RELNOTES

% 20090306 Changed Grail's "load grammar" menu item (and command line
%          option) so that subsequent "load grammar" commands start in
%          the directory of the previously loaded grammar.
%
% 20090303 Updated the semantics output to allow for different ways to
%          display variables of different types. So, for example,
%          variables of type "e" are displayed as x, y, z and variables
%          of type "e->t" are displayed as P, Q, R. You can define your
%          own rules in sem_utils.pl
%
% 20090227 Added "paper_size" parameter both to the menu and to the
%          LaTeX output (for the semantics only, since the lambda-
%          terms can grow rather big there).
%          Grail restarts LaTeX (and updates the semantics.tex file
%          with sed) when the paper size is changed.
%
% 20090226 Updated the semantic type verification in sem_utils.pl to
%          be able to handle Philippe de Groote's dynamic semantics
%          as used by the grammar file dynamics.pl.
%
% 20090226 Updated Grail's grammar save mechanism, adding the new 
%          dynamic predicates and producing slightly better looking
%          ouput.
%
% 20090225 Added a new option to the LaTeX semantics output:
%          collapse_lambda which, when set to @on, will portray a
%          sequence lx.ly.lz.T as lxyz.T and does the same for
%          sequences of identical quantifiers.
%
% 20090116 Replaced reduce_sem.pl with a more general sem_utils.pl.
%          There are predicates for verifying the lexical type
%          assignments (given atomic_type/2 declarations for the
%          atomic types in your grammar) and a database query
%          component, which converts lambda terms to Datalog queries
%          or assertions if sentence_category/2 declarations are
%          given.
%
% 20081215 Smoothed out the statistics window, which is now simply
%          a window titled "Statistics".
%          Changed the default options, so that neither the
%          statistics nor the ghostview window open atomatically.
%
% 20081215 Fixed XPCE/OS X font problems. This is just a workaround
%          which avoids using bold fonts altogether.
%
% 20081215 Fixed placement of activate_items calls so that aborting
%          anywhere now reactives all the menu items (load/parse,
%          etc.) which were deactived at the start of the parse.
%
% 20081215 Added a finished_dialong call to the prove/2 predicate.
%
% 20071018 Added new options to restricting the total runtime, the
%          total number of inferences and the maximum number of
%          generations for the structural rewrites. This allows
%          the user to automatically abort (too) lengthy
%          computations
%
% 20071017 Added Gabow's strong component and Regin's all_different
%          algorithm to the graph library in the main branch.
%
% 20071003 Added command line options to switch off applications
%          of Regin's algorithm as well as the immediate failure
%          upon finding an axiomatic formula with no linking
%          possibilities in the axiom heap. These are useful for
%          debugging overeager optimisation and will be included
%          as proper menu options in the future.
%
% 20071016 Corrected error in the context-free grammar for the
%          unary contractions.
%
% 20070914 Rewritten the external_component predicate to use simple
%          depth first search to find a component of the nodes
%          reachable using only the external modes. It seems more
%          effective than the previous bottom up strategy, but I
%          need to do more testing, especially for "dead end" nodes
%          which have no external daughters.
%
% 20070914 Added text and log message indicating count check failure.
%          Should I make this a dialog window instead?
%
% 20070912 Added a first graphical display of the parse statistics
%          using XPCE's bar graph library.
%
% 20070912 Added new options for switching of Regin's algorithm and
%          the constraint that no element of the axiom link heap
%          can have zero possibilities. This is mainly useful for
%          debugging grammars, where it's interesting to see why a
%          parse fails.
%
% 20070326 Added a first implementation of Regin's algorithm for
%          filtering axiom links.
%
% 20070316 Added automatic log file which is updated with the
%          parse and result information. Information will be
%          written to the file grail_log (or to /dev/null if the
%          user has no write permissions in the current directory.
%
% 20070315 Added `About this grammar' item to the help menu.
%          Selecting this menu item will show the file with the
%          same name as the grammar file but with an html
%          extension in the Help window. This will allow grammar
%          writers to comment on their grammar and the design
%          choices made.
%
% 20070314 Logged more information for axiom linkings: the total
%          number of axiom links performed and the `perfect' number
%          of axiom links, which would change only the axioms which
%          actually differ between readings.
%
% 20070313 Added a new `totality' constraint specifying that at
%          least one total linking needs to be possible, which is
%          done by simply applying the Hungarian algorithm. This is
%          a preface to implementing Regin's algorithm for constraints
%          of set-difference.
