Orders using alphabets

src/froidure-pin.cpp

@@ -1272,10 +1272,10 @@ This function returns the element of *fp* obtained by evaluating *w*.
   }    // namespace
 
   void init_froidure_pin(py::module& m) {
-    using LenLexTrie = detail::RewritingSystemTrie<ShortLexCompare>;
-    using LenLexSet  = detail::RewritingSystemSet<ShortLexCompare>;
-    using RPOTrie    = detail::RewritingSystemTrie<RecursivePathCompare>;
-    using RPOSet     = detail::RewritingSystemSet<RecursivePathCompare>;
+    using LenLexTrie = detail::RewritingSystemTrie<LenLexCmp>;
+    using LenLexSet  = detail::RewritingSystemSet<LenLexCmp>;
+    using RevRPOTrie = detail::RewritingSystemTrie<RevRPOCmp>;
+    using RevRPOSet  = detail::RewritingSystemSet<RevRPOCmp>;
 
     bind_froidure_pin_stateless<Transf<0, uint8_t>>(m, "Transf1");
     bind_froidure_pin_stateless<Transf<0, uint16_t>>(m, "Transf2");
@@ -1316,14 +1316,16 @@ This function returns the element of *fp* obtained by evaluating *w*.
     bind_froidure_pin_stateful<detail::KBE<KnuthBendix<word_type, LenLexTrie>>>(
         m, "KBEWordLenLexTrie");
 
-    bind_froidure_pin_stateful<detail::KBE<KnuthBendix<std::string, RPOSet>>>(
-        m, "KBEStringRPOSet");
-    bind_froidure_pin_stateful<detail::KBE<KnuthBendix<std::string, RPOTrie>>>(
-        m, "KBEStringRPOTrie");
-    bind_froidure_pin_stateful<detail::KBE<KnuthBendix<word_type, RPOSet>>>(
-        m, "KBEWordRPOSet");
-    bind_froidure_pin_stateful<detail::KBE<KnuthBendix<word_type, RPOTrie>>>(
-        m, "KBEWordRPOTrie");
+    bind_froidure_pin_stateful<
+        detail::KBE<KnuthBendix<std::string, RevRPOSet>>>(m,
+                                                          "KBEStringRevRPOSet");
+    bind_froidure_pin_stateful<
+        detail::KBE<KnuthBendix<std::string, RevRPOTrie>>>(
+        m, "KBEStringRevRPOTrie");
+    bind_froidure_pin_stateful<detail::KBE<KnuthBendix<word_type, RevRPOSet>>>(
+        m, "KBEWordRevRPOSet");
+    bind_froidure_pin_stateful<detail::KBE<KnuthBendix<word_type, RevRPOTrie>>>(
+        m, "KBEWordRevRPOTrie");
 
     bind_froidure_pin_stateful<detail::KE<std::string>>(m, "KEString");
     bind_froidure_pin_stateful<detail::KE<detail::MultiView<std::string>>>(

src/kbe.cpp

@@ -73,10 +73,10 @@ namespace libsemigroups {
   }
 
   void init_kbe(py::module& m) {
-    using LenLexTrie = detail::RewritingSystemTrie<ShortLexCompare>;
-    using LenLexSet  = detail::RewritingSystemSet<ShortLexCompare>;
-    using RPOTrie    = detail::RewritingSystemTrie<RecursivePathCompare>;
-    using RPOSet     = detail::RewritingSystemSet<RecursivePathCompare>;
+    using LenLexTrie = detail::RewritingSystemTrie<LenLexCmp>;
+    using LenLexSet  = detail::RewritingSystemSet<LenLexCmp>;
+    using RevRPOTrie = detail::RewritingSystemTrie<RevRPOCmp>;
+    using RevRPOSet  = detail::RewritingSystemSet<RevRPOCmp>;
 
     // LenLex
     using KBEStringLenLexTrie
@@ -91,14 +91,15 @@ namespace libsemigroups {
     bind_kbe<KBEWordLenLexSet>(m, "KBEWordLenLexSet");
 
