]]; then
-        nixTalkativeLog "sourcing setup hook '$pkg/nix-support/setup-hook'";
-        source "$pkg/nix-support/setup-hook";
-    fi
-}
-addEnvHooks ()
-{
- 
-    local depHostOffset="$1";
-    shift;
-    local pkgHookVarsSlice="${pkgHookVarVars[$depHostOffset + 1]}[@]";
-    local pkgHookVar;
-    for pkgHookVar in "${!pkgHookVarsSlice}";
-    do
-        eval "${pkgHookVar}s"'+=("$@")';
-    done
-}
-addToSearchPath ()
-{
- 
-    addToSearchPathWithCustomDelimiter ":" "$@"
-}
-addToSearchPathWithCustomDelimiter ()
-{
- 
-    local delimiter="$1";
-    local varName="$2";
-    local dir="$3";
-    if [[ -d "$dir" && "${!varName:+${delimiter}${!varName}${delimiter}}" != *"${delimiter}${dir}${delimiter}"* ]]; then
-        export "${varName}=${!varName:+${!varName}${delimiter}}${dir}";
-    fi
-}
-appendToVar ()
-{
- 
-    local -n nameref="$1";
-    local useArray type;
-    if [ -n "$__structuredAttrs" ]; then
-        useArray=true;
-    else
-        useArray=false;
-    fi;
-    if type=$(declare -p "$1" 2> /dev/null); then
-        case "${type#* }" in 
-            -A*)
-                echo "appendToVar(): ERROR: trying to use appendToVar on an associative array, use variable+=([\"X\"]=\"Y\") instead." 1>&2;
-                return 1
-            ;;
-            -a*)
-                useArray=true
-            ;;
-            *)
-                useArray=false
-            ;;
-        esac;
-    fi;
-    shift;
-    if $useArray; then
-        nameref=(${nameref+"${nameref[@]}"} "$@");
-    else
-        nameref="${nameref-} $*";
-    fi
-}
-auditTmpdir ()
-{
- 
-    local dir="$1";
-    [ -e "$dir" ] || return 0;
-    echo "checking for references to $TMPDIR/ in $dir...";
-    local tmpdir elf_fifo script_fifo;
-    tmpdir="$(mktemp -d)";
-    elf_fifo="$tmpdir/elf";
-    script_fifo="$tmpdir/script";
-    mkfifo "$elf_fifo" "$script_fifo";
-    ( find "$dir" -type f -not -path '*/.build-id/*' -print0 | while IFS= read -r -d '' file; do
-        if isELF "$file"; then
-            printf '%s\0' "$file" 1>&3;
-        else
-            if isScript "$file"; then
-                filename=${file##*/};
-                dir=${file%/*};
-                if [ -e "$dir/.$filename-wrapped" ]; then
-                    printf '%s\0' "$file" 1>&4;
-                fi;
-            fi;
-        fi;
-    done;
-    exec 3>&- 4>&- ) 3> "$elf_fifo" 4> "$script_fifo" & ( xargs -0 -r -P "$NIX_BUILD_CORES" -n 1 sh -c '
-            if { printf :; patchelf --print-rpath "$1"; } | grep -q -F ":$TMPDIR/"; then
-                echo "RPATH of binary $1 contains a forbidden reference to $TMPDIR/"
-                exit 1
-            fi
-        ' _ < "$elf_fifo" ) & local pid_elf=$!;
-    local pid_script;
-    ( xargs -0 -r -P "$NIX_BUILD_CORES" -n 1 sh -c '
-            if grep -q -F "$TMPDIR/" "$1"; then
-                echo "wrapper script $1 contains a forbidden reference to $TMPDIR/"
-                exit 1
-            fi
-        ' _ < "$script_fifo" ) & local pid_script=$!;
-    wait "$pid_elf" || { 
-        echo "Some binaries contain forbidden references to $TMPDIR/. Check the error above!";
-        exit 1
-    };
-    wait "$pid_script" || { 
-        echo "Some scripts contain forbidden references to $TMPDIR/. Check the error above!";
-        exit 1
-    };
-    rm -r "$tmpdir"
-}
-bintoolsWrapper_addLDVars ()
-{
- 
-    local role_post;
-    getHostRoleEnvHook;
-    if [[ -d "$1/lib64" && ! -L "$1/lib64" ]]; then
-        export NIX_LDFLAGS${role_post}+=" -L$1/lib64";
-    fi;
-    if [[ -d "$1/lib" ]]; then
-        local -a glob=($1/lib/lib*);
-        if [ "${#glob[*]}" -gt 0 ]; then
-            export NIX_LDFLAGS${role_post}+=" -L$1/lib";
-        fi;
-    fi
-}
-buildPhase ()
-{
- 
-    runHook preBuild;
-    if [[ -z "${makeFlags-}" && -z "${makefile:-}" && ! ( -e Makefile || -e makefile || -e GNUmakefile ) ]]; then
-        echo "no Makefile or custom buildPhase, doing nothing";
-    else
-        foundMakefile=1;
-        local flagsArray=(${enableParallelBuilding:+-j${NIX_BUILD_CORES}} SHELL="$SHELL");
-        concatTo flagsArray makeFlags makeFlagsArray buildFlags buildFlagsArray;
-        echoCmd 'build flags' "${flagsArray[@]}";
-        make ${makefile:+-f $makefile} "${flagsArray[@]}";
-        unset flagsArray;
-    fi;
-    runHook postBuild
-}
-ccWrapper_addCVars ()
-{
- 
-    local role_post;
-    getHostRoleEnvHook;
-    local found=;
-    if [ -d "$1/include" ]; then
-        export NIX_CFLAGS_COMPILE${role_post}+=" -isystem $1/include";
-        found=1;
-    fi;
-    if [ -d "$1/Library/Frameworks" ]; then
-        export NIX_CFLAGS_COMPILE${role_post}+=" -iframework $1/Library/Frameworks";
-        found=1;
-    fi;
-    if [[ -n "" && -n ${NIX_STORE:-} && -n $found ]]; then
-        local scrubbed="$NIX_STORE/eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee-${1#"$NIX_STORE"/*-}";
-        export NIX_CFLAGS_COMPILE${role_post}+=" -fmacro-prefix-map=$1=$scrubbed";
-    fi
-}
-checkPhase ()
-{
- 
-    runHook preCheck;
-    if [[ -z "${foundMakefile:-}" ]]; then
-        echo "no Makefile or custom checkPhase, doing nothing";
-        runHook postCheck;
-        return;
-    fi;
-    if [[ -z "${checkTarget:-}" ]]; then
-        if make -n ${makefile:+-f $makefile} check > /dev/null 2>&1; then
-            checkTarget="check";
-        else
-            if make -n ${makefile:+-f $makefile} test > /dev/null 2>&1; then
-                checkTarget="test";
-            fi;
-        fi;
-    fi;
-    if [[ -z "${checkTarget:-}" ]]; then
-        echo "no check/test target in ${makefile:-Makefile}, doing nothing";
-    else
-        local flagsArray=(${enableParallelChecking:+-j${NIX_BUILD_CORES}} SHELL="$SHELL");
-        concatTo flagsArray makeFlags makeFlagsArray checkFlags=VERBOSE=y checkFlagsArray checkTarget;
-        echoCmd 'check flags' "${flagsArray[@]}";
-        make ${makefile:+-f $makefile} "${flagsArray[@]}";
-        unset flagsArray;
-    fi;
-    runHook postCheck
-}
-compressManPages ()
-{
- 
-    local dir="$1";
-    if [ -L "$dir"/share ] || [ -L "$dir"/share/man ] || [ ! -d "$dir/share/man" ]; then
-        return;
-    fi;
-    echo "gzipping man pages under $dir/share/man/";
-    find "$dir"/share/man/ -type f -a '!' -regex '.*\.\(bz2\|gz\|xz\)$' -print0 | xargs -0 -n1 -P "$NIX_BUILD_CORES" gzip -n -f;
-    find "$dir"/share/man/ -type l -a '!' -regex '.*\.\(bz2\|gz\|xz\)$' -print0 | sort -z | while IFS= read -r -d '' f; do
-        local target;
-        target="$(readlink -f "$f")";
-        if [ -f "$target".gz ]; then
-            ln -sf "$target".gz "$f".gz && rm "$f";
-        fi;
-    done
-}
-concatStringsSep ()
-{
- 
-    local sep="$1";
-    local name="$2";
-    local type oldifs;
-    if type=$(declare -p "$name" 2> /dev/null); then
-        local -n nameref="$name";
-        case "${type#* }" in 
-            -A*)
-                echo "concatStringsSep(): ERROR: trying to use concatStringsSep on an associative array." 1>&2;
-                return 1
-            ;;
-            -a*)
-                local IFS="$(printf '\036')"
-            ;;
-            *)
-                local IFS=" "
-            ;;
-        esac;
-        local ifs_separated="${nameref[*]}";
-        echo -n "${ifs_separated//"$IFS"/"$sep"}";
-    fi
-}
-concatTo ()
-{
- 
-    local -;
-    set -o noglob;
-    local -n targetref="$1";
-    shift;
-    local arg default name type;
-    for arg in "$@";
-    do
-        IFS="=" read -r name default <<< "$arg";
-        local -n nameref="$name";
-        if [[ -z "${nameref[*]}" && -n "$default" ]]; then
-            targetref+=("$default");
-        else
-            if type=$(declare -p "$name" 2> /dev/null); then
-                case "${type#* }" in 
-                    -A*)
-                        echo "concatTo(): ERROR: trying to use concatTo on an associative array." 1>&2;
-                        return 1
-                    ;;
-                    -a*)
-                        targetref+=("${nameref[@]}")
-                    ;;
-                    *)
-                        if [[ "$name" = *"Array" ]]; then
-                            nixErrorLog "concatTo(): $name is not declared as array, treating as a singleton. This will become an error in future";
-                            targetref+=(${nameref+"${nameref[@]}"});
-                        else
-                            targetref+=(${nameref-});
-                        fi
-                    ;;
-                esac;
-            fi;
-        fi;
-    done
-}
-configurePhase ()
-{
- 
-    runHook preConfigure;
-    : "${configureScript=}";
-    if [[ -z "$configureScript" && -x ./configure ]]; then
-        configureScript=./configure;
-    fi;
-    if [ -z "${dontFixLibtool:-}" ]; then
-        export lt_cv_deplibs_check_method="${lt_cv_deplibs_check_method-pass_all}";
-        local i;
-        find . -iname "ltmain.sh" -print0 | while IFS='' read -r -d '' i; do
-            echo "fixing libtool script $i";
-            fixLibtool "$i";
-        done;
-        CONFIGURE_MTIME_REFERENCE=$(mktemp configure.mtime.reference.XXXXXX);
-        find . -executable -type f -name configure -exec grep -l 'GNU Libtool is free software; you can redistribute it and/or modify' {} \; -exec touch -r {} "$CONFIGURE_MTIME_REFERENCE" \; -exec sed -i s_/usr/bin/file_file_g {} \; -exec touch -r "$CONFIGURE_MTIME_REFERENCE" {} \;;
-        rm -f "$CONFIGURE_MTIME_REFERENCE";
-    fi;
-    if [[ -z "${dontAddPrefix:-}" && -n "$prefix" ]]; then
-        prependToVar configureFlags "${prefixKey:---prefix=}$prefix";
-    fi;
-    if [[ -f "$configureScript" ]]; then
-        if [ -z "${dontAddDisableDepTrack:-}" ]; then
-            if grep -q dependency-tracking "$configureScript"; then
-                prependToVar configureFlags --disable-dependency-tracking;
-            fi;
-        fi;
-        if [ -z "${dontDisableStatic:-}" ]; then
-            if grep -q enable-static "$configureScript"; then
-                prependToVar configureFlags --disable-static;
-            fi;
-        fi;
-        if [ -z "${dontPatchShebangsInConfigure:-}" ]; then
-            patchShebangs --build "$configureScript";
-        fi;
-    fi;
-    if [ -n "$configureScript" ]; then
-        local -a flagsArray;
-        concatTo flagsArray configureFlags configureFlagsArray;
-        echoCmd 'configure flags' "${flagsArray[@]}";
-        $configureScript "${flagsArray[@]}";
-        unset flagsArray;
-    else
-        echo "no configure script, doing nothing";
-    fi;
-    runHook postConfigure
-}
-consumeEntire ()
-{
- 
-    if IFS='' read -r -d '' "$1"; then
-        echo "consumeEntire(): ERROR: Input null bytes, won't process" 1>&2;
-        return 1;
-    fi
-}
-distPhase ()
-{
- 
-    runHook preDist;
-    local flagsArray=();
-    concatTo flagsArray distFlags distFlagsArray distTarget=dist;
-    echo 'dist flags: %q' "${flagsArray[@]}";
-    make ${makefile:+-f $makefile} "${flagsArray[@]}";
-    if [ "${dontCopyDist:-0}" != 1 ]; then
-        mkdir -p "$out/tarballs";
-        cp -pvd ${tarballs[*]:-*.tar.gz} "$out/tarballs";
-    fi;
-    runHook postDist
-}
-dumpVars ()
-{
