This directory contains the rec-thy package. This package provides a large
number of macros to express standard pieces of notation in recursion theory
aka computability theory. The file rec-thy.pdf (which can be generated from
rec-thy.tex) provides a guide to usage and examples of almost all the macros
and package options as well as release notes.

Comments, feedback and patches welcomes.  

Since my goal is to provide something of use to the community (and myself) 
and having seen some of the problems that can result from even well 
intentioned licenses later down the road, e.g., difficulties updating TeX,
and since I still hold sole copyright I'm releasing this into the public 
domain (this applies retroactively to  prior releases).  I would *ask* 
anyone who reuses it not to be a dick about it (give credit, commit upgrades back, 
rename if forking etc..).  Note, I will assume that any contributions to this
package are implicitly released into the public domain as well unless told
otherwise. 

Author: Peter Gerdes email: gerdes@invariant.org   
Github URL: https://github.com/TruePath/Recursion-Theory-Latex-Package

10/15/2010 - v1.0 - Original Release
01/01/2011 - v1.2
06/20/2012 - v1.3
09/26/2017 - v2.0 - Added support for introducing requirements, the subfunction relation and probably other undocumented features
10/05/2017 - v2.1 - Fixed way packages are required so rec-thy can be loaded in a flexible order.  Also fixed one or two bugs.
11/14/2017 - v2.2 - Fixed \Tdeg so it works different on symbols and vars and added \Tdegof and \Tvarof.  Added \subfunneq and \supfunneq.
12/31/2017 - v2.3 - Added proof cases helper. Also fixed the issue with \ncequiv in XeLaTeX
1/17/2018 - v2.4 - Added priority tree helpers.  Should be more robust with respect to existing definitions of common commands
2/14/2018 - v2.4.1 - Moved to using xparse to define the case macros and several other macros to allow nested brackets for optional arguments.  Added the recf command and cleaned up some option processing. Also worked around the mathtools/unicode-math font bug described here: https://tex.stackexchange.com/questions/335164/incompatibility-with-mathtools-and-unicode-math-in-xelatex/335177
11/29/2018 - v2.4.2 - Fixed horrible bugs introduced in last version and fixed many symbols to work even in pdflatex mode.  Also things are compiling again.
11/29/2018 - v2.4.3 - Rendered compatible with beamer by removing enumitem requirement if beamer is loaded.
02/16/2019 - v3.0 - Added requirements environment for multiple requirements.  Changed the \req and \require commands to take their optional argument after the first mandatory arguments as well as before.  Added the commands \module and \modof.  Added operator \xor.  Fixed corner quotes.  Added \leftofeq, \rightof, \rightofeq.  Added \RE, \CE, \Ce, \Re and \Tincompat, \Tincomp, \Tcompat.  Changed the way strings are symbolized and coded.  Fixed commands to work even with unicode-math.  Also added \require* inside \requirements. Added \nleftofeq, \nrightof, \nrightofeq, \nleftof.  Commands \ancestor, \descendant, etc... and \reqof, \Astages and \Vstages now require the option suppPriorityTrees be passed to the class to use and should be viewed as depreciated.  Fixed the options system so different symbols can be correctly passed to the class.  
02/17/2019 - v3.01 - Fixed \RE \CE \Re and \Ce for the various capitalized versions.  Fixed weird bug with recfnl not printing.  Removed \interior and \closure as not really appropriate commands for the package and having bugs.  Also fixed package to indicate correct version.
02/26/2019 - v3.1 - Fixed \wck to use roman capital CK.
??         - v3.2 Removed \reaop, \alphaREAop, \aREAop in favor of using the single form \REAop.  Removed \functo, \map and funcomp, \hgtO as useless synonyms and removed \KleeneOBelow and KleeneOLess as beyond what the package should define. Added package option compat31 to ensure package compatibility with version 3.1.  An optional parentheses delimited argument specifying the base has been added to  \REAop.  Both \REAop and the pair \REA/\CEA have been updated to ignore order of optional arguments.  The square brackets used to delimit the argument to the use command are now auto-sized.  Added \pmapsto, \pmapsfrom, \kleeneZero, \kleeneNum, \entersat.  Also Misc typesetting fixes. 
05/08/2020 - v3.3 Fixed/added tweak to overline so it looks correct.  Also added real symbols so that \subfunneq and \supfunneq can be defined appropriately.  Fixed incorrect use of tiny in math mode.
06/01/2020 - v3.3.1 Fixed typo causing error under pdflatex.
06/04/2020 - v3.4 Eliminated dependence on undertilde which is missing from texlive
v3.5 - Added \Hop command and misc code cleanup.  
v3.6 - Fixed \REA[n] so that dash is shorter.  Added BeamerRequirements to add a block for requirements in beamer and fixed the requirements environment for beamer.  Fixed \req* command.  Improved syntax for \recfnl so it can accept a () delimited argument via the same standard as \REset and \recf.  Improved \setcol to allow it to be used repeatedly without typesetting bugs.  Changed the code and pair commands to use only a single angle bracket.
v3.7 - Fixed cases enviornment (both prettier and no problem with creating newline).  Major refactor to fix all options.  Fixed bug with \set display.  Added \st command inside the \set command to depreciate second argument.  Added experimental commands \finSsets (alt \ssetsOfsize), \finsets and optional argument to \powset.  Changed \REAop so the hat is on the starred version as intended.  Added the steps (experimental) code which requires an option to enable and fixed some problems with existing options.  Reimplemented \REset to use xparse to avoid some errors in unusual contexts.  Fixed the display of \tpath.  Depreciated \iREAop and \oneREAop.
v3.8 - Adjusted \Tdeg to be more beamer friendly and fixed it not to dumbly underline 0^n.  Fixed BeamerRequirements to work with differing values of \abovedisplayskip.  Removed a few typos in docs for the requirements assistance.  Added BeamerRequire and BeamerRequire* that put the requirements in a block and offer overlay specifications.
v3.8.1 Fixed issues displaying the prime for jump operations
v3.8.2 Removed option to put the set at the end of an \REset operation to avoid capturing later paren arguments, e.g. \REset{i}(A) no longer works to avoid confusion with \REset{i}(x).
