src/Pure/pure_thy.ML

slightly more explicit/syntactic modelling of morphisms;

(*  Title:      Pure/pure_thy.ML
    Author:     Markus Wenzel, TU Muenchen

Pure theory syntax and further logical content.
*)

signature PURE_THY =
sig
  val old_appl_syntax: theory -> bool
  val old_appl_syntax_setup: theory -> theory
end;

structure Pure_Thy: PURE_THY =
struct

val typ = Simple_Syntax.read_typ;
val prop = Simple_Syntax.read_prop;

val tycon = Lexicon.mark_type;
val const = Lexicon.mark_const;


(* application syntax variants *)

val appl_syntax =
 [("_appl", typ "('b => 'a) => args => logic", Mixfix ("(1_/(1'(_')))", [1000, 0], 1000)),
  ("_appl", typ "('b => 'a) => args => aprop", Mixfix ("(1_/(1'(_')))", [1000, 0], 1000))];

val applC_syntax =
 [("",       typ "'a => cargs",                  Delimfix "_"),
  ("_cargs", typ "'a => cargs => cargs",         Mixfix ("_/ _", [1000, 1000], 1000)),
  ("_applC", typ "('b => 'a) => cargs => logic", Mixfix ("(1_/ _)", [1000, 1000], 999)),
  ("_applC", typ "('b => 'a) => cargs => aprop", Mixfix ("(1_/ _)", [1000, 1000], 999))];

structure Old_Appl_Syntax = Theory_Data
(
  type T = bool;
  val empty = false;
  val extend = I;
  fun merge (b1, b2) : T =
    if b1 = b2 then b1
    else error "Cannot merge theories with different application syntax";
);

val old_appl_syntax = Old_Appl_Syntax.get;

val old_appl_syntax_setup =
  Old_Appl_Syntax.put true #>
  Sign.del_modesyntax_i Syntax.mode_default applC_syntax #>
  Sign.add_syntax_i appl_syntax;


(* main content *)