- 
-    if [[ "${noDumpEnvVars:-0}" != 1 && -d "$NIX_BUILD_TOP" ]]; then
-        local old_umask;
-        old_umask=$(umask);
-        umask 0077;
-        export 2> /dev/null > "$NIX_BUILD_TOP/env-vars";
-        umask "$old_umask";
-    fi
-}
-echoCmd ()
-{
- 
-    printf "%s:" "$1";
-    shift;
-    printf ' %q' "$@";
-    echo
-}
-exitHandler ()
-{
- 
-    exitCode="$?";
-    set +e;
-    if [ -n "${showBuildStats:-}" ]; then
-        read -r -d '' -a buildTimes < <(times);
-        echo "build times:";
-        echo "user time for the shell             ${buildTimes[0]}";
-        echo "system time for the shell           ${buildTimes[1]}";
-        echo "user time for all child processes   ${buildTimes[2]}";
-        echo "system time for all child processes ${buildTimes[3]}";
-    fi;
-    if (( "$exitCode" != 0 )); then
-        runHook failureHook;
-        if [ -n "${succeedOnFailure:-}" ]; then
-            echo "build failed with exit code $exitCode (ignored)";
-            mkdir -p "$out/nix-support";
-            printf "%s" "$exitCode" > "$out/nix-support/failed";
-            exit 0;
-        fi;
-    else
-        runHook exitHook;
-    fi;
-    return "$exitCode"
-}
-findInputs ()
-{
- 
-    local -r pkg="$1";
-    local -r hostOffset="$2";
-    local -r targetOffset="$3";
-    (( hostOffset <= targetOffset )) || exit 1;
-    local varVar="${pkgAccumVarVars[hostOffset + 1]}";
-    local varRef="$varVar[$((targetOffset - hostOffset))]";
-    local var="${!varRef}";
-    unset -v varVar varRef;
-    local varSlice="$var[*]";
-    case " ${!varSlice-} " in 
-        *" $pkg "*)
-            return 0
-        ;;
-    esac;
-    unset -v varSlice;
-    eval "$var"'+=("$pkg")';
-    if ! [ -e "$pkg" ]; then
-        echo "build input $pkg does not exist" 1>&2;
-        exit 1;
-    fi;
-    function mapOffset () 
-    { 
-        local -r inputOffset="$1";
-        local -n outputOffset="$2";
-        if (( inputOffset <= 0 )); then
-            outputOffset=$((inputOffset + hostOffset));
-        else
-            outputOffset=$((inputOffset - 1 + targetOffset));
-        fi
-    };
-    local relHostOffset;
-    for relHostOffset in "${allPlatOffsets[@]}";
-    do
-        local files="${propagatedDepFilesVars[relHostOffset + 1]}";
-        local hostOffsetNext;
-        mapOffset "$relHostOffset" hostOffsetNext;
-        (( -1 <= hostOffsetNext && hostOffsetNext <= 1 )) || continue;
-        local relTargetOffset;
-        for relTargetOffset in "${allPlatOffsets[@]}";
-        do
-            (( "$relHostOffset" <= "$relTargetOffset" )) || continue;
-            local fileRef="${files}[$relTargetOffset - $relHostOffset]";
-            local file="${!fileRef}";
-            unset -v fileRef;
-            local targetOffsetNext;
-            mapOffset "$relTargetOffset" targetOffsetNext;
-            (( -1 <= hostOffsetNext && hostOffsetNext <= 1 )) || continue;
-            [[ -f "$pkg/nix-support/$file" ]] || continue;
-            local pkgNext;
-            read -r -d '' pkgNext < "$pkg/nix-support/$file" || true;
-            for pkgNext in $pkgNext;
-            do
-                findInputs "$pkgNext" "$hostOffsetNext" "$targetOffsetNext";
-            done;
-        done;
-    done
-}
-fixLibtool ()
-{
- 
-    local search_path;
-    for flag in $NIX_LDFLAGS;
-    do
-        case $flag in 
-            -L*)
-                search_path+=" ${flag#-L}"
-            ;;
-        esac;
-    done;
-    sed -i "$1" -e "s^eval \(sys_lib_search_path=\).*^\1'${search_path:-}'^" -e 's^eval sys_lib_.+search_path=.*^^'
-}
-fixupPhase ()
-{
- 
-    local output;
-    for output in $(getAllOutputNames);
-    do
-        if [ -e "${!output}" ]; then
-            chmod -R u+w,u-s,g-s "${!output}";
-        fi;
-    done;
-    runHook preFixup;
-    local output;
-    for output in $(getAllOutputNames);
-    do
-        prefix="${!output}" runHook fixupOutput;
-    done;
-    recordPropagatedDependencies;
-    if [ -n "${setupHook:-}" ]; then
-        mkdir -p "${!outputDev}/nix-support";
-        substituteAll "$setupHook" "${!outputDev}/nix-support/setup-hook";
-    fi;
-    if [ -n "${setupHooks:-}" ]; then
-        mkdir -p "${!outputDev}/nix-support";
-        local hook;
-        for hook in ${setupHooks[@]};
-        do
-            local content;
-            consumeEntire content < "$hook";
-            substituteAllStream content "file '$hook'" >> "${!outputDev}/nix-support/setup-hook";
-            unset -v content;
-        done;
-        unset -v hook;
-    fi;
-    if [ -n "${propagatedUserEnvPkgs[*]:-}" ]; then
-        mkdir -p "${!outputBin}/nix-support";
-        printWords "${propagatedUserEnvPkgs[@]}" > "${!outputBin}/nix-support/propagated-user-env-packages";
-    fi;
-    runHook postFixup
-}
-genericBuild ()
-{
- 
-    export GZIP_NO_TIMESTAMPS=1;
-    if [ -f "${buildCommandPath:-}" ]; then
-        source "$buildCommandPath";
-        return;
-    fi;
-    if [ -n "${buildCommand:-}" ]; then
-        eval "$buildCommand";
-        return;
-    fi;
-    if [ -z "${phases[*]:-}" ]; then
-        phases="${prePhases[*]:-} unpackPhase patchPhase ${preConfigurePhases[*]:-}             configurePhase ${preBuildPhases[*]:-} buildPhase checkPhase             ${preInstallPhases[*]:-} installPhase ${preFixupPhases[*]:-} fixupPhase installCheckPhase             ${preDistPhases[*]:-} distPhase ${postPhases[*]:-}";
-    fi;
-    for curPhase in ${phases[*]};
-    do
-        runPhase "$curPhase";
-    done
-}
-getAllOutputNames ()
-{
- 
-    if [ -n "$__structuredAttrs" ]; then
-        echo "${!outputs[*]}";
-    else
-        echo "$outputs";
-    fi
-}
-getHostRole ()
-{
- 
-    getRole "$hostOffset"
-}
-getHostRoleEnvHook ()
-{
- 
-    getRole "$depHostOffset"
-}
-getRole ()
-{
- 
-    case $1 in 
-        -1)
-            role_post='_FOR_BUILD'
-        ;;
-        0)
-            role_post=''
-        ;;
-        1)
-            role_post='_FOR_TARGET'
-        ;;
-        *)
-            echo "binutils-wrapper-2.44: used as improper sort of dependency" 1>&2;
-            return 1
-        ;;
-    esac
-}
-getTargetRole ()
-{
- 
-    getRole "$targetOffset"
-}
-getTargetRoleEnvHook ()
-{
- 
-    getRole "$depTargetOffset"
-}
-getTargetRoleWrapper ()
-{
- 
-    case $targetOffset in 
-        -1)
-            export NIX_BINTOOLS_WRAPPER_TARGET_BUILD_x86_64_unknown_linux_gnu=1
-        ;;
-        0)
-            export NIX_BINTOOLS_WRAPPER_TARGET_HOST_x86_64_unknown_linux_gnu=1
-        ;;
-        1)
-            export NIX_BINTOOLS_WRAPPER_TARGET_TARGET_x86_64_unknown_linux_gnu=1
-        ;;
-        *)
-            echo "binutils-wrapper-2.44: used as improper sort of dependency" 1>&2;
-            return 1
-        ;;
-    esac
-}
-installCheckPhase ()
-{
- 
-    runHook preInstallCheck;
-    if [[ -z "${foundMakefile:-}" ]]; then
-        echo "no Makefile or custom installCheckPhase, doing nothing";
-    else
-        if [[ -z "${installCheckTarget:-}" ]] && ! make -n ${makefile:+-f $makefile} "${installCheckTarget:-installcheck}" > /dev/null 2>&1; then
-            echo "no installcheck target in ${makefile:-Makefile}, doing nothing";
-        else
-            local flagsArray=(${enableParallelChecking:+-j${NIX_BUILD_CORES}} SHELL="$SHELL");
-            concatTo flagsArray makeFlags makeFlagsArray installCheckFlags installCheckFlagsArray installCheckTarget=installcheck;
-            echoCmd 'installcheck flags' "${flagsArray[@]}";
-            make ${makefile:+-f $makefile} "${flagsArray[@]}";
-            unset flagsArray;
-        fi;
-    fi;
-    runHook postInstallCheck
-}
-installPhase ()
-{
- 
-    runHook preInstall;
-    if [[ -z "${makeFlags-}" && -z "${makefile:-}" && ! ( -e Makefile || -e makefile || -e GNUmakefile ) ]]; then
-        echo "no Makefile or custom installPhase, doing nothing";
-        runHook postInstall;
-        return;
-    else
-        foundMakefile=1;
-    fi;
-    if [ -n "$prefix" ]; then
-        mkdir -p "$prefix";
-    fi;
-    local flagsArray=(${enableParallelInstalling:+-j${NIX_BUILD_CORES}} SHELL="$SHELL");
-    concatTo flagsArray makeFlags makeFlagsArray installFlags installFlagsArray installTargets=install;
-    echoCmd 'install flags' "${flagsArray[@]}";
-    make ${makefile:+-f $makefile} "${flagsArray[@]}";
-    unset flagsArray;
-    runHook postInstall
-}
-isELF ()
-{
- 
-    local fn="$1";
-    local fd;
-    local magic;
-    exec {fd}< "$fn";
-    LANG=C read -r -n 4 -u "$fd" magic;
-    exec {fd}>&-;
-    if [ "$magic" = 'ELF' ]; then
-        return 0;
-    else
-        return 1;
-    fi
-}
-isMachO ()
-{
- 
-    local fn="$1";
-    local fd;
-    local magic;
-    exec {fd}< "$fn";
-    LANG=C read -r -n 4 -u "$fd" magic;
-    exec {fd}>&-;
-    if [[ "$magic" = $(echo -ne "\xfe\xed\xfa\xcf") || "$magic" = $(echo -ne "\xcf\xfa\xed\xfe") ]]; then
-        return 0;
-    else
-        if [[ "$magic" = $(echo -ne "\xfe\xed\xfa\xce") || "$magic" = $(echo -ne "\xce\xfa\xed\xfe") ]]; then
-            return 0;
-        else
-            if [[ "$magic" = $(echo -ne "\xca\xfe\xba\xbe") || "$magic" = $(echo -ne "\xbe\xba\xfe\xca") ]]; then
-                return 0;
-            else
-                return 1;
-            fi;
-        fi;
-    fi
-}
-isScript ()
-{
- 
-    local fn="$1";
-    local fd;
-    local magic;
-    exec {fd}< "$fn";
-    LANG=C read -r -n 2 -u "$fd" magic;
-    exec {fd}>&-;
-    if [[ "$magic" =~ \#! ]]; then
-        return 0;
-    else
-        return 1;
-    fi
-}
-mapOffset ()
-{
- 
-    local -r inputOffset="$1";
-    local -n outputOffset="$2";
-    if (( inputOffset <= 0 )); then
-        outputOffset=$((inputOffset + hostOffset));
-    else
-        outputOffset=$((inputOffset - 1 + targetOffset));
-    fi
-}
-moveToOutput ()
-{
- 
-    local patt="$1";
-    local dstOut="$2";
-    local output;
-    for output in $(getAllOutputNames);
-    do
-        if [ "${!output}" = "$dstOut" ]; then
-            continue;
-        fi;
-        local srcPath;
-        for srcPath in "${!output}"/$patt;
-        do
-            if [ ! -e "$srcPath" ] && [ ! -L "$srcPath" ]; then
-                continue;
-            fi;
-            if [ "$dstOut" = REMOVE ]; then
-                echo "Removing $srcPath";
-                rm -r "$srcPath";
-            else
-                local dstPath="$dstOut${srcPath#${!output}}";
-                echo "Moving $srcPath to $dstPath";
-                if [ -d "$dstPath" ] && [ -d "$srcPath" ]; then
-                    rmdir "$srcPath" --ignore-fail-on-non-empty;
-                    if [ -d "$srcPath" ]; then
-                        mv -t "$dstPath" "$srcPath"/*;
-                        rmdir "$srcPath";
-                    fi;
-                else
-                    mkdir -p "$(readlink -m "$dstPath/..")";
-                    mv "$srcPath" "$dstPath";
-                fi;
-            fi;
-            local srcParent="$(readlink -m "$srcPath/..")";
-            if [ -n "$(find "$srcParent" -maxdepth 0 -type d -empty 2> /dev/null)" ]; then
-                echo "Removing empty $srcParent/ and (possibly) its parents";
-                rmdir -p --ignore-fail-on-non-empty "$srcParent" 2> /dev/null || true;
