[Axiom-developer] Re: dependency visualization with VCG

[root]

Bill,

Crashed linux. damn. that's a HUGE bug in that program. Can't imagine how
they do that.

I'd approach the problem somewhat differently. The lattice LEVEL order
is specified in the Makefile.pamphlet file. Given the first level as a
base you can graph the second level. Then iterate with the second level
as a base. The program should complain if it can find a file at level i
that can be pushed into level i-1 (which means I made a mistake). To find
the level of a file the steps were:

1) collect the files it depends upon
     this was the output of the compiler that I mentioned.
     each file in the makefile has a long list of other files it uses.
     call this the "depends on" list.
2) create a lisp association list that contains the bootstrap layer.
3) write a trivial lisp program (attached) that does:
     for each file in the "depends on" list 
       look up the height of the file in the lattice
       if the height doesn't exist
         then we can't compile this file yet -- fail
         else record the maximum of all the heights so far
     print the (max height) + 1
 
I've attached the lattice information.

Drawing this lattice involves taking an infinite 3-space of paper,
laying out the base level, adding the succeeding levels until done.
Next you have to project the 3-space to 2-space minimizing the 
crossings. This is hard (possibly theoretically hard). Search the
web for papers about "embedding data structures into trees". Very
old "flowchart" programs used to do this. (Flowcharts were a technology
before your time I imagine :-) ). The hack introduced with flowcharts
was "the connector box" which was just a pair of numbered boxes. You
break any line into two, number the inner ends with number boxes that
have unique equal numbers (so you can find them) and lay them out.
Create a numbered box at every line crossing.

(Theoretically a more interesting thing to do is to look upon the
cycle set as a "braid" structure and find the minimal cut).

One last step that I have yet to perform is to re-cast the bootstrap
code to its proper level in the lattice. It isn't necessary for the
compile that I do but each bootstrap files is part of a cycle. The
choice of which file to choose to break the cycle is arbitrary. However
using an arbitrary choice could make the bootstrap set larger. Why?

Consider two cycles A-B-C-D-E-A, F-G-A-F

If we choose A from both cycles then we only have 1 bootstrap file.
If we choose B from the first we need 2 bootstrap files.
I failed to do the complete analysis of this and we ought to.

In any case, it would make a nice algebra problem to solve using
Axiom. We could create a lattice domain which we use to construct
Axiom (creating yet one MORE instance of cyclic building behavior).
We can't be the first person to visit this problem so there must
be some general theory worth encoding. (Due next week. Show all
work. Use literate programming. Use #2 pencils :-) ).

Tim
address@hidden
address@hidden


(defun height (dependson)
 (let ((h -2))
 (dolist (dep dependson)
  (setq num (assoc dep lattice))
  (if (null num)
   (progn
    (format t "~a does not exist yet" dep)
    (break))
   (progn
    (setq h (max h (cdr (assoc dep lattice))))
    (format t "height=~a based on ~a~%" h dep))))
 (format t "put into layer ~a~%" (+ h 1))))