val _ = Context.>> (Context.map_theory
  (Sign.map_naming (Name_Space.set_theory_name Context.PureN) #>
   Old_Appl_Syntax.put false #>
   Sign.add_types_global
   [(Binding.name "fun", 2, NoSyn),
    (Binding.name "prop", 0, NoSyn),
    (Binding.name "itself", 1, NoSyn),
    (Binding.name "dummy", 0, NoSyn)]
  #> Sign.add_nonterminals_global (map Binding.name Syntax.basic_nonterms)
  #> Sign.add_syntax_i (map (fn x => (x, typ "'a", NoSyn)) Syntax.token_markers)
  #> Sign.add_syntax_i
   [("",            typ "prop' => prop",               Delimfix "_"),
    ("",            typ "logic => any",                Delimfix "_"),
    ("",            typ "prop' => any",                Delimfix "_"),
    ("",            typ "logic => logic",              Delimfix "'(_')"),
    ("",            typ "prop' => prop'",              Delimfix "'(_')"),
    ("_constrain",  typ "logic => type => logic",      Mixfix ("_::_", [4, 0], 3)),
    ("_constrain",  typ "prop' => type => prop'",      Mixfix ("_::_", [4, 0], 3)),
    ("",            typ "tid => type",                 Delimfix "_"),
    ("",            typ "tvar => type",                Delimfix "_"),
    ("",            typ "type_name => type",           Delimfix "_"),
    ("_type_name",  typ "id => type_name",             Delimfix "_"),
    ("_type_name",  typ "longid => type_name",         Delimfix "_"),
    ("_ofsort",     typ "tid => sort => type",         Mixfix ("_::_", [1000, 0], 1000)),
    ("_ofsort",     typ "tvar => sort => type",        Mixfix ("_::_", [1000, 0], 1000)),
    ("_dummy_ofsort", typ "sort => type",              Mixfix ("'_()::_", [0], 1000)),
    ("",            typ "class_name => sort",          Delimfix "_"),
    ("_class_name", typ "id => class_name",            Delimfix "_"),
    ("_class_name", typ "longid => class_name",        Delimfix "_"),
    ("_topsort",    typ "sort",                        Delimfix "{}"),
    ("_sort",       typ "classes => sort",             Delimfix "{_}"),
    ("",            typ "class_name => classes",       Delimfix "_"),
    ("_classes",    typ "class_name => classes => classes", Delimfix "_,_"),
    ("_tapp",       typ "type => type_name => type",   Mixfix ("_ _", [1000, 0], 1000)),
    ("_tappl",      typ "type => types => type_name => type", Delimfix "((1'(_,/ _')) _)"),
    ("",            typ "type => types",               Delimfix "_"),
    ("_types",      typ "type => types => types",      Delimfix "_,/ _"),
    ("\\<^type>fun", typ "type => type => type",       Mixfix ("(_/ => _)", [1, 0], 0)),
    ("_bracket",    typ "types => type => type",       Mixfix ("([_]/ => _)", [0, 0], 0)),
    ("",            typ "type => type",                Delimfix "'(_')"),
    ("\\<^type>dummy", typ "type",                     Delimfix "'_"),
    ("_type_prop",  typ "'a",                          NoSyn),
    ("_lambda",     typ "pttrns => 'a => logic",       Mixfix ("(3%_./ _)", [0, 3], 3)),
    ("_abs",        typ "'a",                          NoSyn),
    ("",            typ "'a => args",                  Delimfix "_"),
    ("_args",       typ "'a => args => args",          Delimfix "_,/ _"),
    ("",            typ "id_position => idt",          Delimfix "_"),
    ("_idtdummy",   typ "idt",                         Delimfix "'_"),
    ("_idtyp",      typ "id_position => type => idt",  Mixfix ("_::_", [], 0)),
    ("_idtypdummy", typ "type => idt",                 Mixfix ("'_()::_", [], 0)),
    ("",            typ "idt => idt",                  Delimfix "'(_')"),
    ("",            typ "idt => idts",                 Delimfix "_"),
    ("_idts",       typ "idt => idts => idts",         Mixfix ("_/ _", [1, 0], 0)),
    ("",            typ "idt => pttrn",                Delimfix "_"),
    ("",            typ "pttrn => pttrns",             Delimfix "_"),
    ("_pttrns",     typ "pttrn => pttrns => pttrns",   Mixfix ("_/ _", [1, 0], 0)),
    ("",            typ "aprop => aprop",              Delimfix "'(_')"),
    ("",            typ "id_position => aprop",        Delimfix "_"),
    ("",            typ "longid_position => aprop",    Delimfix "_"),
    ("",            typ "var => aprop",                Delimfix "_"),
    ("_DDDOT",      typ "aprop",                       Delimfix "..."),
    ("_aprop",      typ "aprop => prop",               Delimfix "PROP _"),
    ("_asm",        typ "prop => asms",                Delimfix "_"),
    ("_asms",       typ "prop => asms => asms",        Delimfix "_;/ _"),
    ("_bigimpl",    typ "asms => prop => prop",        Mixfix ("((3[| _ |])/ ==> _)", [0, 1], 1)),
    ("_ofclass",    typ "type => logic => prop",       Delimfix "(1OFCLASS/(1'(_,/ _')))"),
    ("_mk_ofclass", typ "dummy",                       NoSyn),
    ("_TYPE",       typ "type => logic",               Delimfix "(1TYPE/(1'(_')))"),
    ("",            typ "id_position => logic",        Delimfix "_"),
    ("",            typ "longid_position => logic",    Delimfix "_"),
    ("",            typ "var => logic",                Delimfix "_"),
    ("_DDDOT",      typ "logic",                       Delimfix "..."),
    ("_strip_positions", typ "'a", NoSyn),
    ("_constify",   typ "num => num_const",            Delimfix "_"),
    ("_constify",   typ "float_token => float_const",  Delimfix "_"),
    ("_index1",     typ "index",                       Delimfix "\\<^sub>1"),