-            fi;
-        done;
-    done
-}
-nixChattyLog ()
-{
- 
-    _nixLogWithLevel 5 "$*"
-}
-nixDebugLog ()
-{
- 
-    _nixLogWithLevel 6 "$*"
-}
-nixErrorLog ()
-{
- 
-    _nixLogWithLevel 0 "$*"
-}
-nixInfoLog ()
-{
- 
-    _nixLogWithLevel 3 "$*"
-}
-nixLog ()
-{
- 
-    [[ -z ${NIX_LOG_FD-} ]] && return 0;
-    local callerName="${FUNCNAME[1]}";
-    if [[ $callerName == "_callImplicitHook" ]]; then
-        callerName="${hookName:?}";
-    fi;
-    printf "%s: %s\n" "$callerName" "$*" >&"$NIX_LOG_FD"
-}
-nixNoticeLog ()
-{
- 
-    _nixLogWithLevel 2 "$*"
-}
-nixTalkativeLog ()
-{
- 
-    _nixLogWithLevel 4 "$*"
-}
-nixVomitLog ()
-{
- 
-    _nixLogWithLevel 7 "$*"
-}
-nixWarnLog ()
-{
- 
-    _nixLogWithLevel 1 "$*"
-}
-noBrokenSymlinks ()
-{
- 
-    local -r output="${1:?}";
-    local path;
-    local pathParent;
-    local symlinkTarget;
-    local -i numDanglingSymlinks=0;
-    local -i numReflexiveSymlinks=0;
-    local -i numUnreadableSymlinks=0;
-    if [[ ! -e $output ]]; then
-        nixWarnLog "skipping non-existent output $output";
-        return 0;
-    fi;
-    nixInfoLog "running on $output";
-    while IFS= read -r -d '' path; do
-        pathParent="$(dirname "$path")";
-        if ! symlinkTarget="$(readlink "$path")"; then
-            nixErrorLog "the symlink $path is unreadable";
-            numUnreadableSymlinks+=1;
-            continue;
-        fi;
-        if [[ $symlinkTarget == /* ]]; then
-            nixInfoLog "symlink $path points to absolute target $symlinkTarget";
-        else
-            nixInfoLog "symlink $path points to relative target $symlinkTarget";
-            symlinkTarget="$(realpath --no-symlinks --canonicalize-missing "$pathParent/$symlinkTarget")";
-        fi;
-        if [[ $symlinkTarget = "$TMPDIR"/* ]]; then
-            nixErrorLog "the symlink $path points to $TMPDIR directory: $symlinkTarget";
-            numDanglingSymlinks+=1;
-            continue;
-        fi;
-        if [[ $symlinkTarget != "$NIX_STORE"/* ]]; then
-            nixInfoLog "symlink $path points outside the Nix store; ignoring";
-            continue;
-        fi;
-        if [[ $path == "$symlinkTarget" ]]; then
-            nixErrorLog "the symlink $path is reflexive";
-            numReflexiveSymlinks+=1;
-        else
-            if [[ ! -e $symlinkTarget ]]; then
-                nixErrorLog "the symlink $path points to a missing target: $symlinkTarget";
-                numDanglingSymlinks+=1;
-            else
-                nixDebugLog "the symlink $path is irreflexive and points to a target which exists";
-            fi;
-        fi;
-    done < <(find "$output" -type l -print0);
-    if ((numDanglingSymlinks > 0 || numReflexiveSymlinks > 0 || numUnreadableSymlinks > 0)); then
-        nixErrorLog "found $numDanglingSymlinks dangling symlinks, $numReflexiveSymlinks reflexive symlinks and $numUnreadableSymlinks unreadable symlinks";
-        exit 1;
-    fi;
-    return 0
-}
-noBrokenSymlinksInAllOutputs ()
-{
- 
-    if [[ -z ${dontCheckForBrokenSymlinks-} ]]; then
-        for output in $(getAllOutputNames);
-        do
-            noBrokenSymlinks "${!output}";
-        done;
-    fi
-}
-patchELF ()
-{
- 
-    local dir="$1";
-    [ -e "$dir" ] || return 0;
-    echo "shrinking RPATHs of ELF executables and libraries in $dir";
-    local i;
-    while IFS= read -r -d '' i; do
-        if [[ "$i" =~ .build-id ]]; then
-            continue;
-        fi;
-        if ! isELF "$i"; then
-            continue;
-        fi;
-        echo "shrinking $i";
-        patchelf --shrink-rpath "$i" || true;
-    done < <(find "$dir" -type f -print0)
-}
-patchPhase ()
-{
- 
-    runHook prePatch;
-    local -a patchesArray;
-    concatTo patchesArray patches;
-    local -a flagsArray;
-    concatTo flagsArray patchFlags=-p1;
-    for i in "${patchesArray[@]}";
-    do
-        echo "applying patch $i";
-        local uncompress=cat;
-        case "$i" in 
-            *.gz)
-                uncompress="gzip -d"
-            ;;
-            *.bz2)
-                uncompress="bzip2 -d"
-            ;;
-            *.xz)
-                uncompress="xz -d"
-            ;;
-            *.lzma)
-                uncompress="lzma -d"
-            ;;
-        esac;
-        $uncompress < "$i" 2>&1 | patch "${flagsArray[@]}";
-    done;
-    runHook postPatch
-}
-patchShebangs ()
-{
- 
-    local pathName;
-    local update=false;
-    while [[ $# -gt 0 ]]; do
-        case "$1" in 
-            --host)
-                pathName=HOST_PATH;
-                shift
-            ;;
-            --build)
-                pathName=PATH;
-                shift
-            ;;
-            --update)
-                update=true;
-                shift
-            ;;
-            --)
-                shift;
-                break
-            ;;
-            -* | --*)
-                echo "Unknown option $1 supplied to patchShebangs" 1>&2;
-                return 1
-            ;;
-            *)
-                break
-            ;;
-        esac;
-    done;
-    echo "patching script interpreter paths in $@";
-    local f;
-    local oldPath;
-    local newPath;
-    local arg0;
-    local args;
-    local oldInterpreterLine;
-    local newInterpreterLine;
-    if [[ $# -eq 0 ]]; then
-        echo "No arguments supplied to patchShebangs" 1>&2;
-        return 0;
-    fi;
-    local f;
-    while IFS= read -r -d '' f; do
-        isScript "$f" || continue;
-        read -r oldInterpreterLine < "$f" || [ "$oldInterpreterLine" ];
-        read -r oldPath arg0 args <<< "${oldInterpreterLine:2}";
-        if [[ -z "${pathName:-}" ]]; then
-            if [[ -n $strictDeps && $f == "$NIX_STORE"* ]]; then
-                pathName=HOST_PATH;
-            else
-                pathName=PATH;
-            fi;
-        fi;
-        if [[ "$oldPath" == *"/bin/env" ]]; then
-            if [[ $arg0 == "-S" ]]; then
-                arg0=${args%% *};
-                [[ "$args" == *" "* ]] && args=${args#* } || args=;
-                newPath="$(PATH="${!pathName}" type -P "env" || true)";
-                args="-S $(PATH="${!pathName}" type -P "$arg0" || true) $args";
-            else
-                if [[ $arg0 == "-"* || $arg0 == *"="* ]]; then
-                    echo "$f: unsupported interpreter directive \"$oldInterpreterLine\" (set dontPatchShebangs=1 and handle shebang patching yourself)" 1>&2;
-                    exit 1;
-                else
-                    newPath="$(PATH="${!pathName}" type -P "$arg0" || true)";
-                fi;
-            fi;
-        else
-            if [[ -z $oldPath ]]; then
-                oldPath="/bin/sh";
-            fi;
-            newPath="$(PATH="${!pathName}" type -P "$(basename "$oldPath")" || true)";
-            args="$arg0 $args";
-        fi;
-        newInterpreterLine="$newPath $args";
-        newInterpreterLine=${newInterpreterLine%${newInterpreterLine##*[![:space:]]}};
-        if [[ -n "$oldPath" && ( "$update" == true || "${oldPath:0:${#NIX_STORE}}" != "$NIX_STORE" ) ]]; then
-            if [[ -n "$newPath" && "$newPath" != "$oldPath" ]]; then
-                echo "$f: interpreter directive changed from \"$oldInterpreterLine\" to \"$newInterpreterLine\"";
-                escapedInterpreterLine=${newInterpreterLine//\\/\\\\};
-                timestamp=$(stat --printf "%y" "$f");
-                tmpFile=$(mktemp -t patchShebangs.XXXXXXXXXX);
-                sed -e "1 s|.*|#\!$escapedInterpreterLine|" "$f" > "$tmpFile";
-                local restoreReadOnly;
-                if [[ ! -w "$f" ]]; then
-                    chmod +w "$f";
-                    restoreReadOnly=true;
-                fi;
-                cat "$tmpFile" > "$f";
-                rm "$tmpFile";
-                if [[ -n "${restoreReadOnly:-}" ]]; then
-                    chmod -w "$f";
-                fi;
-                touch --date "$timestamp" "$f";
-            fi;
-        fi;
-    done < <(find "$@" -type f -perm -0100 -print0)
-}
-patchShebangsAuto ()
-{
- 
-    if [[ -z "${dontPatchShebangs-}" && -e "$prefix" ]]; then
-        if [[ "$output" != out && "$output" = "$outputDev" ]]; then
-            patchShebangs --build "$prefix";
-        else
-            patchShebangs --host "$prefix";
-        fi;
-    fi
-}
-prependToVar ()
-{
- 
-    local -n nameref="$1";
-    local useArray type;
-    if [ -n "$__structuredAttrs" ]; then
-        useArray=true;
-    else
-        useArray=false;
-    fi;
-    if type=$(declare -p "$1" 2> /dev/null); then
-        case "${type#* }" in 
-            -A*)
-                echo "prependToVar(): ERROR: trying to use prependToVar on an associative array." 1>&2;
-                return 1
-            ;;
-            -a*)
-                useArray=true
-            ;;
-            *)
-                useArray=false
-            ;;
-        esac;
-    fi;
-    shift;
-    if $useArray; then
-        nameref=("$@" ${nameref+"${nameref[@]}"});
-    else
-        nameref="$* ${nameref-}";
-    fi
-}
-printLines ()
-{
- 
-    (( "$#" > 0 )) || return 0;
-    printf '%s\n' "$@"
-}
-printWords ()
-{
- 
-    (( "$#" > 0 )) || return 0;
-    printf '%s ' "$@"
-}
-recordPropagatedDependencies ()
-{
- 
-    declare -ra flatVars=(depsBuildBuildPropagated propagatedNativeBuildInputs depsBuildTargetPropagated depsHostHostPropagated propagatedBuildInputs depsTargetTargetPropagated);
-    declare -ra flatFiles=("${propagatedBuildDepFiles[@]}" "${propagatedHostDepFiles[@]}" "${propagatedTargetDepFiles[@]}");
-    local propagatedInputsIndex;
-    for propagatedInputsIndex in "${!flatVars[@]}";
-    do
-        local propagatedInputsSlice="${flatVars[$propagatedInputsIndex]}[@]";
-        local propagatedInputsFile="${flatFiles[$propagatedInputsIndex]}";
-        [[ -n "${!propagatedInputsSlice}" ]] || continue;
-        mkdir -p "${!outputDev}/nix-support";
-        printWords ${!propagatedInputsSlice} > "${!outputDev}/nix-support/$propagatedInputsFile";
-    done
-}
-runHook ()
-{
- 
-    local hookName="$1";
-    shift;
-    local hooksSlice="${hookName%Hook}Hooks[@]";
-    local hook;
-    for hook in "_callImplicitHook 0 $hookName" ${!hooksSlice+"${!hooksSlice}"};
-    do
-        _logHook "$hookName" "$hook" "$@";
-        _eval "$hook" "$@";
-    done;
-    return 0
-}
-runOneHook ()
-{
- 
-    local hookName="$1";
-    shift;
-    local hooksSlice="${hookName%Hook}Hooks[@]";
-    local hook ret=1;
-    for hook in "_callImplicitHook 1 $hookName" ${!hooksSlice+"${!hooksSlice}"};
-    do
-        _logHook "$hookName" "$hook" "$@";
-        if _eval "$hook" "$@"; then
-            ret=0;
-            break;
-        fi;
-    done;
-    return "$ret"
-}
-runPhase ()
-{
- 
-    local curPhase="$*";
-    if [[ "$curPhase" = unpackPhase && -n "${dontUnpack:-}" ]]; then
-        return;
-    fi;
-    if [[ "$curPhase" = patchPhase && -n "${dontPatch:-}" ]]; then
-        return;
-    fi;
-    if [[ "$curPhase" = configurePhase && -n "${dontConfigure:-}" ]]; then
-        return;
-    fi;
-    if [[ "$curPhase" = buildPhase && -n "${dontBuild:-}" ]]; then
-        return;
-    fi;
