Make functions print as valid julia expressions.

Previously, function instances would be printed in `static_show()` as
elements of a `DataType`, with no special printing for `<:Function`s.
This led to printing them via _invalid_ syntax, since there is no empty
constructor for `T<:Function`.

Before:
```julia
julia> g() = 2
g (generic function with 1 method)

julia> println(static_shown(g))
typeof(Main.g)()

julia> eval(Meta.parse(static_shown(g)))
ERROR: MethodError: no method matching typeof(g)()
```

After:
```julia
julia> g() = 2
g (generic function with 1 method)

julia> println(static_shown(g))
Main.g

julia> eval(Meta.parse(static_shown(g)))
g (generic function with 1 method)
```

I chose to keep the Module prefix on the functions, so that they will
be valid julia expressions that you can enter at the REPL to reproduce
the function instance, even though this is a break from the julia
`show()` behavior.

One caveat is that this is still not correct for anonymous functions,
but I'm also not really sure what would be a better way to print
anonymous functions... I think this is _probably_ better than it was
before, but very open to suggestions for how to improve it.
Before:
```julia
julia> l = (x,y)->x+y

julia> println(static_shown(l))
getfield(Main, Symbol("#3#4"))()

julia> eval(Meta.parse(static_shown(l)))
ERROR: MethodError: no method matching var"#3#4"()
```
After:
```julia
julia> l = (x,y)->x+y

julia> println(static_shown(l))
Main.var"#3"

julia> eval(Meta.parse(static_shown(l)))
ERROR: UndefVarError: #3 not defined
```

Author: NHDaly

src/julia.h

@@ -1105,6 +1105,7 @@ static inline int jl_is_layout_opaque(const jl_datatype_layout_t *l) JL_NOTSAFEP
 #define jl_is_svec(v)        jl_typeis(v,jl_simplevector_type)
 #define jl_is_simplevector(v) jl_is_svec(v)
 #define jl_is_datatype(v)    jl_typeis(v,jl_datatype_type)
+#define jl_is_function(v)    jl_typeis(v,jl_function_type)
 #define jl_is_mutable(t)     (((jl_datatype_t*)t)->mutabl)
 #define jl_is_mutable_datatype(t) (jl_is_datatype(t) && (((jl_datatype_t*)t)->mutabl))
 #define jl_is_immutable(t)   (!((jl_datatype_t*)t)->mutabl)

src/rtutils.c

@@ -604,6 +604,22 @@ JL_DLLEXPORT jl_value_t *jl_argument_datatype(jl_value_t *argt JL_PROPAGATES_ROO
     return (jl_value_t*)dt;
 }
 