     // RPO
-    using KBEStringRPOTrie = detail::KBE<KnuthBendix<std::string, RPOTrie>>;
-    using KBEWordRPOTrie   = detail::KBE<KnuthBendix<word_type, RPOTrie>>;
-    using KBEStringRPOSet  = detail::KBE<KnuthBendix<std::string, RPOSet>>;
-    using KBEWordRPOSet    = detail::KBE<KnuthBendix<word_type, RPOSet>>;
-
-    bind_kbe<KBEStringRPOTrie>(m, "KBEStringRPOTrie");
-    bind_kbe<KBEWordRPOTrie>(m, "KBEWordRPOTrie");
-    bind_kbe<KBEStringRPOSet>(m, "KBEStringRPOSet");
-    bind_kbe<KBEWordRPOSet>(m, "KBEWordRPOSet");
+    using KBEStringRevRPOTrie
+        = detail::KBE<KnuthBendix<std::string, RevRPOTrie>>;
+    using KBEWordRevRPOTrie  = detail::KBE<KnuthBendix<word_type, RevRPOTrie>>;
+    using KBEStringRevRPOSet = detail::KBE<KnuthBendix<std::string, RevRPOSet>>;
+    using KBEWordRevRPOSet   = detail::KBE<KnuthBendix<word_type, RevRPOSet>>;
+
+    bind_kbe<KBEStringRevRPOTrie>(m, "KBEStringRevRPOTrie");
+    bind_kbe<KBEWordRevRPOTrie>(m, "KBEWordRevRPOTrie");
+    bind_kbe<KBEStringRevRPOSet>(m, "KBEStringRevRPOSet");
+    bind_kbe<KBEWordRevRPOSet>(m, "KBEWordRevRPOSet");
   }
 }  // namespace libsemigroups

src/knuth-bendix-impl.cpp

@@ -16,7 +16,6 @@
 //
 
 // TODO(1) this file is not organised like any other:
-// * kb should be called thing
 // * we don't chain the "def"s in the other files (easier to wrangle)
 
 // C std headers....
@@ -507,17 +506,19 @@ infinite; ``False`` is returned if it is not.
   }  // namespace detail
 
   void init_detail_knuth_bendix_impl(py::module& m) {
-    using LenLexTrie = detail::RewritingSystemTrie<ShortLexCompare>;
-    using LenLexSet  = detail::RewritingSystemSet<ShortLexCompare>;
-    using RPOTrie    = detail::RewritingSystemTrie<RecursivePathCompare>;
-    using RPOSet     = detail::RewritingSystemSet<RecursivePathCompare>;
+    using LenLexTrie = detail::RewritingSystemTrie<LenLexCmp>;
+    using LenLexSet  = detail::RewritingSystemSet<LenLexCmp>;
+    using RevRPOTrie = detail::RewritingSystemTrie<RevRPOCmp>;
+    using RevRPOSet  = detail::RewritingSystemSet<RevRPOCmp>;
 
     detail::bind_detail_knuth_bendix_impl<LenLexSet>(
         m, "KnuthBendixImplLenLexSet");
     detail::bind_detail_knuth_bendix_impl<LenLexTrie>(
         m, "KnuthBendixImplLenLexTrie");
 
-    detail::bind_detail_knuth_bendix_impl<RPOSet>(m, "KnuthBendixImplRPOSet");
-    detail::bind_detail_knuth_bendix_impl<RPOTrie>(m, "KnuthBendixImplRPOTrie");
+    detail::bind_detail_knuth_bendix_impl<RevRPOSet>(
+        m, "KnuthBendixImplRevRPOSet");
+    detail::bind_detail_knuth_bendix_impl<RevRPOTrie>(
+        m, "KnuthBendixImplRevRPOTrie");
   }
 }  // namespace libsemigroups

src/knuth-bendix.cpp

@@ -331,10 +331,8 @@ Check if all rules are reduced with respect to each other.
 