%
% 20070208 Updated the semantic reduction relation to give a slightly
%          more flexible DRS composition relation.
%
% 20070111 Simplified the implementation of the Floyd-Warshall
%          algorithm in the graph library.
%
% 20060220 Minor bugfix release. Fixes errors in the lexicon display
%          (which hadn't been updated for the latest additions yet)
%          and a more serious (but apparently quite rare) one, where
%          two components were joined, but the resulting component
%          would join the two new sets instead of treating one of the
%          two old components as fully new. Another error, where
%          load_fragment would not delete the previous phrases because
%          of incorrect invocation of retractall has been fixed. 
%          A final error, causing par links to be erroneously
%          identified as `active' after a contraction, has been 
%          corrected as well.
%
% 20050926 Added new command line invocation possibilities as well
%          as items for the option menu to choose between automatic,
%          kbest and manual linking, as well as between automatic and
%          manual par contractions.
%          When using kbest, it is possible to give a Prolog
%          expression containing at most one variable (which will be
%          instantiated to the the number of rows/columns in the
%          graph at runtime).
%
% 20050923 Added kbest possibility for axiom linkings, using the
%          Kuhn-Munkres algorithm.
%
% 20050913 Added filtering for readings which are impossible because
%          of the `sentence ordering' as used by Bernardi & Moot to
%          restrict scope ambiguities and by Moot & Retore to rescrict
%          clitic ordering.
%          Any mode declared inert (by using inert_mode/1 in the
%          fragment file) will be subjected to this filtering. Note
%          that (for the moment at least) this requires this mode to
%          be internal.
%
% 20050912 Corrected old mistake in tokenize.pl.
%
% 20050615 Updated save_fragment to take the new information
%          (continuity and custom first-order) into account.
%
% 20050609 Fixed mistake in floyd_warshall; added missing ord_union
%          cases and removed order switch between the two sets, since
%          we do care about the order.
%
% 20050606 Separated the first order labeling and added support for
%          `custom' labeling, where you can specify the first order
%          translation of formulas yourself.
%
% 20050525 Finally implemented proper cleanup of unreachable leaves
%          for the diamond and product contractions.
%
% 20050524 Added check for (sound) unification to axiom links;
%          looking for a way to subsume this with a more
%          sophisticated strategy.
%
% 20050513 Fixed mistake in planarity check for product types.
%          Added semantics when substituting a known word for an
%          unknown.
%
% 20050512 Added support for the use of first-order variables to
%          check for planarity. This will be applied to any modes
%          declared continuous in a fragment (as in Grail 2). More
%          sophisticated schemes are possible, however, when using
%          more than two variables, or by using extraction (and
%          infixation) strategies.
% 
% 20050511 Included a semantic component for the first time and added
%          (as of yet unused) support for using first-order variables
%          to eliminate readings. More test are necessary to verify
%          everything works correctly.
%
% 20050311 Added first attempt at a `standard' autoconf structure.
%          Probably needs to be updated to be fully robust, but in
%          principle 
%
%          ./configure [--prefix=... if not /usr/local]
%          make 
%          make install
%
%          should configure, compile and install grail.
%          Compilation into executable is also new and makes Grail
%          startup quite a bit faster.
%
% 20050311 Removed mistake in initial_yield/4 which resulted in
%           `word order mismatch' for all single-word phrases.
%
% 20041104 Added the possibility for using an external GraphViz
%          implementation (eg. PixelGlow's for MacOS X). To use
%          this feature, simply open the file tmp.dot, which is in
%          the directory from where you started Grail, with GraphViz.
%
% 20041104 Added word order check for solutions. Now, if a potential
%          proof net does not have the words in the order of the
%          input sentence, a message to this effect will be displayed.
%          The possible word orders for this reading will still be
%          sent to the terminal
%
% 20041028 Minor modification for SWI-Prolog 5.4.3: numbervars is no
%          longer in the quintus library, so the line
%
%          :- use_module(library(quintus),    [numbervars/3]).
%
%          has been suppressed from the includes. Add it again if
%          you are using an older version of SWI Prolog.
%
% 20040917 Added "abort" option to the dialogs, giving the user the
%          possibility to abondon the proof search.
%
% 20040821 Added possibility to open a new gv window.
%
% 20040816 Added workaround for (probable) XPCE bug which removes
%          value_set information when the lexicon window is destroyed
%          and then reopened.
