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Diffstat (limited to 'tex/prooftree.sty')
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diff --git a/tex/prooftree.sty b/tex/prooftree.sty new file mode 100644 index 0000000..abb7d44 --- /dev/null +++ b/tex/prooftree.sty @@ -0,0 +1,347 @@ +\message{<Paul Taylor's Proof Trees, 2 August 1996>} +%% Build proof tree for Natural Deduction, Sequent Calculus, etc. +%% WITH SHORTENING OF PROOF RULES! +%% Paul Taylor, begun 10 Oct 1989 +%% *** THIS IS ONLY A PRELIMINARY VERSION AND THINGS MAY CHANGE! *** +%% +%% 2 Aug 1996: fixed \mscount and \proofdotnumber +%% +%% \prooftree +%% hyp1 produces: +%% hyp2 +%% hyp3 hyp1 hyp2 hyp3 +%% \justifies -------------------- rulename +%% concl concl +%% \thickness=0.08em +%% \shiftright 2em +%% \using +%% rulename +%% \endprooftree +%% +%% where the hypotheses may be similar structures or just formulae. +%% +%% To get a vertical string of dots instead of the proof rule, do +%% +%% \prooftree which produces: +%% [hyp] +%% \using [hyp] +%% name . +%% \proofdotseparation=1.2ex .name +%% \proofdotnumber=4 . +%% \leadsto . +%% concl concl +%% \endprooftree +%% +%% Within a prooftree, \[ and \] may be used instead of \prooftree and +%% \endprooftree; this is not permitted at the outer level because it +%% conflicts with LaTeX. Also, +%% \Justifies +%% produces a double line. In LaTeX you can use \begin{prooftree} and +%% \end{prootree} at the outer level (however this will not work for the inner +%% levels, but in any case why would you want to be so verbose?). +%% +%% All of of the keywords except \prooftree and \endprooftree are optional +%% and may appear in any order. They may also be combined in \newcommand's +%% eg "\def\Cut{\using\sf cut\thickness.08em\justifies}" with the abbreviation +%% "\prooftree hyp1 hyp2 \Cut \concl \endprooftree". This is recommended and +%% some standard abbreviations will be found at the end of this file. +%% +%% \thickness specifies the breadth of the rule in any units, although +%% font-relative units such as "ex" or "em" are preferable. +%% It may optionally be followed by "=". +%% \proofrulebreadth=.08em or \setlength\proofrulebreadth{.08em} may also be +%% used either in place of \thickness or globally; the default is 0.04em. +%% \proofdotseparation and \proofdotnumber control the size of the +%% string of dots +%% +%% If proof trees and formulae are mixed, some explicit spacing is needed, +%% but don't put anything to the left of the left-most (or the right of +%% the right-most) hypothesis, or put it in braces, because this will cause +%% the indentation to be lost. +%% +%% By default the conclusion is centered wrt the left-most and right-most +%% immediate hypotheses (not their proofs); \shiftright or \shiftleft moves +%% it relative to this position. (Not sure about this specification or how +%% it should affect spreading of proof tree.) +% +% global assignments to dimensions seem to have the effect of stretching +% diagrams horizontally. +% +%%========================================================================== + +\def\introrule{{\cal I}}\def\elimrule{{\cal E}}%% +\def\andintro{\using{\land}\introrule\justifies}%% +\def\impelim{\using{\Rightarrow}\elimrule\justifies}%% +\def\allintro{\using{\forall}\introrule\justifies}%% +\def\allelim{\using{\forall}\elimrule\justifies}%% +\def\falseelim{\using{\bot}\elimrule\justifies}%% +\def\existsintro{\using{\exists}\introrule\justifies}%% + +%% #1 is meant to be 1 or 2 for the first or second formula +\def\andelim#1{\using{\land}#1\elimrule\justifies}%% +\def\orintro#1{\using{\lor}#1\introrule\justifies}%% + +%% #1 is meant to be a label corresponding to the discharged hypothesis/es +\def\impintro#1{\using{\Rightarrow}\introrule_{#1}\justifies}%% +\def\orelim#1{\using{\lor}\elimrule_{#1}\justifies}%% +\def\existselim#1{\using{\exists}\elimrule_{#1}\justifies} + +%%========================================================================== + +\newdimen\proofrulebreadth \proofrulebreadth=.05em +\newdimen\proofdotseparation \proofdotseparation=1.25ex +\newdimen\proofrulebaseline \proofrulebaseline=2ex +\newcount\proofdotnumber \proofdotnumber=3 +\let\then\relax +\def\hfi{\hskip0pt plus.0001fil} +\mathchardef\squigto="3A3B +% +% flag where we are +\newif\ifinsideprooftree\insideprooftreefalse +\newif\ifonleftofproofrule\onleftofproofrulefalse +\newif\ifproofdots\proofdotsfalse +\newif\ifdoubleproof\doubleprooffalse +\let\wereinproofbit\relax +% +% dimensions and boxes of bits +\newdimen\shortenproofleft +\newdimen\shortenproofright +\newdimen\proofbelowshift +\newbox\proofabove +\newbox\proofbelow +\newbox\proofrulename +% +% miscellaneous commands for setting values +\def\shiftproofbelow{\let\next\relax\afterassignment\setshiftproofbelow\dimen0 } +\def\shiftproofbelowneg{\def\next{\multiply\dimen0 by-1 }% +\afterassignment\setshiftproofbelow\dimen0 } +\def\setshiftproofbelow{\next\proofbelowshift=\dimen0 } +\def\setproofrulebreadth{\proofrulebreadth} + +%============================================================================= +\def\prooftree{% NESTED ZERO (\ifonleftofproofrule) +% +% first find out whether we're at the left-hand end of a proof rule +\ifnum \lastpenalty=1 +\then \unpenalty +\else \onleftofproofrulefalse +\fi +% +% some space on left (except if we're on left, and no infinity for outermost) +\ifonleftofproofrule +\else \ifinsideprooftree + \then \hskip.5em plus1fil + \fi +\fi +% +% begin our proof tree environment +\bgroup% NESTED ONE (\proofbelow, \proofrulename, \proofabove, +% \shortenproofleft, \shortenproofright, \proofrulebreadth) +\setbox\proofbelow=\hbox{}\setbox\proofrulename=\hbox{}% +\let\justifies\proofover\let\leadsto\proofoverdots\let\Justifies\proofoverdbl +\let\using\proofusing\let\[\prooftree +\ifinsideprooftree\let\]\endprooftree\fi +\proofdotsfalse\doubleprooffalse +\let\thickness\setproofrulebreadth +\let\shiftright\shiftproofbelow \let\shift\shiftproofbelow +\let\shiftleft\shiftproofbelowneg +\let\ifwasinsideprooftree\ifinsideprooftree +\insideprooftreetrue +% +% now begin to set the top of the rule (definitions local to it) +\setbox\proofabove=\hbox\bgroup$\displaystyle % NESTED TWO +\let\wereinproofbit\prooftree +% +% these local variables will be copied out: +\shortenproofleft=0pt \shortenproofright=0pt \proofbelowshift=0pt +% +% flags to enable inner proof tree to detect if on left: +\onleftofproofruletrue\penalty1 +} + +%============================================================================= +% end whatever box and copy crucial values out of it +\def\eproofbit{% NESTED TWO +% +% various hacks applicable to hypothesis list +\ifx \wereinproofbit\prooftree +\then \ifcase \lastpenalty + \then \shortenproofright=0pt % 0: some other object, no indentation + \or \unpenalty\hfil % 1: empty hypotheses, just glue + \or \unpenalty\unskip % 2: just had a tree, remove glue + \else \shortenproofright=0pt % eh? + \fi +\fi +% +% pass out crucial values from scope +\global\dimen0=\shortenproofleft +\global\dimen1=\shortenproofright +\global\dimen2=\proofrulebreadth +\global\dimen3=\proofbelowshift +\global\dimen4=\proofdotseparation +\global\count255=\proofdotnumber +% +% end the box +$\egroup % NESTED ONE +% +% restore the values +\shortenproofleft=\dimen0 +\shortenproofright=\dimen1 +\proofrulebreadth=\dimen2 +\proofbelowshift=\dimen3 +\proofdotseparation=\dimen4 +\proofdotnumber=\count255 +} + +%============================================================================= +\def\proofover{% NESTED TWO +\eproofbit % NESTED ONE +\setbox\proofbelow=\hbox\bgroup % NESTED TWO +\let\wereinproofbit\proofover +$\displaystyle +}% +% +%============================================================================= +\def\proofoverdbl{% NESTED TWO +\eproofbit % NESTED ONE +\doubleprooftrue +\setbox\proofbelow=\hbox\bgroup % NESTED TWO +\let\wereinproofbit\proofoverdbl +$\displaystyle +}% +% +%============================================================================= +\def\proofoverdots{% NESTED TWO +\eproofbit % NESTED ONE +\proofdotstrue +\setbox\proofbelow=\hbox\bgroup % NESTED TWO +\let\wereinproofbit\proofoverdots +$\displaystyle +}% +% +%============================================================================= +\def\proofusing{% NESTED TWO +\eproofbit % NESTED ONE +\setbox\proofrulename=\hbox\bgroup % NESTED TWO +\let\wereinproofbit\proofusing +\kern0.3em$ +} + +%============================================================================= +\def\endprooftree{% NESTED TWO +\eproofbit % NESTED ONE +% \dimen0 = length of proof rule +% \dimen1 = indentation of conclusion wrt rule +% \dimen2 = new \shortenproofleft, ie indentation of conclusion +% \dimen3 = new \shortenproofright, ie +% space on right of conclusion to end of tree +% \dimen4 = space on right of conclusion below rule + \dimen5 =0pt% spread of hypotheses +% \dimen6, \dimen7 = height & depth of rule +% +% length of rule needed by proof above +\dimen0=\wd\proofabove \advance\dimen0-\shortenproofleft +\advance\dimen0-\shortenproofright +% +% amount of spare space below +\dimen1=.5\dimen0 \advance\dimen1-.5\wd\proofbelow +\dimen4=\dimen1 +\advance\dimen1\proofbelowshift \advance\dimen4-\proofbelowshift +% +% conclusion sticks out to left of immediate hypotheses +\ifdim \dimen1<0pt +\then \advance\shortenproofleft\dimen1 + \advance\dimen0-\dimen1 + \dimen1=0pt +% now it sticks out to left of tree! + \ifdim \shortenproofleft<0pt + \then \setbox\proofabove=\hbox{% + \kern-\shortenproofleft\unhbox\proofabove}% + \shortenproofleft=0pt + \fi +\fi +% +% and to the right +\ifdim \dimen4<0pt +\then \advance\shortenproofright\dimen4 + \advance\dimen0-\dimen4 + \dimen4=0pt +\fi +% +% make sure enough space for label +\ifdim \shortenproofright<\wd\proofrulename +\then \shortenproofright=\wd\proofrulename +\fi +% +% calculate new indentations +\dimen2=\shortenproofleft \advance\dimen2 by\dimen1 +\dimen3=\shortenproofright\advance\dimen3 by\dimen4 +% +% make the rule or dots, with name attached +\ifproofdots +\then + \dimen6=\shortenproofleft \advance\dimen6 .5\dimen0 + \setbox1=\vbox to\proofdotseparation{\vss\hbox{$\cdot$}\vss}% + \setbox0=\hbox{% + \advance\dimen6-.5\wd1 + \kern\dimen6 + $\vcenter to\proofdotnumber\proofdotseparation + {\leaders\box1\vfill}$% + \unhbox\proofrulename}% +\else \dimen6=\fontdimen22\the\textfont2 % height of maths axis + \dimen7=\dimen6 + \advance\dimen6by.5\proofrulebreadth + \advance\dimen7by-.5\proofrulebreadth + \setbox0=\hbox{% + \kern\shortenproofleft + \ifdoubleproof + \then \hbox to\dimen0{% + $\mathsurround0pt\mathord=\mkern-6mu% + \cleaders\hbox{$\mkern-2mu=\mkern-2mu$}\hfill + \mkern-6mu\mathord=$}% + \else \vrule height\dimen6 depth-\dimen7 width\dimen0 + \fi + \unhbox\proofrulename}% + \ht0=\dimen6 \dp0=-\dimen7 +\fi +% +% set up to centre outermost tree only +\let\doll\relax +\ifwasinsideprooftree +\then \let\VBOX\vbox +\else \ifmmode\else$\let\doll=$\fi + \let\VBOX\vcenter +\fi +% this \vbox or \vcenter is the actual output: +\VBOX {\baselineskip\proofrulebaseline \lineskip.2ex + \expandafter\lineskiplimit\ifproofdots0ex\else-0.6ex\fi + \hbox spread\dimen5 {\hfi\unhbox\proofabove\hfi}% + \hbox{\box0}% + \hbox {\kern\dimen2 \box\proofbelow}}\doll% +% +% pass new indentations out of scope +\global\dimen2=\dimen2 +\global\dimen3=\dimen3 +\egroup % NESTED ZERO +\ifonleftofproofrule +\then \shortenproofleft=\dimen2 +\fi +\shortenproofright=\dimen3 +% +% some space on right and flag we've just made a tree +\onleftofproofrulefalse +\ifinsideprooftree +\then \hskip.5em plus 1fil \penalty2 +\fi +} + +%========================================================================== +% IDEAS +% 1. Specification of \shiftright and how to spread trees. +% 2. Spacing command \m which causes 1em+1fil spacing, over-riding +% exisiting space on sides of trees and not affecting the +% detection of being on the left or right. +% 3. Hack using \@currenvir to detect LaTeX environment; have to +% use \aftergroup to pass \shortenproofleft/right out. +% 4. (Pie in the sky) detect how much trees can be "tucked in" +% 5. Discharged hypotheses (diagonal lines). |