Improve two rarely-seen diagnostics.

compiler/parse_type_defn.m:
    As above.

tests/invalid/field_syntax_error.{m,err_exp}:
tests/invalid/types.{m,err_exp}:
    Add an instance of each bug the diagnostics are for,
    and test for the updated diagnostic text.

compiler/parse_type_defn.m

@@ -2,7 +2,7 @@
 % vim: ft=mercury ts=4 sw=4 et
 %-----------------------------------------------------------------------------e
 % Copyright (C) 2008-2011 The University of Melbourne.
-% Copyright (C) 2016-2025 The Mercury team.
+% Copyright (C) 2016-2026 The Mercury team.
 % This file may only be copied under the terms of the GNU General
 % Public License - see the file COPYING in the Mercury distribution.
 %---------------------------------------------------------------------------%
@@ -525,9 +525,12 @@ convert_constructor_arg_list(ModuleName, VarSet, [Term | Terms])
             MaybeSymNameAndArgs = ok2(SymName, SymNameArgs),
             (
                 SymNameArgs = [_ | _],
-                % XXX Should we add "... at function symbol ..."?
-                Pieces = [words("Error: syntax error in constructor name."),
-                    nl],
+                NameTermStr = describe_error_term(VarSet, NameTerm),
+                Pieces = [words("Error: expected a")] ++
+                    color_as_correct([words("simple identifier")]) ++
+                    [words("as the field name, got")] ++
+                    color_as_incorrect([words(NameTermStr), suffix(".")]) ++
+                    [nl],
                 Spec = spec($pred, severity_error, phase_t2pt,
                     get_term_context(Term), Pieces),
                 MaybeConstructorArgs = error1([Spec])
@@ -906,8 +909,8 @@ parse_eqv_type_defn(ModuleName, VarSet, HeadTerm, BodyTerm, Context, SeqNum,
         cord.from_list([words("On the left hand side of type definition:")]),
     parse_type_defn_head(HeadContextPieces, ModuleName, VarSet, HeadTerm,
         MaybeNameAndParams),
-    % XXX Should pass more correct BodyContextPieces.
-    BodyContextPieces = cord.init,
+    BodyContextPieces = cord.from_list(
+        [words("On the right hand side of equivalence type definition:")]),
     parse_type(allow_ho_inst_info, VarSet, BodyContextPieces, BodyTerm,
         MaybeType),
     ( if

tests/invalid/field_syntax_error.err_exp

@@ -45,4 +45,6 @@ field_syntax_error.m:034:   probably typed `=' where you meant to typ
 field_syntax_error.m:034: Warning: if the expression `!Foo ^ f2' is intended to
 field_syntax_error.m:034:   be part of a field update, then it should be
 field_syntax_error.m:034:   followed by `:=', not `='.
+field_syntax_error.m:037: Error: expected a simple identifier as the field
+field_syntax_error.m:037:   name, got f(N).
 For more information, recompile with `-E'.

tests/invalid/field_syntax_error.m

@@ -32,3 +32,6 @@ baz4(Foo) = Foo^44:=45.
 baz5(!.Foo) = !:Foo :-
     !Foo ^ f1 := 42,
     !Foo ^ f2 = 43.
+
+:- type bar
+    --->    bar(f(N) :: int).

tests/invalid/types.err_exp

@@ -44,3 +44,5 @@ types.m:063:   declaration for module `string'.
 types.m:072: In clause for predicate `repeated_arity'/3:
 types.m:072:   error: wrong number of arguments (2; should be 3)
 types.m:072:   in call to predicate `append'.
+types.m:080: On the right hand side of equivalence type definition: error: `5'
+types.m:080:   is not a type.

tests/invalid/types.m

@@ -76,3 +76,5 @@ repeated_arity(A, B, C) :-
 
 append(A, B, C) :-
     C = A + B.
+
+:- type nonsense == 5.