+int is_globfunction(jl_value_t *v, jl_datatype_t *dv, jl_sym_t **globname_out) {
+    jl_sym_t *globname = dv->name->mt != NULL ? dv->name->mt->name : NULL;
+    *globname_out = globname;
+    int globfunc = 0;
+    if (globname && !strchr(jl_symbol_name(globname), '#') &&
+        !strchr(jl_symbol_name(globname), '@') && dv->name->module &&
+        jl_binding_resolved_p(dv->name->module, globname)) {
+        jl_binding_t *b = jl_get_module_binding(dv->name->module, globname);
+        // The `||` makes this function work for both function instances and function types.
+        if (b && b->value && (b->value == v || jl_typeof(b->value) == v)) {
+            globfunc = 1;
+        }
+    }
+    return globfunc;
+}
+
 static size_t jl_static_show_x_sym_escaped(JL_STREAM *out, jl_sym_t *name) JL_NOTSAFEPOINT
 {
     size_t n = 0;
@@ -688,25 +704,18 @@ static size_t jl_static_show_x_(JL_STREAM *out, jl_value_t *v, jl_datatype_t *vt
     }
     else if (vt == jl_datatype_type) {
         jl_datatype_t *dv = (jl_datatype_t*)v;
-        jl_sym_t *globname = dv->name->mt != NULL ? dv->name->mt->name : NULL;
-        int globfunc = 0;
-        if (globname && !strchr(jl_symbol_name(globname), '#') &&
-            !strchr(jl_symbol_name(globname), '@') && dv->name->module &&
-            jl_binding_resolved_p(dv->name->module, globname)) {
-            jl_binding_t *b = jl_get_module_binding(dv->name->module, globname);
-            if (b && b->value && jl_typeof(b->value) == v)
-                globfunc = 1;
-        }
+        jl_sym_t *globname;
+        int globfunc = is_globfunction(v, dv, &globname);
         jl_sym_t *sym = globfunc ? globname : dv->name->name;
         char *sn = jl_symbol_name(sym);
-        size_t i = 0;
         size_t quote = 0;
         if (globfunc) {
             n += jl_printf(out, "typeof(");
         }
         if (jl_core_module && (dv->name->module != jl_core_module || !jl_module_exports_p(jl_core_module, sym))) {
             n += jl_static_show_x(out, (jl_value_t*)dv->name->module, depth);
             n += jl_printf(out, ".");
+            size_t i = 0;
             if (globfunc && !jl_id_start_char(u8_nextchar(sn, &i))) {
                 n += jl_printf(out, ":(");
                 quote = 1;
@@ -715,8 +724,9 @@ static size_t jl_static_show_x_(JL_STREAM *out, jl_value_t *v, jl_datatype_t *vt
         n += jl_static_show_x_sym_escaped(out, sym);
         if (globfunc) {
             n += jl_printf(out, ")");
-            if (quote)
+            if (quote) {
                 n += jl_printf(out, ")");
+            }
         }
         if (dv->parameters && (jl_value_t*)dv != dv->name->wrapper &&
             (jl_has_free_typevars(v) ||
@@ -982,6 +992,33 @@ static size_t jl_static_show_x_(JL_STREAM *out, jl_value_t *v, jl_datatype_t *vt
         n += jl_static_show_x(out, *(jl_value_t**)v, depth);
         n += jl_printf(out, ")");
     }
+    else if (jl_function_type && jl_isa(v, (jl_value_t*)jl_function_type)) {
+        jl_datatype_t *dv = (jl_datatype_t*)vt;
+        jl_sym_t *sym = dv->name->mt->name;
+        char *sn = jl_symbol_name(sym);
+
+        jl_sym_t *globname;
+        int globfunc = is_globfunction(v, dv, &globname);
+        int quote = 0;
+        if (jl_core_module && (dv->name->module != jl_core_module || !jl_module_exports_p(jl_core_module, sym))) {
+            n += jl_static_show_x(out, (jl_value_t*)dv->name->module, depth);
+            n += jl_printf(out, ".");
+
+            size_t i = 0;
+            if (globfunc && !jl_id_start_char(u8_nextchar(sn, &i))) {
+                n += jl_printf(out, ":(");
+                quote = 1;
+            }
+        }
+
+        n += jl_static_show_x_sym_escaped(out, sym);
+
+        if (globfunc) {
+            if (quote) {
+                n += jl_printf(out, ")");
+            }
+        }
+    }
     else if (jl_datatype_type && jl_is_datatype(vt)) {
         int istuple = jl_is_tuple_type(vt), isnamedtuple = jl_is_namedtuple_type(vt);
         size_t tlen = jl_datatype_nfields(vt);

test/show.jl

@@ -1338,6 +1338,7 @@ end
 
 # PR #38049
 struct var"#X#" end
+var"#f#"() = 2
 
 @test static_shown(var"#X#") == "Main.var\"#X#\""
 # (Just to make this test more sustainable,) for types, we don't necesssarily need to test
@@ -1349,8 +1350,13 @@ struct var"#X#" end
     @testset for v in (
             var"#X#",
             var"#X#"(),
+            Vector,
             Vector{<:Any},
             Vector{var"#X#"},
+            +,
+            typeof(+),
+            var"#f#",
+            typeof(var"#f#"),
         )
         @test v == eval(Meta.parse(static_shown(v)))
     end