% 
% 20040815 Added informational messages for when a solution has been 
%          found or proof search is finished.
%
% 20040815 Added error message when a word is not in the lexicon, with
%          the possibility to select similar words from the lexicon.
%
% 20040814 Created icons for the lexical edit facilities.
%
% 20040810 Created help-brower using XPCE's html-support.
%          Modified paths to be less dependent on the actual locations
%          of the Grail and GraphViz directories.
%
% 20040809 Made the XPCE structure more modular, avoiding the
%          use of named entities (except for the windows).
%          Added a lexicon window as a way of viewing the different
%          entries.
%
% 20040504 First release implementing ideas from my CG2004 paper.
%
% 20040503 Removed a mistake in the par_graph predicate. Everything
%          appears to work now. Fun to see the reduction in possible
%          links. Unsuprisingly, the reductions for the Pentus
%          fragment are quite limited.
%
% 20040430 First implementation of the connectedness check using the
%          Floyd-Warshall algorithm. Some extra testing necessary.
%
% 20040423 Added some functionality to the ordset library for the case
%          where we have an ordered set of Key-Value pairs.
%
% 20040305 Added a floyd_warshall predicate to the graph library.
%
% 20040129 Minor update to interface.pl, allowing the par contractions
%          to be performed without user input.
%
% 20040120 Added a very basic user interface using XPCE. examples/0
%          will display a list of examples (similar to the main window
%          of Grail2) and for atom selection a matrix is now displayed.
%
% 20030820 Added interface to disjoint set data structures to be able
%          to use a standard disjoint set implementation thereby
%          preventing global substitutions across the array. Early
%          test data (ds_dummy vs. disjsetb) show an increase in
%          performance, especially if there are reasonably many
%          unions/replacements.
%
% 20030820 Updated the logarr implementation to give a choice of
%          log4 (as previous), log8 and log16 arrays.
%
% 20030707 Removed strange mistake in the atomic formula selection
%          which prevented the user from making a choice inconsistent
%          with the default choice. 
%
% 20030604 Finally added some acyclicity tests. Now, for every atomic
%          formula, the number of possible connections is computed and
%          the atomic formula with the least possibilities is
%          preferred. The user can still override this decision.
%
% 20030604 Reprogrammed the user_link predicate to make it a bit more
%          general, having only the heap of atomic formulas as input
%          argument and the formula name and two indices of the linked
%          formulas as output.
%
% 20030602 Added a graph library containing a modification of
%          O'Keefe's implementation of Warshall's algorithm for
%          transitive closure which works with 234trees instead of
%          associative lists. The only other predicates at the moment
%          are a reflexive closure and a transitive, reflexive closure
%          which is a simple combination of the two.
%
% 20030527 Found a mistake in the product par contraction. Failure to
%          clean up unreachable vertices leads to problems and needs a
%          structural solution.
%
% 20030527 Added a file pentus.pl which converts SAT formulas to Grail
%          queries according to Pentus' recent paper. This file is
%          good for generating large proof nets, but would probably
%          require implementation of planarity to function properly.
%
% 20030418 Corrected mistake in the interactive atomic formula
%          selection which prevented retrying axiom links.
%
% 20030417 Made some corrections to the clitics fragment, where some
%          missing box(h(0),A) items made multiple solutions possible
%          for the `laisser'/`vouloir' cases.
%
% 20030417 Corrected the root percolation in the unfold1
%          clauses. Looking at it now, I think there is no need for
%          any percolation for positive formulas at all and we can do
%          with one less argument.

% 20030415 Added a primitive interface where the user can determine
%          which par link is contracted to the theorem prover. In the
%          case of multiple active components, however, no choice is
%          yet offered.
%
% 20030415 Discovered and fixed an annoying bug in the
%          btree_remove_2c1 > case of the tree234 library where a
%          copy/paste error caused the return value to accidentally
%          become instantiated too early, causing the entire remove
%          operation to fail.
%          Another annoying error: '/' instead of '.' caused the three
%          case of fix_3node_t3 to fail in certain cases.
%          Sentences of the clitics fragment now work correctly! (but
%          need a rather large amount of local stack)
%
% 20030414 The idea of a short stack subgraph with top item as source
%          and bottom item as sink does not appear to work; both items
%          end up next to eachother.
%
%          Made it possible for the user to define which record type
%          and outline color to use for both internal (atomic
%          formulas) and external nodes (goal and leaves).