-    if [[ "$curPhase" = checkPhase && -z "${doCheck:-}" ]]; then
-        return;
-    fi;
-    if [[ "$curPhase" = installPhase && -n "${dontInstall:-}" ]]; then
-        return;
-    fi;
-    if [[ "$curPhase" = fixupPhase && -n "${dontFixup:-}" ]]; then
-        return;
-    fi;
-    if [[ "$curPhase" = installCheckPhase && -z "${doInstallCheck:-}" ]]; then
-        return;
-    fi;
-    if [[ "$curPhase" = distPhase && -z "${doDist:-}" ]]; then
-        return;
-    fi;
-    showPhaseHeader "$curPhase";
-    dumpVars;
-    local startTime endTime;
-    startTime=$(date +"%s");
-    eval "${!curPhase:-$curPhase}";
-    endTime=$(date +"%s");
-    showPhaseFooter "$curPhase" "$startTime" "$endTime";
-    if [ "$curPhase" = unpackPhase ]; then
-        [ -n "${sourceRoot:-}" ] && chmod +x -- "${sourceRoot}";
-        cd -- "${sourceRoot:-.}";
-    fi
-}
-showPhaseFooter ()
-{
- 
-    local phase="$1";
-    local startTime="$2";
-    local endTime="$3";
-    local delta=$(( endTime - startTime ));
-    (( delta < 30 )) && return;
-    local H=$((delta/3600));
-    local M=$((delta%3600/60));
-    local S=$((delta%60));
-    echo -n "$phase completed in ";
-    (( H > 0 )) && echo -n "$H hours ";
-    (( M > 0 )) && echo -n "$M minutes ";
-    echo "$S seconds"
-}
-showPhaseHeader ()
-{
- 
-    local phase="$1";
-    echo "Running phase: $phase";
-    if [[ -z ${NIX_LOG_FD-} ]]; then
-        return;
-    fi;
-    printf "@nix { \"action\": \"setPhase\", \"phase\": \"%s\" }\n" "$phase" >&"$NIX_LOG_FD"
-}
-stripDirs ()
-{
- 
-    local cmd="$1";
-    local ranlibCmd="$2";
-    local paths="$3";
-    local stripFlags="$4";
-    local excludeFlags=();
-    local pathsNew=;
-    [ -z "$cmd" ] && echo "stripDirs: Strip command is empty" 1>&2 && exit 1;
-    [ -z "$ranlibCmd" ] && echo "stripDirs: Ranlib command is empty" 1>&2 && exit 1;
-    local pattern;
-    if [ -n "${stripExclude:-}" ]; then
-        for pattern in "${stripExclude[@]}";
-        do
-            excludeFlags+=(-a '!' '(' -name "$pattern" -o -wholename "$prefix/$pattern" ')');
-        done;
-    fi;
-    local p;
-    for p in ${paths};
-    do
-        if [ -e "$prefix/$p" ]; then
-            pathsNew="${pathsNew} $prefix/$p";
-        fi;
-    done;
-    paths=${pathsNew};
-    if [ -n "${paths}" ]; then
-        echo "stripping (with command $cmd and flags $stripFlags) in $paths";
-        local striperr;
-        striperr="$(mktemp --tmpdir="$TMPDIR" 'striperr.XXXXXX')";
-        find $paths -type f "${excludeFlags[@]}" -a '!' -path "$prefix/lib/debug/*" -printf '%D-%i,%p\0' | sort -t, -k1,1 -u -z | cut -d, -f2- -z | xargs -r -0 -n1 -P "$NIX_BUILD_CORES" -- $cmd $stripFlags 2> "$striperr" || exit_code=$?;
-        [[ "$exit_code" = 123 || -z "$exit_code" ]] || ( cat "$striperr" 1>&2 && exit 1 );
-        rm "$striperr";
-        find $paths -name '*.a' -type f -exec $ranlibCmd '{}' \; 2> /dev/null;
-    fi
-}
-stripHash ()
-{
- 
-    local strippedName casematchOpt=0;
-    strippedName="$(basename -- "$1")";
-    shopt -q nocasematch && casematchOpt=1;
-    shopt -u nocasematch;
-    if [[ "$strippedName" =~ ^[a-z0-9]{32}- ]]; then
-        echo "${strippedName:33}";
-    else
-        echo "$strippedName";
-    fi;
-    if (( casematchOpt )); then
-        shopt -s nocasematch;
-    fi
-}
-substitute ()
-{
- 
-    local input="$1";
-    local output="$2";
-    shift 2;
-    if [ ! -f "$input" ]; then
-        echo "substitute(): ERROR: file '$input' does not exist" 1>&2;
-        return 1;
-    fi;
-    local content;
-    consumeEntire content < "$input";
-    if [ -e "$output" ]; then
-        chmod +w "$output";
-    fi;
-    substituteStream content "file '$input'" "$@" > "$output"
-}
-substituteAll ()
-{
- 
-    local input="$1";
-    local output="$2";
-    local -a args=();
-    _allFlags;
-    substitute "$input" "$output" "${args[@]}"
-}
-substituteAllInPlace ()
-{
- 
-    local fileName="$1";
-    shift;
-    substituteAll "$fileName" "$fileName" "$@"
-}
-substituteAllStream ()
-{
- 
-    local -a args=();
-    _allFlags;
-    substituteStream "$1" "$2" "${args[@]}"
-}
-substituteInPlace ()
-{
- 
-    local -a fileNames=();
-    for arg in "$@";
-    do
-        if [[ "$arg" = "--"* ]]; then
-            break;
-        fi;
-        fileNames+=("$arg");
-        shift;
-    done;
-    if ! [[ "${#fileNames[@]}" -gt 0 ]]; then
-        echo "substituteInPlace called without any files to operate on (files must come before options!)" 1>&2;
-        return 1;
-    fi;
-    for file in "${fileNames[@]}";
-    do
-        substitute "$file" "$file" "$@";
-    done
-}
-substituteStream ()
-{
- 
-    local var=$1;
-    local description=$2;
-    shift 2;
-    while (( "$#" )); do
-        local replace_mode="$1";
-        case "$1" in 
-            --replace)
-                if ! "$_substituteStream_has_warned_replace_deprecation"; then
-                    echo "substituteStream() in derivation $name: WARNING: '--replace' is deprecated, use --replace-{fail,warn,quiet}. ($description)" 1>&2;
-                    _substituteStream_has_warned_replace_deprecation=true;
-                fi;
-                replace_mode='--replace-warn'
-            ;&
-            --replace-quiet | --replace-warn | --replace-fail)
-                pattern="$2";
-                replacement="$3";
-                shift 3;
-                if ! [[ "${!var}" == *"$pattern"* ]]; then
-                    if [ "$replace_mode" == --replace-warn ]; then
-                        printf "substituteStream() in derivation $name: WARNING: pattern %q doesn't match anything in %s\n" "$pattern" "$description" 1>&2;
-                    else
-                        if [ "$replace_mode" == --replace-fail ]; then
-                            printf "substituteStream() in derivation $name: ERROR: pattern %q doesn't match anything in %s\n" "$pattern" "$description" 1>&2;
-                            return 1;
-                        fi;
-                    fi;
-                fi;
-                eval "$var"'=${'"$var"'//"$pattern"/"$replacement"}'
-            ;;
-            --subst-var)
-                local varName="$2";
-                shift 2;
-                if ! [[ "$varName" =~ ^[a-zA-Z_][a-zA-Z0-9_]*$ ]]; then
-                    echo "substituteStream() in derivation $name: ERROR: substitution variables must be valid Bash names, \"$varName\" isn't." 1>&2;
-                    return 1;
-                fi;
-                if [ -z ${!varName+x} ]; then
-                    echo "substituteStream() in derivation $name: ERROR: variable \$$varName is unset" 1>&2;
-                    return 1;
-                fi;
-                pattern="@$varName@";
-                replacement="${!varName}";
-                eval "$var"'=${'"$var"'//"$pattern"/"$replacement"}'
-            ;;
-            --subst-var-by)
-                pattern="@$2@";
-                replacement="$3";
-                eval "$var"'=${'"$var"'//"$pattern"/"$replacement"}';
-                shift 3
-            ;;
-            *)
-                echo "substituteStream() in derivation $name: ERROR: Invalid command line argument: $1" 1>&2;
-                return 1
-            ;;
-        esac;
-    done;
-    printf "%s" "${!var}"
-}
-unpackFile ()
-{
- 
-    curSrc="$1";
-    echo "unpacking source archive $curSrc";
-    if ! runOneHook unpackCmd "$curSrc"; then
-        echo "do not know how to unpack source archive $curSrc";
-        exit 1;
-    fi
-}
-unpackPhase ()
-{
- 
-    runHook preUnpack;
-    if [ -z "${srcs:-}" ]; then
-        if [ -z "${src:-}" ]; then
-            echo 'variable $src or $srcs should point to the source';
-            exit 1;
-        fi;
-        srcs="$src";
-    fi;
-    local -a srcsArray;
-    concatTo srcsArray srcs;
-    local dirsBefore="";
-    for i in *;
-    do
-        if [ -d "$i" ]; then
-            dirsBefore="$dirsBefore $i ";
-        fi;
-    done;
-    for i in "${srcsArray[@]}";
-    do
-        unpackFile "$i";
-    done;
-    : "${sourceRoot=}";
-    if [ -n "${setSourceRoot:-}" ]; then
-        runOneHook setSourceRoot;
-    else
-        if [ -z "$sourceRoot" ]; then
-            for i in *;
-            do
-                if [ -d "$i" ]; then
-                    case $dirsBefore in 
-                        *\ $i\ *)
-
-                        ;;
-                        *)
-                            if [ -n "$sourceRoot" ]; then
-                                echo "unpacker produced multiple directories";
-                                exit 1;
-                            fi;
-                            sourceRoot="$i"
-                        ;;
-                    esac;
-                fi;
-            done;
-        fi;
-    fi;
-    if [ -z "$sourceRoot" ]; then
-        echo "unpacker appears to have produced no directories";
-        exit 1;
-    fi;
-    echo "source root is $sourceRoot";
-    if [ "${dontMakeSourcesWritable:-0}" != 1 ]; then
-        chmod -R u+w -- "$sourceRoot";
-    fi;
-    runHook postUnpack
-}
-updateAutotoolsGnuConfigScriptsPhase ()
-{
- 
-    if [ -n "${dontUpdateAutotoolsGnuConfigScripts-}" ]; then
-        return;
-    fi;
-    for script in config.sub config.guess;
-    do
-        for f in $(find . -type f -name "$script");
-        do
-            echo "Updating Autotools / GNU config script to a newer upstream version: $f";
-            cp -f "/nix/store/yhwnzyhfqd9ficmxmbbryp2s8ymkzmdf-gnu-config-2024-01-01/$script" "$f";
-        done;
-    done
-}
-updateSourceDateEpoch ()
-{
- 
-    local path="$1";
-    [[ $path == -* ]] && path="./$path";
-    local -a res=($(find "$path" -type f -not -newer "$NIX_BUILD_TOP/.." -printf '%T@ "%p"\0' | sort -n --zero-terminated | tail -n1 --zero-terminated | head -c -1));
-    local time="${res[0]//\.[0-9]*/}";
-    local newestFile="${res[1]}";
-    if [ "${time:-0}" -gt "$SOURCE_DATE_EPOCH" ]; then
-        echo "setting SOURCE_DATE_EPOCH to timestamp $time of file $newestFile";
-        export SOURCE_DATE_EPOCH="$time";
-        local now="$(date +%s)";
-        if [ "$time" -gt $((now - 60)) ]; then
-            echo "warning: file $newestFile may be generated; SOURCE_DATE_EPOCH may be non-deterministic";
-        fi;
-    fi
-}
-PATH="$PATH${nix_saved_PATH:+:$nix_saved_PATH}"
-XDG_DATA_DIRS="$XDG_DATA_DIRS${nix_saved_XDG_DATA_DIRS:+:$nix_saved_XDG_DATA_DIRS}"
-export NIX_BUILD_TOP="$(mktemp -d -t nix-shell.XXXXXX)"
-export TMP="$NIX_BUILD_TOP"
-export TMPDIR="$NIX_BUILD_TOP"
-export TEMP="$NIX_BUILD_TOP"
-export TEMPDIR="$NIX_BUILD_TOP"
-eval "${shellHook:-}"
diff --git a/haskell-experiments/.gitignore b/haskell-experiments/.gitignore
new file mode 100644
index 0000000..9b42106
--- /dev/null
+++ b/haskell-experiments/.gitignore
@@ -0,0 +1 @@
+.direnv/
diff --git a/twelf-experiments/peano/README.md b/twelf-experiments/peano/README.md
new file mode 100644
index 0000000..f76bfdf
--- /dev/null
+++ b/twelf-experiments/peano/README.md
@@ -0,0 +1,279 @@
+# Peano Arithmetic in Twelf
+
+This directory contains a formalization of Peano arithmetic and basic number theory in Twelf, including definitions, proofs of fundamental properties, and statements of advanced theorems.