(setq lattice
 '(
( ABELGRP   . -1 )
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( DIFRING-  . -1 )
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( DIVRING-  . -1 )
( ENTIRER   . -1 )
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( FPS       . -1 )
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( SORTPAK   . 6 )
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( ALGEBRA   . 7 )
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( APPLYORE  . 11 )
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( QALGSET   . 14 )
( QFCAT2    . 14 )
( RADIX     . 14 )
( RATFACT   . 14 )
( RCFIELD   . 14 )
( RDETR     . 14 )
( RDETRS    . 14 )
( REAL0     . 14 )
( REAL0Q    . 14 )
( REALSOLV  . 14 )
( RESRING   . 14 )
( RETSOL    . 14 )
( RF        . 14 )
( RFFACTOR  . 14 )
( RMATCAT   . 14 )
( RRCC      . 14 )
( SCPKG     . 14 )
( SHDP      . 14 )
( SHP       . 14 )
( SIGNRF    . 14 )
( SMITH     . 14 )
( SMP       . 14 )
( SMTS      . 14 )
( SOLVEFOR  . 14 )
( SPLTREE   . 14 )
( STINPROD  . 14 )
( STTFNC    . 14 )
( SUBRESP   . 14 )
( SUMRF     . 14 )
( SUP       . 14 )
( SUPFRACF  . 14 )
( TANEXP    . 14 )
( TEMUTL    . 14 )
( TEX       . 14 )
( TEXTFILE  . 14 )
( TREE      . 14 )
( TWOFACT   . 14 )
( UNIFACT   . 14 )
( UP        . 14 )
( UPCDEN    . 14 )
( UPDECOMP  . 14 )
( UPDIVP    . 14 )
( UPMP      . 14 )
( UPOLYC2   . 14 )
( UPXSCAT   . 14 )
( VIEWDEF   . 14 )
( UPSQFREE  . 14 )
( VIEW2D    . 14 )
( VOID      . 14 )
( WEIER     . 14 )
( WP        . 14 )
( DIAGG     . 15 )
( DIAGG-    . 15 )
( DSMP      . 15 )
( EXPUPXS   . 15 )
( FRAMALG   . 15 )
( FRAMALG-  . 15 )
( MDAGG     . 15 )
( ODPOL     . 15 )
( PLOT      . 15 )
( RMCAT2    . 15 )
( ROIRC     . 15 )
( SDPOL     . 15 )
( SMATCAT   . 15 )
( SMATCAT-  . 15 )
( TUBETOOL  . 15 )
( UPXSCCA   . 15 )
( DPMM      . 16 )
( EFUPXS    . 16 )
( FFINTBAS  . 16 )
( FRIDEAL   . 16 )
( FRIDEAL2  . 16 )
( FRMOD     . 16 )
( FSAGG     . 16 )
( IBATOOL   . 16 )
( INTFACT   . 16 )
( KDAGG     . 16 )
( KDAGG-    . 16 )
( MSETAGG   . 16 )
( MONOGEN   . 16 )
( MONOGEN-  . 16 )
( NFINTBAS  . 16 )
( SPACE3    . 16 )
( CCLASS    . 17 )
( FSAGG2    . 17 )
( GALFACT   . 17 )
( IALGFACT  . 17 )
( IBACHIN   . 17 )
( NORMMA    . 17 )
( ODERED    . 17 )
( OMSAGG    . 17 )
( PERM      . 17 )
( PERMGRP   . 17 )
( PRIMES    . 17 )
( PWFFINTB  . 17 )
( RDIST     . 17 )
( SAE       . 17 )
( SAEFACT   . 17 )
( SAERFFC   . 17 )
( SGCF      . 17 )
( TBAGG     . 17 )
( VIEW3D    . 17 )
( ALIST     . 18 )
( EQTBL     . 18 )
( GSTBL     . 18 )
( HASHTBL   . 18 )
( INTABL    . 18 )
( INTFTBL   . 18 )
( INTPACK   . 18 )
( IPF       . 18 )
( KAFILE    . 18 )