%
% 20030410 Atomic formulas are now displayed as well, either as the
%          top element of a record (for positive atomic formulas) or
%          as the bottom element of a record (for negative atomic
%          formulas). Note that this can lead to confusion between
%          atomic formulas and lexical anchors. I'm thinking about
%          replacing the records by something else to improve the
%          visual appearance a bit; maybe a short stack of items.
%
% 20030410 Improved the distributed layout a bit by adding invisible
%          edges between node copies, which seems te recapture most of
%          the tree structure.
%
% 20030409 Added a new display mode `distributed' where components are
%          displayed with the edges listed and vertices which occur
%          multiple times are copied. This leads to *very* wide
%          components after structural rules. A system with invisible
%          edges between the copied nodes would help.
%          Added an option to display both the word and the vertex
%          number.
%
% 20030409 Fixed old mistake in the unfold clauses, where the root was
%          incorrectly calculated.
%
% 20030409 Updated the manual axiom linking to make it
%          nondeterministic.
%
% 20030407 Added a very basic interface to perform axiom links
%          manually.
%          Restructured interface.pl to make the places for modifying
%          colors and output options more clear.
%
% 20030404 Finally implemented the top-down equality enforcion in such
%          a way that it works in the unary and multimodal case as
%          well.
%
%                 A
%                 |
%                 i
%                / \
%               B   C
%
%          Two nodes B and B' are equal if they share the following
%          attributes:
% 
%          1) parent A is the same
%          2) mode i from A to B is the same
%          3) B and B' have the same yield (note that for unary modes
%            this is condition is a consequence of condition 1)
%
%          To accomplish this we keep track of two associative arrays:
%          one from vertices to yields and one from Parent, Mode,
%          Yield triples (or pairs in the case of unary modes) to
%          vertices.
%
%          This guarantees that for a dl, dr or box contraction only
%          a single tensor link can satisfy it.
%
%          Unfortunately, the Dutch fragment shows that for the dia
%          contraction (and presumably for the p contraction as well)
%          there can be many tensor links, meaning it may be necessary
%          to identfy many nodes, which can lead to new
%          identifications etc.
%          THIS VERSION IS G3B3.PL
%
% 20030403 Fixed some mistakes in the `abstract' graph representation,
%          where every component is a vertex (showing the component
%          number (the root) and the total number of edges in it) and
%          only the par links are drawn explicitly.
%
%          Added some extra output steps between the axiom links and
%          some extra (re)computation of active par links after each
%          axiom link.
%
%          Suppressed graph output if the graph is identical to the
%          previous graph (in the case a component expansion adds no
%          new links).
%
% 20030403 Fixed some very old mistakes. Most importantly, the `Avoid'
%          list of components not ready to be expanded is a multiset
%          instead of a set (ie. if the root nodes of two par links
%          are inside a component it does not become active until both
%          have been contracted). Added an ord_dup_insert/3 predicate
%          into the ordsets library to remedy this. Also added an
%          ord_select/3 predicate, which uses the ordering.
%
% 20030403 Moved the graph predicates into a separate `interface'
%          module. This should make it possible to have output into
%          different types of formats, while doing so modularly.
%
%          Updated the placement of tensor nodes to make them more
%          tree-like.
%
% 20030402 First code on the graphviz interface. Placement of vertices
%          needs some more work.
%          THIS IS VERSION G3G.PL
%
% 20030331 Some corrections to the 234tree module, plus conversion of
%          the remaining predicates into Prolog.
%
% 20030327 Corrected the computation of the yields. It now works
%          correctly in the associative/commutative case as well.
%          Have to modify it to take the modes into account to work
%          correctly for the unary modes as well.
%
% 20030327 Finished updating the 234tree package (hopefully).
%
% 20030326 Updated the 234tree package to be more `Prolog-like' using
%          first argument indexing wherever possible. Code can
%          probably still be cleaned up a bit, since right now there
%          are a number of similar-looking predicates which can
%          probably be identified. 
%
% 20030325 Converted the Mercury 234tree package to the standardized
%          btree format and added the necessary clauses for
%          modularity. Initial results suggest the 234tree is
%          marginally better than all other tree formats used.
%          THIS VERSION IS G3B2.PL
%
% 20030324 Added some extra clauses to make the choice between the
%          different binary tree packages more modular.