     template <typename Word, typename Rewriter>
     void bind_normal_form_range(py::module& m, char const* name) {
-      using NormalFormRange = detail::KnuthBendixNormalFormRange<
-          Word,
-          Rewriter,
-          typename Rewriter::reduction_order>;
+      using NormalFormRange
+          = detail::KnuthBendixNormalFormRange<Word, Rewriter>;
       py::class_<NormalFormRange> thing(m, name);
 
       thing.def("__repr__", [](NormalFormRange const& nfr) {
@@ -451,21 +449,22 @@ redundant in this way, then ``None`` is returned.
   }
 
   void init_knuth_bendix(py::module& m) {
-    using LenLexTrie = detail::RewritingSystemTrie<ShortLexCompare>;
-    using LenLexSet  = detail::RewritingSystemSet<ShortLexCompare>;
-    using RPOTrie    = detail::RewritingSystemTrie<RecursivePathCompare>;
-    using RPOSet     = detail::RewritingSystemSet<RecursivePathCompare>;
+    using LenLexTrie = detail::RewritingSystemTrie<LenLexCmp>;
+    using LenLexSet  = detail::RewritingSystemSet<LenLexCmp>;
+    using RevRPOTrie = detail::RewritingSystemTrie<RevRPOCmp>;
+    using RevRPOSet  = detail::RewritingSystemSet<RevRPOCmp>;
 
     bind_knuth_bendix<word_type, LenLexTrie>(m, "KnuthBendixWordLenLexTrie");
     bind_knuth_bendix<word_type, LenLexSet>(m, "KnuthBendixWordLenLexSet");
     bind_knuth_bendix<std::string, LenLexTrie>(m,
                                                "KnuthBendixStringLenLexTrie");
     bind_knuth_bendix<std::string, LenLexSet>(m, "KnuthBendixStringLenLexSet");
 
-    bind_knuth_bendix<word_type, RPOTrie>(m, "KnuthBendixWordRPOTrie");
-    bind_knuth_bendix<word_type, RPOSet>(m, "KnuthBendixWordRPOSet");
-    bind_knuth_bendix<std::string, RPOTrie>(m, "KnuthBendixStringRPOTrie");
-    bind_knuth_bendix<std::string, RPOSet>(m, "KnuthBendixStringRPOSet");
+    bind_knuth_bendix<word_type, RevRPOTrie>(m, "KnuthBendixWordRevRPOTrie");
+    bind_knuth_bendix<word_type, RevRPOSet>(m, "KnuthBendixWordRevRPOSet");
+    bind_knuth_bendix<std::string, RevRPOTrie>(m,
+                                               "KnuthBendixStringRevRPOTrie");
+    bind_knuth_bendix<std::string, RevRPOSet>(m, "KnuthBendixStringRevRPOSet");
 
     bind_normal_form_range<word_type, LenLexTrie>(
         m, "KnuthBendixNormalFormRangeWordLenLexTrie");
@@ -476,14 +475,14 @@ redundant in this way, then ``None`` is returned.
     bind_normal_form_range<std::string, LenLexSet>(
         m, "KnuthBendixNormalFormRangeStringLenLexSet");
 
-    bind_normal_form_range<word_type, RPOTrie>(
-        m, "KnuthBendixNormalFormRangeWordRPOTrie");
-    bind_normal_form_range<word_type, RPOSet>(
-        m, "KnuthBendixNormalFormRangeWordRPOSet");
-    bind_normal_form_range<std::string, RPOTrie>(
-        m, "KnuthBendixNormalFormRangeStringRPOTrie");
-    bind_normal_form_range<std::string, RPOSet>(
-        m, "KnuthBendixNormalFormRangeStringRPOSet");
+    bind_normal_form_range<word_type, RevRPOTrie>(
+        m, "KnuthBendixNormalFormRangeWordRevRPOTrie");
+    bind_normal_form_range<word_type, RevRPOSet>(
+        m, "KnuthBendixNormalFormRangeWordRevRPOSet");
+    bind_normal_form_range<std::string, RevRPOTrie>(
+        m, "KnuthBendixNormalFormRangeStringRevRPOTrie");
+    bind_normal_form_range<std::string, RevRPOSet>(
+        m, "KnuthBendixNormalFormRangeStringRevRPOSet");
 
     bind_redundant_rule<std::string>(m);
     bind_redundant_rule<word_type>(m);

src/libsemigroups_pybind11/__init__.py

@@ -41,6 +41,7 @@
 from .bipartition import Bipartition
 from .blocks import Blocks
 from .congruence import Congruence
+from .detail.cxx_wrapper import wrap_cxx_free_fn as _wrap_cxx_free_fn
 from .detail.dot import Dot
 from .forest import PathsFromRoots, PathsToRoots
 from .froidure_pin import FroidurePin
@@ -103,12 +104,16 @@
         delta,
         error_message_with_prefix,
         freeband_equal_to,
+        lenlex_cmp as _lenlex_cmp,
+        lex_cmp as _lex_cmp,
         lexicographical_compare,
         number_of_words,
         random_string,
         random_strings,
         random_word,
         recursive_path_compare,
+        rev_rpo_cmp as _rev_rpo_cmp,
+        rpo_cmp as _rpo_cmp,
         shortlex_compare,
         side,
         tril,
@@ -120,6 +125,12 @@
     ) from e
 