( PATRES    . 18 )
( STBL      . 18 )
( STRTBL    . 18 )
( TABLE     . 18 )
( TBCMPPK   . 18 )
( ACF       . 19 )
( ACF-      . 19 )
( ACPLOT    . 19 )
( ANTISYM   . 19 )
( ANY       . 19 )
( ASP12     . 19 )
( ASP27     . 19 )
( ASP28     . 19 )
( ASP33     . 19 )
( ASP49     . 19 )
( ASP55     . 19 )
( ASP7      . 19 )
( ASP78     . 19 )
( ASP8      . 19 )
( ASP9      . 19 )
( ATTRBUT   . 19 )
( BOP       . 19 )
( BOP1      . 19 )
( COMMONOP  . 19 )
( COMPCAT   . 19 )
( COMPCAT-  . 19 )
( DRAW      . 19 )
( DRAWCFUN  . 19 )
( DROPT     . 19 )
( DROPT0    . 19 )
( D01ANFA   . 19 )
( D01ASFA   . 19 )
( D03AGNT   . 19 )
( EP        . 19 )
( E04AGNT   . 19 )
( FCPAK1    . 19 )
( FEXPR     . 19 )
( FFCAT     . 19 )
( FFCGP     . 19 )
( FFNBP     . 19 )
( FFP       . 19 )
( FLOAT     . 19 )
( FPARFRAC  . 19 )
( FR        . 19 )
( FRNAALG   . 19 )
( FS        . 19 )
( FST       . 19 )
( FUNCTION  . 19 )
( GDMP      . 19 )
( HACKPI    . 19 )
( IDEAL     . 19 )
( INFORM    . 19 )
( INFORM1   . 19 )
( IPRNTPK   . 19 )
( IR        . 19 )
( ISUPS     . 19 )
( KERNEL    . 19 )
( LIB       . 19 )
( LMDICT    . 19 )
( LODOOPS   . 19 )
( MATRIX    . 19 )
( MKFLCFN   . 19 )
( MSET      . 19 )
( M3D       . 19 )
( NAGC02    . 19 )
( NAGC05    . 19 )
( NAGC06    . 19 )
( NAGD03    . 19 )
( NAGE01    . 19 )
( NAGE02    . 19 )
( NAGE04    . 19 )
( NAGF07    . 19 )
( NAGS      . 19 )
( NAGSP     . 19 )
( NREP      . 19 )
( NUMFMT    . 19 )
( OC        . 19 )
( ODEPACK   . 19 )
( ODERAT    . 19 )
( OMERR     . 19 )
( OMERRK    . 19 )
( OPTPACK   . 19 )
( OSI       . 19 )
( OVAR      . 19 )
( PATTERN   . 19 )
( PMKERNEL  . 19 )
( PMSYM     . 19 )
( POLY      . 19 )
( PRIMELT   . 19 )
( QALGSET2  . 19 )
( QEQUAT    . 19 )
( QUATCAT   . 19 )
( RECLOS    . 19 )
( REP1      . 19 )
( RESULT    . 19 )
( RFFACT    . 19 )
( RMATRIX   . 19 )
( ROMAN     . 19 )
( ROUTINE   . 19 )
( RPOLCAT   . 19 )
( RULECOLD  . 19 )
( SAOS      . 19 )
( SEGBIND   . 19 )
( SET       . 19 )
( SPECOUT   . 19 )
( SQMATRIX  . 19 )
( SWITCH    . 19 )
( SYMS      . 19 )
( SYMTAB    . 19 )
( SYSSOLP   . 19 )
( UTSCAT    . 19 )
( VARIABLE  . 19 )
( WFFINTBS  . 19 )
( ACFS      . 20 )
( AF        . 20 )
( ALGFACT   . 20 )
( ALGFF     . 20 )
( ALGMANIP  . 20 )
( ALGMFACT  . 20 )
( ALGPKG    . 20 )
( ALGSC     . 20 )
( AN        . 20 )
( APPRULE   . 20 )
( ASP19     . 20 )
( ASP20     . 20 )
( ASP30     . 20 )
( ASP31     . 20 )
( ASP35     . 20 )
( ASP41     . 20 )
( ASP42     . 20 )
( ASP74     . 20 )
( ASP77     . 20 )
( ASP80     . 20 )
( ASP9      . 20 )
( CINTSLPE  . 20 )
( COMPFACT  . 20 )
( COMPLEX   . 20 )
( COMPLPAT  . 20 )
( CMPLXRT   . 20 )
( CPMATCH   . 20 )