%
% 20030324 Removed a mistake in replace_tensor_list; in the previous
%          version replacing a vertex name could cause the tensor list
%          to become unordered.
%
% 20030321 Some comments on the identification of vertices in the note
%          from 20030314:
%          The top-down method sketched there is incorrect, look for
%          example at the associative-commutative calculus, where
%          equality of the left leaf does *not* entail equality of the
%          right leaf as well. We should start with noting that a
%          necessary (but in the presence of inclusion postulates and
%          unary modes, not sufficient) condition for equality between
%          two vertices is that they have the same yield of leaves. In
%          combination with the modes, we might get a good equality
%          criterion from this.
% 
% 20030321 Added some changes to the way balanced binary trees are
%          used; now we can choose between red-black trees
%          (implementation from Mercury) and AVL trees (implementation
%          from Gert-Jan van Noord's finite state tools). Both of
%          these seem slightly less fast than the SICStus assoc.pl
%          library. I have renamed predicates from both packages in
%          order to making switching back and forth more easy.
%          Also, I've added a btree_get_replace predicate, as we
%          frequently get the value of a key first then put a new
%          value back for this same key. The btree_get_replace
%          predicate allows us to do this in one go, preventing
%          possibly some unnecessary restructuring.
%
% 20030314 Moved the merge_vertices call to the add_outs predicate,
%          implementing the top-down strategy described below. There
%          is still the problem than when two vertices are identified,
%          this can force further identifications. Specifically the
%          ord_union/3 call in replace_component/4 should take into
%          account that OrdSet1 can contain p(i,A,x) and OrdSet2 can
%          contain p(i,B,x) forcing identification of A and B.
%
% 20030314 Implemented a merge_vertices predicate which solves the
%          problem with the overly greedy selection of tensor links
%          during the contraction phase, at least for the dl, dr, box
%          cases. I'm not sure what the p, dia cases would look
%          like. It would be better to have a separate merging stage
%          immediately after (or even during) the add_outs predicate,
%          enforcing the following:
%
%            p(i,x,A) ... p(i,x,B)  =>  A = B
%            p(i,A,x) ... p(i,B,x)  =>  A = B
%            dia(i,A) ... dia(i,B)  =>  A = B
%
%          or maybe
%
%            X-L ... Y-L            =>  X = Y
%
%          The fragment ass.pl seems to suggest the two are
%          equivalent, but I'm not sure if I prefer the bottom-up or
%          the top-down version. Top-down seems cheaper to implement.
%
% 20030314 Switched to ordered set representation for the list of
%          tensors; this makes it easer to merge two vertices as we
%          can now use ord_union/3 instead of append/3 followed by
%          sort/3.
%          Given that every vertex starts out with this list either
%          empty of containing one element, we never have to
%          explicitly sort the list, only make sure we insert the
%          items in the right order.
%
% 20030313 Added a merge_assoc/3 implementation to the assoc library
%          to be able to merge two associative arrays without
%          converting back and forth to ordered lists. This made the
%          replace/n predicates more simple. Also removed the
%          replace_components/4 predicate, since we already know in
%          wich component we need to replace the values. Made a
%          simpler replace_component/4 predicate which uses simple
%          structural induction on the associative array, eliminating
%          another use to assoc_to_list/2 followed by list_to_assoc/2.
%          Reorganizing unfold would eliminate the remaining
%          list_to_assoc/2 and list_to_array/2 calls.
%
% 20030312 A problem with this version is that there can now be
%          multiple solutions for a contraction (test9 from dutch.pl
%          is an example of this, where the first, wrong, alternative
%          is chosen and the because, unlike with
%          the version which added the edges top-down it is now
%          possible to have 5-dia(i,49) and 5-dia(i,50) with 49 and 50
%          different vertices. It seems a either a more `hybrid'
%          strategy for adding the edges is needed or a separate
%          identification phase, possibly as late as during
%          apply_contraction.
%
% 20030312 Fixed mistake in apply_contraction where we wrongly assumed
%          to know the root of the tensor link to remove in the p and
%          dia case.
%
% 20030312 As a workaround for the nontermination, new rules are added
%          bottom-up again with the difference that only if X-[Y] (as
%          opposed to X-[...,Y,...] already exists no edges will be
%          added. I'm pretty sure this still won't always terminate
%          but it will at least prevent the overeager identification.