+
+## Quick Start
+
+### Loading All Files
+
+Using the Twelf server interactively:
+
+```bash
+twelf-server
+```
+
+Then at the Twelf prompt:
+
+```
+loadFile nat.elf
+loadFile add.elf
+loadFile mult.elf
+loadFile exp.elf
+loadFile order.elf
+loadFile div.elf
+loadFile prime.elf
+loadFile theorems.elf
+```
+
+Or load all files at once with a script:
+
+```bash
+twelf-server <<'EOF'
+loadFile nat.elf
+loadFile add.elf
+loadFile mult.elf
+loadFile exp.elf
+loadFile order.elf
+loadFile div.elf
+loadFile prime.elf
+loadFile theorems.elf
+EOF
+```
+
+### Running Computations
+
+Once files are loaded, you can compute with `%solve`:
+
+```
+%solve _ : add (s (s z)) (s (s (s z))) N.   -- 2 + 3 = ?
+%solve _ : mult (s (s z)) (s (s (s z))) N.  -- 2 * 3 = ?
+%solve _ : exp (s (s z)) (s (s (s z))) N.   -- 2^3 = ?
+%solve _ : factorial (s (s (s (s z)))) N.   -- 4! = ?
+```
+
+## File Structure
+
+Files must be loaded in order due to dependencies:
+
+| File | Description | Dependencies |
+|------|-------------|--------------|
+| `nat.elf` | Natural numbers (Peano axioms), equality | none |
+| `add.elf` | Addition, commutativity, associativity | nat.elf |
+| `mult.elf` | Multiplication, basic properties | nat.elf, add.elf |
+| `exp.elf` | Exponentiation | nat.elf, add.elf, mult.elf |
+| `order.elf` | Less-than, less-equal, trichotomy | nat.elf |
+| `div.elf` | Divisibility, GCD, division with remainder | nat.elf, add.elf, mult.elf, order.elf |
+| `prime.elf` | Primes, factorial, prime factorization | all above |
+| `theorems.elf` | Computational tests, theorem summary | all above |
+| `sources.cfg` | Configuration file for batch loading | - |
+
+## Definitions
+
+### Natural Numbers (`nat.elf`)
+
+```
+nat : type.
+z : nat.              -- zero
+s : nat -> nat.       -- successor
+```
+
+Numbers: `z` = 0, `s z` = 1, `s (s z)` = 2, etc.
+
+Abbreviations: `one`, `two`, `three`, `four`, `five`
+
+### Addition (`add.elf`)
+
+```
+add : nat -> nat -> nat -> type.
+add/z : add z N N.                        -- 0 + N = N
+add/s : add (s M) N (s P) <- add M N P.   -- (1+M) + N = 1 + (M + N)
+```
+
+### Multiplication (`mult.elf`)
+
+```
+mult : nat -> nat -> nat -> type.
+mult/z : mult z N z.                              -- 0 * N = 0
+mult/s : mult (s M) N R <- mult M N P <- add N P R.  -- (1+M) * N = N + M*N
+```
+
+### Exponentiation (`exp.elf`)
+
+```
+exp : nat -> nat -> nat -> type.
+exp/z : exp N z (s z).                            -- N^0 = 1
+exp/s : exp N (s M) R <- exp N M P <- mult N P R. -- N^(1+M) = N * N^M
+```
+
+### Ordering (`order.elf`)
+
+```
+lt : nat -> nat -> type.   -- less than
+lt/z : lt z (s N).                      -- 0 < 1+N
+lt/s : lt (s M) (s N) <- lt M N.        -- M < N implies 1+M < 1+N
+
+le : nat -> nat -> type.   -- less than or equal
+le/z : le z N.                          -- 0 <= N
+le/s : le (s M) (s N) <- le M N.        -- M <= N implies 1+M <= 1+N
+```
+
+### Divisibility (`div.elf`)
+
+```
+divides : nat -> nat -> type.
+divides/intro : divides D N <- mult D K N.  -- D | N iff N = D * K for some K
+```
+
+### Primes (`prime.elf`)
+
+```
+prime : nat -> type.
+prime/two   : prime (s (s z)).         -- 2 is prime
+prime/three : prime (s (s (s z))).     -- 3 is prime
+prime/five  : prime (s (s (s (s (s z))))).  -- 5 is prime
+prime/seven : prime (s (s (s (s (s (s (s z))))))).  -- 7 is prime
+```
+
+## Verified Theorems
+
+These theorems have complete proofs checked by Twelf's totality checker (`%total`):
+
+### Addition Properties
+- **add-total**: Addition always produces a result
+- **add-comm**: M + N = N + M (commutativity)
+- **add-assoc**: (A + B) + C = A + (B + C) (associativity)
+- **add-right-z**: N + 0 = N (right identity)
+- **add-right-s**: M + (S N) = S(M + N)
+- **add-cancel-left**: A + B = A + C implies B = C (left cancellation)
+- **add-func**: Addition is deterministic
+
+### Multiplication Properties
+- **mult-total**: Multiplication always produces a result
+- **mult-right-z**: N * 0 = 0
+- **mult-left-one**: 1 * N = N
+- **mult-right-one**: N * 1 = N
+
+### Exponentiation Properties
+- **exp-total**: Exponentiation always produces a result
+- **exp-one**: N^1 = N
+- **exp-base-one**: 1^N = 1
+- **exp-base-zero**: 0^(S N) = 0
+
+### Order Properties
+- **le-refl**: N <= N (reflexivity)
+- **le-trans**: A <= B and B <= C implies A <= C (transitivity)
+- **le-antisym**: A <= B and B <= A implies A = B (antisymmetry)
+- **lt-trans**: A < B and B < C implies A < C
+- **trichotomy-total**: For all M, N: exactly one of M < N, M = N, M > N
+
+### Divisibility Properties
+- **one-divides**: 1 | N for all N
+- **divides-zero**: N | 0 for all N
+- **divides-refl**: N | N for all N
+
+### Factorial
+- **factorial-total**: Factorial always produces a result
+
+## Theorems Stated But Not Fully Proven
+
+The following theorems are stated with proof sketches but require additional infrastructure:
+
+### Multiplication Commutativity
+- **mult-comm**: M * N = N * M
+- Requires the `mult-right-s` lemma (M * (S N) = M + M * N)
+
+### Distributivity
+- **mult-distrib-left**: A * (B + C) = A*B + A*C
+- Provable by induction on A
+
+### Multiplication Associativity
+- **mult-assoc**: (A * B) * C = A * (B * C)
+- Requires distributivity
+
+### Number Theory
+- **has-prime-divisor-total**: Every N > 1 has a prime divisor
+- **infinitude-of-primes**: For any prime P, there exists a prime Q > P
+- **euclid-lemma**: If P is prime and P | AB, then P | A or P | B
+- **fundamental-theorem-existence**: Every N > 1 has a prime factorization
+- **fundamental-theorem-uniqueness**: Prime factorization is unique up to ordering
+
+## How Twelf Proofs Work
+
+Twelf uses the "judgments as types" methodology. A theorem is represented as a type family, and its proof is a term of that type.
+
+### Example: Addition Commutativity
+
+```
+add-comm : add M N P -> add N M P -> type.
+%mode add-comm +D1 -D2.
+```
+
+This declares that `add-comm` takes a derivation `D1` showing `add M N P` and produces a derivation `D2` showing `add N M P`.
+
+The `%mode` declaration specifies that `D1` is an input (+) and `D2` is an output (-).
+
+### Totality Checking
+
+```
+%worlds () (add-comm _ _).
+%total D (add-comm D _).
+```
+
+- `%worlds ()` declares the proof works in the empty world (no hypothetical assumptions)
+- `%total D (add-comm D _)` verifies the proof terminates and covers all cases, with recursion on `D`
+
+## Understanding the Output
+
+When you run `%solve`, Twelf shows the derivation tree:
+
+```
+%solve _ : add two three N.
+```
+
+Output:
+```
+add (s (s z)) (s (s (s z))) (s (s (s (s (s z)))))
+   = add/s (add/s add/z).
+```
+
+This shows:
+- The result: 2 + 3 = 5
+- The proof: apply `add/s` twice, then `add/z`
+
+## Extending This Formalization
+
+### Adding New Theorems
+
+1. Identify what lemmas are needed
+2. Define the theorem type with appropriate mode
+3. Write cases for each constructor
+4. Add `%worlds` and `%total` declarations
+
+### Common Patterns
+
+**Induction on a natural number:**
+```
+my-theorem : {N:nat} ... -> type.
+%mode my-theorem +N ...
+my-theorem/z : my-theorem z ...
+my-theorem/s : my-theorem (s N) ... <- my-theorem N ...
+%worlds () (my-theorem _ _).
+%total N (my-theorem N _).
+```
+
+**Induction on a derivation:**
+```
+my-theorem : some-relation A B -> another-relation A B -> type.
+%mode my-theorem +D1 -D2.
+my-theorem/case1 : my-theorem some-relation/c1 another-relation/c1.
+my-theorem/case2 : my-theorem (some-relation/c2 D) (another-relation/c2 D')
+                    <- my-theorem D D'.
+%worlds () (my-theorem _ _).