( CRFP      . 20 )
( CTRIGMNP  . 20 )
( D02AGNT   . 20 )
( D03EEFA   . 20 )
( DBLRESP   . 20 )
( DERHAM    . 20 )
( DFSFUN    . 20 )
( DRAWCURV  . 20 )
( E04NAFA   . 20 )
( E04UCFA   . 20 )
( EF        . 20 )
( EFSTRUC   . 20 )
( ELFUTS    . 20 )
( ESTOOLS   . 20 )
( EXPEXPAN  . 20 )
( EXPRODE   . 20 )
( EXPRTUBE  . 20 )
( EXPR2     . 20 )
( FC        . 20 )
( FDIVCAT   . 20 )
( FDIV2     . 20 )
( FFCAT2    . 20 )
( FLOATCP   . 20 )
( FORDER    . 20 )
( FORTRAN   . 20 )
( FRNAAF2   . 20 )
( FSPECF    . 20 )
( FSRED     . 20 )
( FSUPFACT  . 20 )
( FS2       . 20 )
( FS2UPS    . 20 )
( GAUSSFAC  . 20 )
( GCNAALG   . 20 )
( GENUFACT  . 20 )
( GENUPS    . 20 )
( GTSET     . 20 )
( GPOLSET   . 20 )
( IAN       . 20 )
( INEP      . 20 )
( INFPROD0  . 20 )
( INFSP     . 20 )
( INPRODFF  . 20 )
( INPRODPF  . 20 )
( INTAF     . 20 )
( INTALG    . 20 )
( INTEF     . 20 )
( INTG0     . 20 )
( INTHERAL  . 20 )
( INTPAF    . 20 )
( INTPM     . 20 )
( INTTOOLS  . 20 )
( ITRIGMNP  . 20 )
( JORDAN    . 20 )
( KOVACIC   . 20 )
( LF        . 20 )
( LIE       . 20 )
( LODOF     . 20 )
( LSQM      . 20 )
( OMEXPR    . 20 )
( MCMPLX    . 20 )
( MULTFACT  . 20 )
( NAGD01    . 20 )
( NAGD02    . 20 )
( NAGF01    . 20 )
( NAGF02    . 20 )
( NAGF04    . 20 )
( NCEP      . 20 )
( NLINSOL   . 20 )
( NSMP      . 20 )
( NUMERIC   . 20 )
( OCT       . 20 )
( OCTCT2    . 20 )
( ODEPAL    . 20 )
( ODERTRIC  . 20 )
( PADE      . 20 )
( PAN2EXPR  . 20 )
( PDEPACK   . 20 )
( PFO       . 20 )
( PFOQ      . 20 )
( PICOERCE  . 20 )
( PMASSFS   . 20 )
( PMFS      . 20 )
( PMPREDFS  . 20 )
( PRIMELT   . 20 )
( PSETPK    . 20 )
( QUAT      . 20 )
( QUATCT2   . 20 )
( RADFF     . 20 )
( RDEEF     . 20 )
( RDEEFS    . 20 )
( RDIV      . 20 )
( RSETCAT   . 20 )
( RULE      . 20 )
( RULESET   . 20 )
( SIMPAN    . 20 )
( SFORT     . 20 )
( SOLVESER  . 20 )
( SUMFS     . 20 )
( SUTS      . 20 )
( TOOLSIGN  . 20 )
( TRIGMNIP  . 20 )
( TRMANIP   . 20 )
( ULSCCAT   . 20 )
( UPXSSING  . 20 )
( UTSODE    . 20 )
( UTSODETL  . 20 )
( UTS2      . 20 )
( WUTSET    . 20 )
( DEFINTEF  . 21 )
( DFINTTLS  . 21 )
( DEFINTRF  . 21 )
( D01TRNS   . 21 )
( EFULS     . 21 )
( ESCONT    . 21 )
( EXPR      . 21 )
( EXPR2UPS  . 21 )
( FDIV      . 21 )
( FSCINT    . 21 )
( FSINT     . 21 )
( FS2EXPXP  . 21 )
( GSERIES   . 21 )
( HELLFDIV  . 21 )
( INVLAPLA  . 21 )
( IR2F      . 21 )
( LAPLACE   . 21 )
( LIMITPS   . 21 )
( LODEEF    . 21 )
( NODE1     . 21 )
( ODECONST  . 21 )
( ODEINT    . 21 )
( REP       . 21 )
( SOLVERAD  . 21 )
( SULS      . 21 )
( SUPXS     . 21 )
( ULS       . 21 )
( ULSCONS   . 21 )
( UPXS      . 21 )
( UPXSCONS  . 21 )
( UTS       . 21 )
))