%
% 20030312 Components are now represented as Root-cmp(New,Old) where
%          New is the subcomponent which is newly added after a
%          contraction. This will remove duplicate work and is more
%          consistent with the new/old distinction in expand_component
%          as well.
%
% 20030311 Identified the specific problem for the Dutch fragment.
%
%                 A                   A
%                 |                   |
%                 1                   1
%                / \                 / \
%               B   C               H   I
%               |   |               |   |
%               w   1    -[P6]->    1  e1
%               |  / \             / \  |
%               D E   F  <-[P10]  J   E G
%                     |           |
%                    e1           w
%                     |           |
%                     G           D
%
%          P6 checks for e1 and introduced a new node J for the parent
%          of w, after which P10 applies, introducing a new node which
%          checks for w and introduces a new parent F' for e1 ...
%
% 20030307 Source of problems was overly aggressive identification of
%          vertices. The question when two vertices are equal turns
%          out to be more challenging than I assumed. The simple
%          associative fragment already shows we cannot be too lazy
%          identifying vertices either. Food for thought.
%          Have implemented a top-down instead of bottom-up
%          identification procedure now, but I suspect this may still
%          be the source of problems with the MA/MC postulates.
%
% 20030307 Have added a small and simple interface to the theorem
%          prover which makes it more simple to use Grail2 fragments
%          without modifications. Imported the tokenizer and macro
%          expansion facilities unchanged.
%
% 20030305 There is something strange going on in the Dutch fragment,
%          dutch.pl, where only one out of two possible rewrites is
%          found. It looks like `P4' applies only at the wrong, higher
%          possibility and not at the right, lower possibility. This
%          is probably caused by the match/2 predicate which was made
%          to function from root to leaves only. 
%
% 20030305 Added preliminary distinction between new and old vertices
%          in expand_component, resulting in a rather remarkable
%          speedup.
%
% 20030304 Replaced association lists for root-component pairs with
%          AVL associative array implementation from the SICStus
%          library. Reimplementation is probably necessary because of
%          copyright reasons. The del_assoc function crucial here, and
%          is not in the public domain associative array
%          implementation. Balance needs to be implemented as well.
%          Updates for both arrays and associative arrays are still
%          done by translating back and forth to lists, which is easy
%          and translating this directly to the arrays is going to be
%          difficult anyway, since the order of the elements may
%          change.
%
% 20030304 Replaced association list for vertex-component map with
%          logarithmic arrays from the DEC-10 Prolog library,
%          replacing linear access to items via member_chk1/2 by
%          logartithmic access through aref/3.
%
% 20030303 Removed nasty bug which prevented finding a solution for
%          multiple clitics in the clitic fragment. The problem was
%          the use of member_chk instead of member when selecting a
%          link for a known root.
%          Added some diagnostics.
%
% 20030228 Only initial par links are contracted, now. When there is a
%          conflict situation (multiple par links with active leaves
%          in the same component) we try nondeterministically.
%
% 20030225 Updated the rest of the code to handle Root-Component pairs.
%          Added filtering of unreachable nodes after contractions;
%          I suspect this still doesn't work properly with the product
%          and diamond contraction.
%          Added vertex->component mapping, making it easier to select
%          a component when you only have a vertex number. This will
%          already prevent many cycles, since now only vertices from
%          different components will be linked. Future implementation
%          with Rem's equivalence class algorithm will make this faster.
%
% 20030220 Unfolding now produces a list of Root-Component pairs, which
%          need to be incorporated better.
%
% 20030219 Added expansion phase before contractions. Again very naive.
%          Would benefit from division into components and from splitting
%          up the component into `old' an `new' links, since for every
%          iteration of the expansion phase we need to consider only those
%          conversions which match on at least one of the new links.
%          Nonetheless, we now have a full theorem prover for the base
%          logic with non-expanding structural rules!
%
% 20030219 Reimplemented the use of integers for vertices to make the code
%          more clean. I think O'Keefe's implementation of Rem's algorithm
%          for equivalence classes might help to remove the ugly
%          replacements which are necessary when two vertices are unified.
%
% 20030218 Added very naive contraction predicate. We are now in operation
%          for the base logic!
%
% 20030218 Added very naive linking predicate.
%
% 20030218 First coding for next-generation Grail. Unfolding appears to work.
%          Used Prolog variables for vertices in the graph to make later
%          identification more simple.
%          Right now all tensors are still generated produced in a single list;
%          a better solution will be to generate the different components
%          separately or at least to separated the components later.