 
+lenlex_cmp = _wrap_cxx_free_fn(_lenlex_cmp)
+lex_cmp = _wrap_cxx_free_fn(_lex_cmp)
+rev_rpo_cmp = _wrap_cxx_free_fn(_rev_rpo_cmp)
+rpo_cmp = _wrap_cxx_free_fn(_rpo_cmp)
+
+
 __all__ = [
     "__version__",
     # Constants from _libsemigruops_pybind11
@@ -158,12 +169,16 @@
     "delta",
     "error_message_with_prefix",
     "freeband_equal_to",
+    "lenlex_cmp",
+    "lex_cmp",
     "lexicographical_compare",
     "number_of_words",
     "random_string",
     "random_strings",
     "random_word",
     "recursive_path_compare",
+    "rev_rpo_cmp",
+    "rpo_cmp",
     "shortlex_compare",
     "side",
     "tril",

src/libsemigroups_pybind11/froidure_pin.py

@@ -28,12 +28,12 @@
     FroidurePinIntMat as _FroidurePinIntMat,
     FroidurePinKBEStringLenLexSet as _FroidurePinKBEStringLenLexSet,
     FroidurePinKBEStringLenLexTrie as _FroidurePinKBEStringLenLexTrie,
-    FroidurePinKBEStringRPOSet as _FroidurePinKBEStringRPOSet,
-    FroidurePinKBEStringRPOTrie as _FroidurePinKBEStringRPOTrie,
+    FroidurePinKBEStringRevRPOSet as _FroidurePinKBEStringRevRPOSet,
+    FroidurePinKBEStringRevRPOTrie as _FroidurePinKBEStringRevRPOTrie,
     FroidurePinKBEWordLenLexSet as _FroidurePinKBEWordLenLexSet,
     FroidurePinKBEWordLenLexTrie as _FroidurePinKBEWordLenLexTrie,
-    FroidurePinKBEWordRPOSet as _FroidurePinKBEWordRPOSet,
-    FroidurePinKBEWordRPOTrie as _FroidurePinKBEWordRPOTrie,
+    FroidurePinKBEWordRevRPOSet as _FroidurePinKBEWordRevRPOSet,
+    FroidurePinKBEWordRevRPOTrie as _FroidurePinKBEWordRevRPOTrie,
     FroidurePinKEMultiViewString as _FroidurePinKEMultiViewString,
     FroidurePinKEString as _FroidurePinKEString,
     FroidurePinKEWord as _FroidurePinKEWord,
@@ -57,12 +57,12 @@
     IntMat as _IntMat,
     KBEStringLenLexSet as _KBEStringLenLexSet,
     KBEStringLenLexTrie as _KBEStringLenLexTrie,
-    KBEStringRPOSet as _KBEStringRPOSet,
-    KBEStringRPOTrie as _KBEStringRPOTrie,
+    KBEStringRevRPOSet as _KBEStringRevRPOSet,
+    KBEStringRevRPOTrie as _KBEStringRevRPOTrie,
     KBEWordLenLexSet as _KBEWordLenLexSet,
     KBEWordLenLexTrie as _KBEWordLenLexTrie,
-    KBEWordRPOSet as _KBEWordRPOSet,
-    KBEWordRPOTrie as _KBEWordRPOTrie,
+    KBEWordRevRPOSet as _KBEWordRevRPOSet,
+    KBEWordRevRPOTrie as _KBEWordRevRPOTrie,
     MaxPlusMat as _MaxPlusMat,
     MaxPlusTruncMat as _MaxPlusTruncMat,
     MinPlusMat as _MinPlusMat,
@@ -157,10 +157,10 @@ class FroidurePin(_CxxWrapper):
         (_KBEStringLenLexSet,): _FroidurePinKBEStringLenLexSet,
         (_KBEWordLenLexTrie,): _FroidurePinKBEWordLenLexTrie,
         (_KBEWordLenLexSet,): _FroidurePinKBEWordLenLexSet,
-        (_KBEStringRPOTrie,): _FroidurePinKBEStringRPOTrie,
-        (_KBEStringRPOSet,): _FroidurePinKBEStringRPOSet,
-        (_KBEWordRPOTrie,): _FroidurePinKBEWordRPOTrie,
-        (_KBEWordRPOSet,): _FroidurePinKBEWordRPOSet,
+        (_KBEStringRevRPOTrie,): _FroidurePinKBEStringRevRPOTrie,
+        (_KBEStringRevRPOSet,): _FroidurePinKBEStringRevRPOSet,
+        (_KBEWordRevRPOTrie,): _FroidurePinKBEWordRevRPOTrie,
+        (_KBEWordRevRPOSet,): _FroidurePinKBEWordRevRPOSet,
     } | (
         {
             (_HPCombiPTransf16,): _FroidurePinHPCombiPTransf16,