+%total D (my-theorem D _).
+```
+
+## References
+
+- [Twelf Wiki](http://twelf.org/wiki/Main_Page)
+- [Twelf User's Guide](http://twelf.org/wiki/User%27s_Guide)
+- Harper & Licata, "Mechanizing Metatheory in a Logical Framework"
diff --git a/twelf-experiments/peano/add.elf b/twelf-experiments/peano/add.elf
new file mode 100644
index 0000000..e3258e4
--- /dev/null
+++ b/twelf-experiments/peano/add.elf
@@ -0,0 +1,122 @@
+%% add.elf - Addition on Natural Numbers
+%%
+%% Addition is defined recursively:
+%%   0 + N = N
+%%   (S M) + N = S (M + N)
+
+add : nat -> nat -> nat -> type.
+%mode add +N +M -R.
+
+add/z : add z N N.
+add/s : add (s M) N (s P)
+         <- add M N P.
+
+%% Addition is total (always produces a result)
+add-total : {M:nat} {N:nat} add M N P -> type.
+%mode add-total +M +N -D.
+add-total/z : add-total z N add/z.
+add-total/s : add-total (s M) N (add/s D)
+               <- add-total M N D.
+%worlds () (add-total _ _ _).
+%total M (add-total M _ _).
+
+%% ============================================================
+%% LEMMAS FOR COMMUTATIVITY
+%% ============================================================
+
+%% Right identity: N + 0 = N
+add-right-z : {N:nat} add N z N -> type.
+%mode add-right-z +N -D.
+add-right-z/z : add-right-z z add/z.
+add-right-z/s : add-right-z (s N) (add/s D)
+                 <- add-right-z N D.
+%worlds () (add-right-z _ _).
+%total N (add-right-z N _).
+
+%% Right successor: M + (S N) = S (M + N)
+%% If add M N P, then add M (s N) (s P)
+add-right-s : add M N P -> add M (s N) (s P) -> type.
+%mode add-right-s +D1 -D2.
+add-right-s/z : add-right-s add/z add/z.
+add-right-s/s : add-right-s (add/s D1) (add/s D2)
+                 <- add-right-s D1 D2.
+%worlds () (add-right-s _ _).
+%total D (add-right-s D _).
+
+%% ============================================================
+%% COMMUTATIVITY OF ADDITION
+%% ============================================================
+
+%% Main theorem: M + N = N + M
+%% If add M N P, then add N M P
+add-comm : add M N P -> add N M P -> type.
+%mode add-comm +D1 -D2.
+
+add-comm/z : add-comm add/z D
+              <- add-right-z _ D.
+
+add-comm/s : add-comm (add/s D1) D3
+              <- add-comm D1 D2
+              <- add-right-s D2 D3.
+
+%worlds () (add-comm _ _).
+%total D (add-comm D _).
+
+%% ============================================================
+%% ASSOCIATIVITY OF ADDITION
+%% ============================================================
+
+%% Associativity using output factoring
+%% We prove: forall A B C AB ABC. add A B AB -> add AB C ABC ->
+%%           exists BC. add B C BC /\ add A BC ABC
+%%
+%% This formulation allows Twelf to find BC as an output.
+
+add-assoc : add A B AB -> add AB C ABC -> add B C BC -> add A BC ABC -> type.
+%mode add-assoc +D1 +D2 -D3 -D4.
+
+add-assoc/z : add-assoc add/z D D add/z.
+
+add-assoc/s : add-assoc (add/s D1) (add/s D2) D3 (add/s D4)
+               <- add-assoc D1 D2 D3 D4.
+
+%worlds () (add-assoc _ _ _ _).
+%total D (add-assoc D _ _ _).
+
+%% ============================================================
+%% CANCELLATION LAWS
+%% ============================================================
+
+%% Left cancellation: if A + B = A + C then B = C
+add-cancel-left : add A B R -> add A C R -> nat-eq B C -> type.
+%mode add-cancel-left +D1 +D2 -E.
+
+add-cancel-left/z : add-cancel-left add/z add/z nat-eq/refl.
+add-cancel-left/s : add-cancel-left (add/s D1) (add/s D2) E
+                     <- add-cancel-left D1 D2 E.
+
+%worlds () (add-cancel-left _ _ _).
+%total D (add-cancel-left D _ _).
+
+%% ============================================================
+%% FUNCTIONALITY (Determinism)
+%% ============================================================
+
+%% Helper: equality lifts through successor
+nat-eq-s : nat-eq M N -> nat-eq (s M) (s N) -> type.
+%mode nat-eq-s +E1 -E2.
+nat-eq-s/refl : nat-eq-s nat-eq/refl nat-eq/refl.
+%worlds () (nat-eq-s _ _).
+%total {} (nat-eq-s _ _).
+
+%% Addition is functional: if add M N P and add M N Q then P = Q
+add-func : add M N P -> add M N Q -> nat-eq P Q -> type.
+%mode add-func +D1 +D2 -E.
+
+add-func/z : add-func add/z add/z nat-eq/refl.
+add-func/s : add-func (add/s D1) (add/s D2) E'
+              <- add-func D1 D2 E
+              <- nat-eq-s E E'.
+
+%worlds () (add-func _ _ _).
+%total D (add-func D _ _).
diff --git a/twelf-experiments/peano/div.elf b/twelf-experiments/peano/div.elf
new file mode 100644
index 0000000..3c0931f
--- /dev/null
+++ b/twelf-experiments/peano/div.elf
@@ -0,0 +1,103 @@
+%% div.elf - Divisibility on Natural Numbers
+%%
+%% We define:
+%%   - divides D N: D divides N (D | N), meaning N = D * K for some K
+
+%% ============================================================
+%% DIVISIBILITY
+%% ============================================================
+
+%% D divides N if there exists K such that D * K = N
+divides : nat -> nat -> type.
+
+divides/intro : divides D N
+                 <- mult D K N.
+
+%% ============================================================
+%% BASIC DIVISIBILITY FACTS
+%% ============================================================
+
+%% 1 divides everything: 1 | N
+one-divides : {N:nat} divides (s z) N -> type.
+%mode one-divides +N -D.
+
+one-divides/base : one-divides N (divides/intro Dmult)
+                    <- mult-left-one N Dmult.
+
+%worlds () (one-divides _ _).
+%total {} (one-divides _ _).
+
+%% Everything divides 0: N | 0
+divides-zero : {N:nat} divides N z -> type.
+%mode divides-zero +N -D.
+
+%% For any N, mult N z z holds (mult/z pattern doesn't work here)
+%% We need to use mult-right-z
+divides-zero/base : divides-zero N (divides/intro D)
+                     <- mult-right-z N D.
+
+%worlds () (divides-zero _ _).
+%total {} (divides-zero _ _).
+
+%% N divides itself: N | N (reflexivity)
+divides-refl : {N:nat} divides N N -> type.
+%mode divides-refl +N -D.
+
+divides-refl/base : divides-refl N (divides/intro Dmult)
+                     <- mult-right-one N Dmult.
+
+%worlds () (divides-refl _ _).
+%total {} (divides-refl _ _).
+
+%% ============================================================
+%% DIVISION WITH REMAINDER (EUCLIDEAN DIVISION)
+%% ============================================================
+
+%% For D > 0 and any N, there exist unique Q, R with N = D*Q + R and R < D
+%% We represent this as: divmod N D Q R means N = D*Q + R and R < D
+
+divmod : nat -> nat -> nat -> nat -> type.
+
+%% Base case: if N < D, then Q = 0, R = N
+divmod/lt : divmod N D z N
+             <- lt N D.
+
+%% Recursive case: if N >= D, we need to compute (N - D) div D
+%% This requires a subtraction relation, which we'll define
+
+%% Subtraction: sub A B C means A = B + C (so C = A - B when B <= A)
+sub : nat -> nat -> nat -> type.
+sub/z : sub N z N.
+sub/s : sub (s A) (s B) C
+         <- sub A B C.
+
+%% Now we can define divmod for the recursive case
+divmod/ge : divmod N D (s Q) R
+             <- le D N                    %% D <= N
+             <- sub N D M                 %% M = N - D
+             <- divmod M D Q R.           %% M = D*Q + R, so N = D*(Q+1) + R
+
+%% ============================================================
+%% GCD (Greatest Common Divisor)
+%% ============================================================
+
+%% Euclidean algorithm: gcd(A, 0) = A, gcd(A, B) = gcd(B, A mod B)
+%% We define gcd using the Euclidean algorithm
+
+%% gcd A B G means G is the GCD of A and B
+gcd : nat -> nat -> nat -> type.
+
+gcd/z : gcd A z A.                       %% gcd(A, 0) = A
+
+gcd/s : gcd A (s B) G
+         <- divmod A (s B) Q R           %% A = (s B)*Q + R with R < s B
+         <- gcd (s B) R G.               %% G = gcd(s B, R)
+
+%% ============================================================
+%% COPRIMALITY
+%% ============================================================
+
+%% A and B are coprime if gcd(A, B) = 1
+coprime : nat -> nat -> type.
+coprime/intro : coprime A B
+                 <- gcd A B (s z).
diff --git a/twelf-experiments/peano/exp.elf b/twelf-experiments/peano/exp.elf
new file mode 100644
index 0000000..aa88f00
--- /dev/null
+++ b/twelf-experiments/peano/exp.elf
@@ -0,0 +1,114 @@
+%% exp.elf - Exponentiation on Natural Numbers
+%%
+%% Exponentiation is defined recursively:
+%%   N^0 = 1
+%%   N^(S M) = N * N^M
+
+exp : nat -> nat -> nat -> type.
+%mode exp +Base +Exponent -Result.
+
+exp/z : exp N z (s z).          %% N^0 = 1
+exp/s : exp N (s M) R
+         <- exp N M P           %% P = N^M
+         <- mult N P R.         %% R = N * P = N * N^M = N^(M+1)
+
+%% Exponentiation is total
+exp-total : {N:nat} {M:nat} exp N M P -> type.
+%mode exp-total +N +M -D.
+
+exp-total/z : exp-total N z exp/z.
+exp-total/s : exp-total N (s M) (exp/s Dmult Dexp)
+               <- exp-total N M Dexp
+               <- mult-total N _ Dmult.
+
+%worlds () (exp-total _ _ _).
+%total M (exp-total _ M _).
+
+%% ============================================================
+%% BASIC EXPONENTIATION PROPERTIES
+%% ============================================================
+
+%% N^1 = N
+exp-one : {N:nat} exp N (s z) N -> type.
+%mode exp-one +N -D.
+
+exp-one/base : exp-one N (exp/s Dmult exp/z)
+                <- mult-right-one N Dmult.
+
+%worlds () (exp-one _ _).
+%total {} (exp-one _ _).
+
+%% 1^N = 1
+exp-base-one : {N:nat} exp (s z) N (s z) -> type.
+%mode exp-base-one +N -D.
+
+exp-base-one/z : exp-base-one z exp/z.
+exp-base-one/s : exp-base-one (s N) (exp/s Dmult Dexp)
+                  <- exp-base-one N Dexp
+                  <- mult-left-one (s z) Dmult.
+
+%worlds () (exp-base-one _ _).
+%total N (exp-base-one N _).
+
+%% 0^(S N) = 0 (0 to any positive power is 0)
+exp-base-zero : {N:nat} exp z (s N) z -> type.
+%mode exp-base-zero +N -D.
+
+exp-base-zero/z : exp-base-zero z (exp/s mult/z exp/z).
+exp-base-zero/s : exp-base-zero (s N) (exp/s mult/z Dexp)
+                   <- exp-base-zero N Dexp.
+
+%worlds () (exp-base-zero _ _).
+%total N (exp-base-zero N _).
+
+%% ============================================================
+%% EXPONENT LAWS
+%% ============================================================
+
+%% Law 1: N^(A+B) = N^A * N^B
+%% exp-add : exp N A PA -> exp N B PB -> add A B AB ->
+%%           mult PA PB PAB -> exp N AB PAB -> type.
+
+%% We'll prove this by induction on B
+
+exp-add : {N:nat} {A:nat} {B:nat} {PA:nat} {PB:nat} {AB:nat} {PAB:nat}
+          exp N A PA -> exp N B PB -> add A B AB ->
+          mult PA PB PAB -> exp N AB PAB -> type.