    ("_indexnum",   typ "num_const => index",          Delimfix "\\<^sub>_"),
    ("_index",      typ "logic => index",              Delimfix "(00\\<^bsub>_\\<^esub>)"),
    ("_indexdefault", typ "index",                     Delimfix ""),
    ("_indexvar",   typ "index",                       Delimfix "'\\<index>"),
    ("_struct",     typ "index => logic",              Mixfix ("\\<struct>_", [1000], 1000)),
    ("_update_name", typ "idt",                        NoSyn),
    ("_constrainAbs", typ "'a",                        NoSyn),
    ("_position",   typ "id => id_position",           Delimfix "_"),
    ("_position",   typ "longid => longid_position",   Delimfix "_"),
    ("_type_constraint_", typ "'a",                    NoSyn),
    ("_context_const", typ "id_position => logic",     Delimfix "CONST _"),
    ("_context_const", typ "id_position => aprop",     Delimfix "CONST _"),
    ("_context_const", typ "longid_position => logic", Delimfix "CONST _"),
    ("_context_const", typ "longid_position => aprop", Delimfix "CONST _"),
    ("_context_xconst", typ "id_position => logic",    Delimfix "XCONST _"),
    ("_context_xconst", typ "id_position => aprop",    Delimfix "XCONST _"),
    ("_context_xconst", typ "longid_position => logic", Delimfix "XCONST _"),
    ("_context_xconst", typ "longid_position => aprop", Delimfix "XCONST _"),
    (const "==>",   typ "prop => prop => prop",        Delimfix "op ==>"),
    (const Term.dummy_patternN, typ "aprop",           Delimfix "'_"),
    ("_sort_constraint", typ "type => prop",           Delimfix "(1SORT'_CONSTRAINT/(1'(_')))"),
    (const "Pure.term", typ "logic => prop",           Delimfix "TERM _"),
    (const "Pure.conjunction", typ "prop => prop => prop", Infixr ("&&&", 2))]
  #> Sign.add_syntax_i applC_syntax
  #> Sign.add_modesyntax_i (Symbol.xsymbolsN, true)
   [(tycon "fun",         typ "type => type => type",   Mixfix ("(_/ \\<Rightarrow> _)", [1, 0], 0)),
    ("_bracket",          typ "types => type => type",  Mixfix ("([_]/ \\<Rightarrow> _)", [0, 0], 0)),
    ("_ofsort",           typ "tid => sort => type",    Mixfix ("_\\<Colon>_", [1000, 0], 1000)),
    ("_constrain",        typ "logic => type => logic", Mixfix ("_\\<Colon>_", [4, 0], 3)),
    ("_constrain",        typ "prop' => type => prop'", Mixfix ("_\\<Colon>_", [4, 0], 3)),
    ("_idtyp",            typ "id_position => type => idt", Mixfix ("_\\<Colon>_", [], 0)),
    ("_idtypdummy",       typ "type => idt",            Mixfix ("'_()\\<Colon>_", [], 0)),
    ("_lambda",           typ "pttrns => 'a => logic",  Mixfix ("(3\\<lambda>_./ _)", [0, 3], 3)),
    (const "==",          typ "'a => 'a => prop",       Infixr ("\\<equiv>", 2)),
    (const "all_binder",  typ "idts => prop => prop",   Mixfix ("(3\\<And>_./ _)", [0, 0], 0)),
    (const "==>",         typ "prop => prop => prop",   Infixr ("\\<Longrightarrow>", 1)),
    ("_DDDOT",            typ "aprop",                  Delimfix "\\<dots>"),
    ("_bigimpl",          typ "asms => prop => prop",   Mixfix ("((1\\<lbrakk>_\\<rbrakk>)/ \\<Longrightarrow> _)", [0, 1], 1)),
    ("_DDDOT",            typ "logic",                  Delimfix "\\<dots>")]
  #> Sign.add_modesyntax_i ("", false)
   [(const "prop", typ "prop => prop", Mixfix ("_", [0], 0))]
  #> Sign.add_modesyntax_i ("HTML", false)
   [("_lambda", typ "pttrns => 'a => logic", Mixfix ("(3\\<lambda>_./ _)", [0, 3], 3))]
  #> Sign.add_consts_i
   [(Binding.name "==", typ "'a => 'a => prop", Infixr ("==", 2)),
    (Binding.name "==>", typ "prop => prop => prop", Mixfix ("(_/ ==> _)", [2, 1], 1)),
    (Binding.name "all", typ "('a => prop) => prop", Binder ("!!", 0, 0)),
    (Binding.name "prop", typ "prop => prop", NoSyn),
    (Binding.name "TYPE", typ "'a itself", NoSyn),
    (Binding.name Term.dummy_patternN, typ "'a", Delimfix "'_")]
  #> Theory.add_deps_global "==" ("==", typ "'a => 'a => prop") []
  #> Theory.add_deps_global "==>" ("==>", typ "prop => prop => prop") []
  #> Theory.add_deps_global "all" ("all", typ "('a => prop) => prop") []
  #> Theory.add_deps_global "TYPE" ("TYPE", typ "'a itself") []
  #> Theory.add_deps_global Term.dummy_patternN (Term.dummy_patternN, typ "'a") []
  #> Sign.add_trfuns Syntax_Trans.pure_trfuns
  #> Sign.local_path
  #> Sign.add_consts_i
   [(Binding.name "term", typ "'a => prop", NoSyn),
    (Binding.name "sort_constraint", typ "'a itself => prop", NoSyn),
    (Binding.name "conjunction", typ "prop => prop => prop", NoSyn)]
  #> (Global_Theory.add_defs false o map Thm.no_attributes)
   [(Binding.name "prop_def", prop "(CONST prop :: prop => prop) (A::prop) == A::prop"),
    (Binding.name "term_def", prop "(CONST Pure.term :: 'a => prop) (x::'a) == (!!A::prop. A ==> A)"),
    (Binding.name "sort_constraint_def",
      prop "(CONST Pure.sort_constraint :: 'a itself => prop) (CONST TYPE :: 'a itself) ==\
      \ (CONST Pure.term :: 'a itself => prop) (CONST TYPE :: 'a itself)"),
    (Binding.name "conjunction_def", prop "(A &&& B) == (!!C::prop. (A ==> B ==> C) ==> C)")] #> snd
  #> Sign.hide_const false "Pure.term"
  #> Sign.hide_const false "Pure.sort_constraint"
  #> Sign.hide_const false "Pure.conjunction"
  #> Global_Theory.add_thmss [((Binding.name "nothing", []), [])] #> snd
  #> fold (fn (a, prop) =>
      snd o Thm.add_axiom_global (Binding.name a, prop)) Proofterm.equality_axms));

end;