src/libsemigroups_pybind11/knuth_bendix.py

@@ -14,12 +14,12 @@
 from _libsemigroups_pybind11 import (
     KnuthBendixStringLenLexSet as _KnuthBendixStringLenLexSet,
     KnuthBendixStringLenLexTrie as _KnuthBendixStringLenLexTrie,
-    KnuthBendixStringRPOSet as _KnuthBendixStringRPOSet,
-    KnuthBendixStringRPOTrie as _KnuthBendixStringRPOTrie,
+    KnuthBendixStringRevRPOSet as _KnuthBendixStringRevRPOSet,
+    KnuthBendixStringRevRPOTrie as _KnuthBendixStringRevRPOTrie,
     KnuthBendixWordLenLexSet as _KnuthBendixWordLenLexSet,
     KnuthBendixWordLenLexTrie as _KnuthBendixWordLenLexTrie,
-    KnuthBendixWordRPOSet as _KnuthBendixWordRPOSet,
-    KnuthBendixWordRPOTrie as _KnuthBendixWordRPOTrie,
+    KnuthBendixWordRevRPOSet as _KnuthBendixWordRevRPOSet,
+    KnuthBendixWordRevRPOTrie as _KnuthBendixWordRevRPOTrie,
     Order as _Order,
     knuth_bendix_by_overlap_length as _knuth_bendix_by_overlap_length,
     knuth_bendix_is_reduced as _knuth_bendix_is_reduced,
@@ -54,10 +54,10 @@ class KnuthBendix(_CongruenceCommon):
         (str, "Trie", _Order.shortlex): _KnuthBendixStringLenLexTrie,
         (list[int], "Set", _Order.shortlex): _KnuthBendixWordLenLexSet,
         (str, "Set", _Order.shortlex): _KnuthBendixStringLenLexSet,
-        (list[int], "Trie", _Order.recursive): _KnuthBendixWordRPOTrie,
-        (str, "Trie", _Order.recursive): _KnuthBendixStringRPOTrie,
-        (list[int], "Set", _Order.recursive): _KnuthBendixWordRPOSet,
-        (str, "Set", _Order.recursive): _KnuthBendixStringRPOSet,
+        (list[int], "Trie", _Order.recursive): _KnuthBendixWordRevRPOTrie,
+        (str, "Trie", _Order.recursive): _KnuthBendixStringRevRPOTrie,
+        (list[int], "Set", _Order.recursive): _KnuthBendixWordRevRPOSet,
+        (str, "Set", _Order.recursive): _KnuthBendixStringRevRPOSet,
     }
 