+%mode exp-add +N +A +B +PA +PB +AB +PAB +Da +Db +Dadd +Dmult -Dab.
+
+%% Base case: B = 0
+%% N^(A+0) = N^A = N^A * 1 = N^A * N^0
+exp-add/z : exp-add N A z PA (s z) A PA
+             Da exp/z Dadd Dmult Da
+             <- add-right-z A Dadd'
+             %% Need: Dadd : add A z A
+             %% Have: Dadd' : add A z A from add-right-z
+             %% Need: Dmult : mult PA (s z) PA
+             <- mult-right-one PA Dmult'.
+
+%% The full proof requires showing the inductive step which involves
+%% associativity of multiplication. We state it here for completeness.
+
+%% Law 2: (N^A)^B = N^(A*B)
+%% This is the power of a power rule
+
+%% Law 3: (M*N)^A = M^A * N^A
+%% This is the power of a product rule
+
+%% These proofs follow similar patterns but require the multiplication
+%% lemmas we've developed.
+
+%% ============================================================
+%% USEFUL COMPUTATIONS
+%% ============================================================
+
+%% Let's verify some concrete exponentiations
+%% 2^2 = 4
+%% 2^3 = 8
+
+%% We can use Twelf's %solve to compute these:
+%% %solve D22 : exp two two R.
+%% Should give R = four
+
+%% %solve D23 : exp two three R.
+%% Should give R = s (s (s (s (s (s (s (s z)))))))  = 8
diff --git a/twelf-experiments/peano/mult.elf b/twelf-experiments/peano/mult.elf
new file mode 100644
index 0000000..14c333b
--- /dev/null
+++ b/twelf-experiments/peano/mult.elf
@@ -0,0 +1,106 @@
+%% mult.elf - Multiplication on Natural Numbers
+%%
+%% Multiplication is defined recursively:
+%%   0 * N = 0
+%%   (S M) * N = N + (M * N)
+
+mult : nat -> nat -> nat -> type.
+%mode mult +M +N -R.
+
+mult/z : mult z N z.
+mult/s : mult (s M) N R
+          <- mult M N P
+          <- add N P R.
+
+%% Multiplication is total
+mult-total : {M:nat} {N:nat} mult M N P -> type.
+%mode mult-total +M +N -D.
+
+mult-total/z : mult-total z N mult/z.
+mult-total/s : mult-total (s M) N (mult/s Dadd Dmult)
+                <- mult-total M N Dmult
+                <- add-total N _ Dadd.
+
+%worlds () (mult-total _ _ _).
+%total M (mult-total M _ _).
+
+%% ============================================================
+%% BASIC MULTIPLICATION LEMMAS
+%% ============================================================
+
+%% Right zero: N * 0 = 0
+mult-right-z : {N:nat} mult N z z -> type.
+%mode mult-right-z +N -D.
+
+mult-right-z/z : mult-right-z z mult/z.
+mult-right-z/s : mult-right-z (s N) (mult/s add/z D)
+                  <- mult-right-z N D.
+
+%worlds () (mult-right-z _ _).
+%total N (mult-right-z N _).
+
+%% Left identity: 1 * N = N
+mult-left-one : {N:nat} mult (s z) N N -> type.
+%mode mult-left-one +N -D.
+
+mult-left-one/base : mult-left-one N (mult/s Dadd mult/z)
+                      <- add-right-z N Dadd.
+
+%worlds () (mult-left-one _ _).
+%total {} (mult-left-one _ _).
+
+%% Right identity: N * 1 = N
+mult-right-one : {N:nat} mult N (s z) N -> type.
+%mode mult-right-one +N -D.
+
+mult-right-one/z : mult-right-one z mult/z.
+mult-right-one/s : mult-right-one (s N) (mult/s (add/s add/z) D)
+                    <- mult-right-one N D.
+
+%worlds () (mult-right-one _ _).
+%total N (mult-right-one N _).
+
+%% ============================================================
+%% COMMUTATIVITY OF MULTIPLICATION
+%% ============================================================
+
+%% Commutativity requires the lemma: M * (S N) = M + M * N
+%% This is subtle because our definition gives: (S M) * N = N + M * N
+%%
+%% The full proof requires careful organization of lemmas involving
+%% associativity and commutativity of addition. We state the theorem:
+%%
+%% mult-comm : mult M N P -> mult N M P -> type.
+%%
+%% The proof structure would be:
+%% 1. Base case: 0 * N = 0 = N * 0 (uses mult-right-z)
+%% 2. Step case: (S M) * N = N + M*N, and by IH M*N = N*M
+%%    Need N * (S M) = N + N*M = N + M*N (by IH), which matches.
+%%    But N * (S M) by definition requires mult-right-s lemma.
+%%
+%% The mult-right-s lemma (M * (S N) = M + M*N) proof requires
+%% showing that addition commutes/associates appropriately through
+%% the recursive structure.
+
+%% For computational verification, we can test specific cases:
+%% mult 2 3 should equal mult 3 2, both giving 6.
+
+%% ============================================================
+%% NOTES ON ADVANCED PROPERTIES
+%% ============================================================
+
+%% Associativity: (A * B) * C = A * (B * C)
+%% Requires: Left distributivity A * (B + C) = A*B + A*C
+
+%% Left Distributivity: A * (B + C) = A*B + A*C
+%% Proof by induction on A:
+%% - Base: 0 * (B + C) = 0 = 0 + 0 = 0*B + 0*C
+%% - Step: (S A) * (B + C) = (B + C) + A*(B+C)
+%%         By IH: = (B + C) + (A*B + A*C)
+%%         By assoc: = B + (C + A*B) + A*C
+%%         By comm:  = B + (A*B + C) + A*C
+%%         By assoc: = (B + A*B) + (C + A*C)
+%%         = (S A)*B + (S A)*C
+
+%% Right Distributivity: (A + B) * C = A*C + B*C
+%% Follows from left distributivity and commutativity
diff --git a/twelf-experiments/peano/nat.elf b/twelf-experiments/peano/nat.elf
new file mode 100644
index 0000000..662d743
--- /dev/null
+++ b/twelf-experiments/peano/nat.elf
@@ -0,0 +1,47 @@
+%% nat.elf - Natural Numbers (Peano Axioms)
+%%
+%% We define the natural numbers inductively:
+%%   - z (zero) is a natural number
+%%   - s N (successor of N) is a natural number if N is
+%%
+%% This gives us: z, s z, s (s z), s (s (s z)), ...
+%%              = 0,   1,       2,           3, ...
+
+nat : type.
+
+z : nat.
+s : nat -> nat.
+
+%% Equality on natural numbers (identity)
+nat-eq : nat -> nat -> type.
+nat-eq/refl : nat-eq N N.
+
+%% Inequality (not equal)
+nat-neq : nat -> nat -> type.
+nat-neq/zs : nat-neq z (s _).
+nat-neq/sz : nat-neq (s _) z.
+nat-neq/ss : nat-neq (s N) (s M) <- nat-neq N M.
+
+%% Some convenient abbreviations for small numbers
+%abbrev one   = s z.
+%abbrev two   = s (s z).
+%abbrev three = s (s (s z)).
+%abbrev four  = s (s (s (s z))).
+%abbrev five  = s (s (s (s (s z)))).
+
+%% Predecessor (partial - undefined for zero)
+pred : nat -> nat -> type.
+pred/s : pred (s N) N.
+
+%% Case analysis principle: every nat is either z or s of something
+nat-case : nat -> type.
+nat-case/z : nat-case z.
+nat-case/s : nat-case (s N).
+
+%% Every natural number has a case
+nat-case-total : {N:nat} nat-case N -> type.
+%mode nat-case-total +N -C.
+nat-case-total/z : nat-case-total z nat-case/z.
+nat-case-total/s : nat-case-total (s N) nat-case/s.
+%worlds () (nat-case-total _ _).
+%total N (nat-case-total N _).
diff --git a/twelf-experiments/peano/order.elf b/twelf-experiments/peano/order.elf
new file mode 100644
index 0000000..368c0f0
--- /dev/null
+++ b/twelf-experiments/peano/order.elf
@@ -0,0 +1,165 @@
+%% order.elf - Ordering Relations on Natural Numbers
+%%
+%% We define:
+%%   - lt (less than): M < N
+%%   - le (less than or equal): M <= N
+
+%% ============================================================
+%% LESS THAN
+%% ============================================================
+
+%% M < N is defined inductively:
+%% - 0 < S(N) for any N
+%% - S(M) < S(N) if M < N
+
+lt : nat -> nat -> type.
+
+lt/z : lt z (s N).                    %% 0 < S(N) for any N
+lt/s : lt (s M) (s N)                 %% S(M) < S(N) if M < N
+        <- lt M N.
+
+%% ============================================================
+%% LESS THAN OR EQUAL
+%% ============================================================
+
+le : nat -> nat -> type.
+
+le/z : le z N.                        %% 0 <= N for any N
+le/s : le (s M) (s N)                 %% S(M) <= S(N) if M <= N
+        <- le M N.
+
+%% le is reflexive
+le-refl : {N:nat} le N N -> type.
+%mode le-refl +N -D.
+le-refl/z : le-refl z le/z.
+le-refl/s : le-refl (s N) (le/s D)
+             <- le-refl N D.
+%worlds () (le-refl _ _).
+%total N (le-refl N _).
+
+%% le is transitive
+le-trans : le A B -> le B C -> le A C -> type.
+%mode le-trans +D1 +D2 -D3.
+
+le-trans/z : le-trans le/z _ le/z.
+le-trans/s : le-trans (le/s D1) (le/s D2) (le/s D3)
+              <- le-trans D1 D2 D3.
+
+%worlds () (le-trans _ _ _).
+%total D (le-trans D _ _).
+
+%% Helper: equality lifts through successor
+nat-eq-s' : nat-eq M N -> nat-eq (s M) (s N) -> type.
+%mode nat-eq-s' +E1 -E2.
+nat-eq-s'/refl : nat-eq-s' nat-eq/refl nat-eq/refl.
+%worlds () (nat-eq-s' _ _).
+%total {} (nat-eq-s' _ _).
+
+%% le is antisymmetric: if M <= N and N <= M then M = N
+le-antisym : le M N -> le N M -> nat-eq M N -> type.
+%mode le-antisym +D1 +D2 -E.
+
+le-antisym/z : le-antisym le/z le/z nat-eq/refl.
+le-antisym/s : le-antisym (le/s D1) (le/s D2) E
+                <- le-antisym D1 D2 E'
+                <- nat-eq-s' E' E.
+
+%worlds () (le-antisym _ _ _).
+%total D (le-antisym D _ _).
+
+%% ============================================================
+%% RELATIONSHIPS BETWEEN lt AND le
+%% ============================================================
+
+%% lt implies le: if M < N then M <= N
+lt-to-le : lt M N -> le M N -> type.
+%mode lt-to-le +D1 -D2.
+
+lt-to-le/z : lt-to-le lt/z le/z.
+lt-to-le/s : lt-to-le (lt/s D1) (le/s D2)
+              <- lt-to-le D1 D2.
+
+%worlds () (lt-to-le _ _).
+%total D (lt-to-le D _).
+
+%% M < S(N) iff M <= N
+lt-s-to-le : lt M (s N) -> le M N -> type.
+%mode lt-s-to-le +D1 -D2.
+
+lt-s-to-le/z : lt-s-to-le lt/z le/z.
+lt-s-to-le/s : lt-s-to-le (lt/s D1) (le/s D2)
+                <- lt-s-to-le D1 D2.
+
+%worlds () (lt-s-to-le _ _).
+%total D (lt-s-to-le D _).
+
+le-to-lt-s : le M N -> lt M (s N) -> type.
+%mode le-to-lt-s +D1 -D2.
+
+le-to-lt-s/z : le-to-lt-s le/z lt/z.
+le-to-lt-s/s : le-to-lt-s (le/s D1) (lt/s D2)
+                <- le-to-lt-s D1 D2.
+
+%worlds () (le-to-lt-s _ _).
+%total D (le-to-lt-s D _).
+
+%% ============================================================
+%% TRICHOTOMY
+%% ============================================================
+
+%% For any M, N: exactly one of M < N, M = N, M > N holds
+
+trichotomy : nat -> nat -> type.
+trichotomy/lt : trichotomy M N <- lt M N.
+trichotomy/eq : trichotomy M N <- nat-eq M N.
+trichotomy/gt : trichotomy M N <- lt N M.
+
+%% Helper to lift trichotomy through successor
+trichotomy-lift : trichotomy M N -> trichotomy (s M) (s N) -> type.
+%mode trichotomy-lift +T1 -T2.
+
+trichotomy-lift/lt : trichotomy-lift (trichotomy/lt D) (trichotomy/lt (lt/s D)).
+trichotomy-lift/eq : trichotomy-lift (trichotomy/eq nat-eq/refl)
+                      (trichotomy/eq nat-eq/refl).
+trichotomy-lift/gt : trichotomy-lift (trichotomy/gt D) (trichotomy/gt (lt/s D)).
+
+%worlds () (trichotomy-lift _ _).
+%total {} (trichotomy-lift _ _).
+
+trichotomy-total : {M:nat} {N:nat} trichotomy M N -> type.
+%mode trichotomy-total +M +N -T.
+
+trichotomy-total/zz : trichotomy-total z z (trichotomy/eq nat-eq/refl).
+trichotomy-total/zs : trichotomy-total z (s N) (trichotomy/lt lt/z).
+trichotomy-total/sz : trichotomy-total (s M) z (trichotomy/gt lt/z).
+trichotomy-total/ss : trichotomy-total (s M) (s N) T'
+                       <- trichotomy-total M N T
+                       <- trichotomy-lift T T'.
+
+%worlds () (trichotomy-total _ _ _).
+%total M (trichotomy-total M _ _).
+
+%% ============================================================
+%% BASIC LEMMAS
+%% ============================================================
+
+%% lt is transitive
+lt-trans : lt A B -> lt B C -> lt A C -> type.
+%mode lt-trans +D1 +D2 -D3.
+
+lt-trans/zs : lt-trans lt/z (lt/s _) lt/z.
+lt-trans/ss : lt-trans (lt/s D1) (lt/s D2) (lt/s D3)
+               <- lt-trans D1 D2 D3.
+
+%worlds () (lt-trans _ _ _).
+%total D (lt-trans D _ _).
+
+%% lt is irreflexive: not (N < N)
+%% We express this as: lt N N implies any conclusion
+%% (In Twelf, we can't directly state "not", but we can show
+%% there's no derivation of lt N N)
+
+%% N is not less than zero - this is witnessed by the fact that
+%% there is no constructor for lt that produces lt _ z.
+%% We cannot state "lt N z -> void" directly in Twelf since void
+%% isn't a built-in. Instead, the absence of matching cases proves it.
diff --git a/twelf-experiments/peano/prime.elf b/twelf-experiments/peano/prime.elf
new file mode 100644
index 0000000..71a1773
--- /dev/null
+++ b/twelf-experiments/peano/prime.elf
@@ -0,0 +1,120 @@
+%% prime.elf - Prime Numbers and Related Theorems
+%%
+%% A prime number P > 1 is a natural number whose only divisors are 1 and P.
+
+%% ============================================================
+%% DEFINITION OF PRIME
+%% ============================================================
+
+%% A number is "greater than 1"
+gt-one : nat -> type.
+gt-one/intro : gt-one (s (s N)).          %% N >= 2 means N > 1
+
+%% A number is composite if it has a non-trivial divisor
+%% composite N means: exists D such that 1 < D < N and D | N
+composite : nat -> type.
+composite/intro : composite N
+                   <- gt-one D           %% D > 1
+                   <- lt D N             %% D < N
+                   <- divides D N.       %% D | N
+
+%% A number is prime if P > 1 and not composite
+%% We'll define small primes directly and provide a general characterization
+
+prime : nat -> type.
+prime/two   : prime (s (s z)).                    %% 2 is prime
+prime/three : prime (s (s (s z))).                %% 3 is prime
+prime/five  : prime (s (s (s (s (s z))))).        %% 5 is prime
+prime/seven : prime (s (s (s (s (s (s (s z))))))). %% 7 is prime
+
+%% ============================================================
+%% FACTORIAL
+%% ============================================================
+
+factorial : nat -> nat -> type.
+%mode factorial +N -R.
+
+factorial/z : factorial z (s z).         %% 0! = 1
+factorial/s : factorial (s N) R
+               <- factorial N F          %% F = N!
+               <- mult (s N) F R.        %% R = (N+1) * N! = (N+1)!
+
+factorial-total : {N:nat} factorial N F -> type.
+%mode factorial-total +N -D.
+
+factorial-total/z : factorial-total z factorial/z.
+factorial-total/s : factorial-total (s N) (factorial/s Dmult Dfact)
+                     <- factorial-total N Dfact
+                     <- mult-total (s N) _ Dmult.
+
+%worlds () (factorial-total _ _).
+%total N (factorial-total N _).
+
+%% ============================================================
+%% PRIME FACTORIZATION (Representation)
+%% ============================================================
+
+%% A list of natural numbers
+nat-list : type.
+nil  : nat-list.
+cons : nat -> nat-list -> nat-list.
+
+%% Product of a list
+list-product : nat-list -> nat -> type.
+%mode list-product +L -P.
+
+list-product/nil  : list-product nil (s z).
+list-product/cons : list-product (cons N L) P
+                     <- list-product L Q
+                     <- mult N Q P.
+
+%% All elements of a list are prime
+all-prime : nat-list -> type.
+all-prime/nil  : all-prime nil.
+all-prime/cons : all-prime (cons P L)
+                  <- prime P
+                  <- all-prime L.
+
+%% A prime factorization of N is a list L where:
+%% 1. All elements of L are prime
+%% 2. The product of L equals N
+prime-factorization : nat -> nat-list -> type.
+prime-factorization/intro : prime-factorization N L
+                             <- all-prime L
+                             <- list-product L N.
+
+%% ============================================================
+%% THEOREMS (Statements)
+%% ============================================================
+
+%% Theorem: Every N > 1 has a prime divisor
+%% has-prime-divisor N P means P is prime and P | N
+has-prime-divisor : nat -> nat -> type.
+has-prime-divisor/intro : has-prime-divisor N P
+                           <- prime P
+                           <- divides P N.
+
+%% Theorem (Euclid): There are infinitely many primes
+%% For any N, there exists a prime P > N
+%% This is expressed as: for any list of primes, there's a prime not in the list
+
+%% Theorem (Fundamental Theorem of Arithmetic):
+%% 1. Existence: Every N > 1 has a prime factorization
+%% 2. Uniqueness: The factorization is unique up to ordering
+
+%% Euclid's Lemma: If P is prime and P | AB, then P | A or P | B
+%% This is key to proving uniqueness of factorization
+
+%% ============================================================
+%% COMPUTATIONAL EXAMPLES
+%% ============================================================
+
+%% These can be verified using %solve:
+%% 2! = 2
+%% 3! = 6
+%% 4! = 24
+%% 5! = 120
+
+%% Example factorizations:
+%% 6 = 2 * 3 = cons 2 (cons 3 nil)
+%% 12 = 2 * 2 * 3 = cons 2 (cons 2 (cons 3 nil))
diff --git a/twelf-experiments/peano/sources.cfg b/twelf-experiments/peano/sources.cfg
new file mode 100644
index 0000000..13a34b5
--- /dev/null
+++ b/twelf-experiments/peano/sources.cfg
@@ -0,0 +1,15 @@
+%% sources.cfg - Twelf configuration file for Peano Arithmetic
+%%
+%% Load this file with: twelf-server < sources.cfg
+%% Or in Twelf server: Config.read "sources.cfg"
+%%
+%% The files must be loaded in dependency order.
+
+nat.elf
+add.elf
+mult.elf
+exp.elf
+order.elf
+div.elf
+prime.elf
+theorems.elf
diff --git a/twelf-experiments/peano/theorems.elf b/twelf-experiments/peano/theorems.elf
new file mode 100644
index 0000000..b43bbca
--- /dev/null
+++ b/twelf-experiments/peano/theorems.elf
@@ -0,0 +1,123 @@
+%% theorems.elf - Verified Computations and Theorem Summary
+%%
+%% This file demonstrates computational verification using %solve
+%% and summarizes the proof status of all theorems.
+
+%% ============================================================
+%% COMPUTATIONAL VERIFICATIONS
+%% ============================================================
+
+%% Basic arithmetic
+%solve add-2-3 : add two three N.
+%% Result: N = five
+
+%solve add-3-2 : add three two N.
+%% Result: N = five (commutativity)
+
+%solve mult-2-3 : mult two three N.
+%% Result: N = s (s (s (s (s (s z))))) = 6
+
+%solve mult-3-2 : mult three two N.
+%% Result: N = 6 (commutativity)
+
+%% Exponentiation
+%solve exp-2-3 : exp two three N.
+%% Result: N = 8
+
+%solve exp-3-2 : exp three two N.
+%% Result: N = 9
+
+%% Factorial (defined in prime.elf)
+%solve fact-3 : factorial three N.
+%% Result: N = 6
+
+%solve fact-4 : factorial four N.
+%% Result: N = 24
+
+%% Order relations
+%solve two-lt-five : lt two five.
+%% Result: lt/s (lt/s lt/z)
+
+%solve three-le-three : le three three.
+%% Result: le/s (le/s (le/s le/z))
+
+%% Divisibility
+%solve two-div-four : divides two four.
+%% Result: divides/intro (mult two two four)
+
+%% ============================================================
+%% VERIFIED THEOREMS (Twelf %total checked)
+%% ============================================================
+
+%% From nat.elf:
+%%   nat-case-total: every nat is z or s of something
+
+%% From add.elf:
+%%   add-total:       addition always produces a result
+%%   add-right-z:     N + 0 = N
+%%   add-right-s:     M + (S N) = S(M + N)
+%%   add-comm:        M + N = N + M
+%%   add-assoc:       (A + B) + C = A + (B + C)
+%%   add-cancel-left: A + B = A + C implies B = C
+%%   add-func:        addition is deterministic
+
+%% From mult.elf:
+%%   mult-total:      multiplication always produces a result
+%%   mult-right-z:    N * 0 = 0
+%%   mult-left-one:   1 * N = N
+%%   mult-right-one:  N * 1 = N
+
+%% From exp.elf:
+%%   exp-total:       exponentiation always produces a result
+%%   exp-one:         N^1 = N
+%%   exp-base-one:    1^N = 1
+%%   exp-base-zero:   0^(S N) = 0
+
+%% From order.elf:
+%%   le-refl:         N <= N
+%%   le-trans:        A <= B and B <= C implies A <= C
+%%   le-antisym:      A <= B and B <= A implies A = B
+%%   lt-to-le:        A < B implies A <= B
+%%   lt-s-to-le:      A < S(B) implies A <= B
+%%   le-to-lt-s:      A <= B implies A < S(B)
+%%   trichotomy-total: for all M, N: M < N or M = N or M > N
+%%   lt-trans:        A < B and B < C implies A < C
+
+%% From div.elf:
+%%   one-divides:     1 | N for all N
+%%   divides-zero:    N | 0 for all N
+%%   divides-refl:    N | N for all N
+
+%% From prime.elf:
+%%   factorial-total: factorial always produces a result
+
+%% ============================================================
+%% THEOREMS STATED BUT NOT FULLY PROVEN
+%% ============================================================
+
+%% Multiplication:
+%%   mult-comm:       M * N = N * M
+%%                    (Requires mult-right-s lemma with careful
+%%                    associativity/commutativity reasoning)
+%%
+%%   mult-assoc:      (A * B) * C = A * (B * C)
+%%                    (Requires distributivity)
+%%
+%%   mult-distrib-l:  A * (B + C) = A*B + A*C
+%%                    (Provable with induction on A)
+
+%% Number theory:
+%%   has-prime-divisor-total: every N > 1 has a prime divisor
+%%                    (Requires strong/well-founded induction)
+%%
+%%   infinitude-of-primes: for any prime P, there exists prime Q > P
+%%                    (Classic Euclidean proof using factorial)
+%%
+%%   euclid-lemma:    if P prime and P | AB then P | A or P | B
+%%                    (Requires Bezout's identity or equivalent)
+%%
+%%   fundamental-theorem-existence: every N > 1 has prime factorization
+%%                    (Follows from has-prime-divisor with induction)
+%%
+%%   fundamental-theorem-uniqueness: prime factorization is unique
+%%                    (Requires Euclid's lemma)