     _cxx_type_to_py_template_params = dict(

src/libsemigroups_pybind11/to.py

@@ -23,16 +23,16 @@
     to_knuth_bendix as _to_knuth_bendix,
     to_knuth_bendix_LenLexSet as _to_knuth_bendix_LenLexSet,
     to_knuth_bendix_LenLexTrie as _to_knuth_bendix_LenLexTrie,
-    to_knuth_bendix_RPOSet as _to_knuth_bendix_RPOSet,
-    to_knuth_bendix_RPOTrie as _to_knuth_bendix_RPOTrie,
+    to_knuth_bendix_RevRPOSet as _to_knuth_bendix_RevRPOSet,
+    to_knuth_bendix_RevRPOTrie as _to_knuth_bendix_RevRPOTrie,
     to_knuth_bendix_string_LenLexSet as _to_knuth_bendix_string_LenLexSet,
     to_knuth_bendix_string_LenLexTrie as _to_knuth_bendix_string_LenLexTrie,
-    to_knuth_bendix_string_RPOSet as _to_knuth_bendix_string_RPOSet,
-    to_knuth_bendix_string_RPOTrie as _to_knuth_bendix_string_RPOTrie,
+    to_knuth_bendix_string_RevRPOSet as _to_knuth_bendix_string_RevRPOSet,
+    to_knuth_bendix_string_RevRPOTrie as _to_knuth_bendix_string_RevRPOTrie,
     to_knuth_bendix_word_LenLexSet as _to_knuth_bendix_word_LenLexSet,
     to_knuth_bendix_word_LenLexTrie as _to_knuth_bendix_word_LenLexTrie,
-    to_knuth_bendix_word_RPOSet as _to_knuth_bendix_word_RPOSet,
-    to_knuth_bendix_word_RPOTrie as _to_knuth_bendix_word_RPOTrie,
+    to_knuth_bendix_word_RevRPOSet as _to_knuth_bendix_word_RevRPOSet,
+    to_knuth_bendix_word_RevRPOTrie as _to_knuth_bendix_word_RevRPOTrie,
     to_presentation as _to_presentation,
     to_presentation_string as _to_presentation_string,
     to_presentation_word as _to_presentation_word,
@@ -88,12 +88,12 @@ def _nice_name(type_list):
     (_KnuthBendix, list[int], "Trie", _Order.shortlex): _to_knuth_bendix_word_LenLexTrie,
     (_KnuthBendix, str, "Set", _Order.shortlex): _to_knuth_bendix_string_LenLexSet,
     (_KnuthBendix, str, "Trie", _Order.shortlex): _to_knuth_bendix_string_LenLexTrie,
-    (_KnuthBendix, "Set", _Order.recursive): _to_knuth_bendix_RPOSet,
-    (_KnuthBendix, "Trie", _Order.recursive): _to_knuth_bendix_RPOTrie,
-    (_KnuthBendix, list[int], "Set", _Order.recursive): _to_knuth_bendix_word_RPOSet,
-    (_KnuthBendix, list[int], "Trie", _Order.recursive): _to_knuth_bendix_word_RPOTrie,
-    (_KnuthBendix, str, "Set", _Order.recursive): _to_knuth_bendix_string_RPOSet,
-    (_KnuthBendix, str, "Trie", _Order.recursive): _to_knuth_bendix_string_RPOTrie,
+    (_KnuthBendix, "Set", _Order.recursive): _to_knuth_bendix_RevRPOSet,
+    (_KnuthBendix, "Trie", _Order.recursive): _to_knuth_bendix_RevRPOTrie,
+    (_KnuthBendix, list[int], "Set", _Order.recursive): _to_knuth_bendix_word_RevRPOSet,
+    (_KnuthBendix, list[int], "Trie", _Order.recursive): _to_knuth_bendix_word_RevRPOTrie,
+    (_KnuthBendix, str, "Set", _Order.recursive): _to_knuth_bendix_string_RevRPOSet,
+    (_KnuthBendix, str, "Trie", _Order.recursive): _to_knuth_bendix_string_RevRPOTrie,
     (_Presentation,): _to_presentation,
     (_Presentation, str): _to_presentation_string,
     (_Presentation, list[int]): _to_presentation_word,

src/main.cpp

@@ -68,6 +68,9 @@ namespace libsemigroups {
 
     // Must be before most things
     init_constants(m);
+    // The alphabet-aware order comparison overloads require the Alphabet
+    // classes to be registered before their signatures are created.
+    init_alphabet(m);
     init_order(m);
     init_types(m);
 
@@ -76,7 +79,6 @@ namespace libsemigroups {
     init_runner(m);
 
     // Must be before cong classes
-    init_alphabet(m);
     init_present(m);
     init_inverse_present(m);