the categories of inheritance:
# type clustering (inclusion polymorphism):
. numbers are the classic type cluster;
that type's major subtypes have overlapping interfaces;
and they need a supertype to coordinate biop's
(binary operations; a function with 2 arg's;
eg, addition's signature is: +:NxN->N )
whenever the param's have unmatched subtypes
(eg, RxC->C, ZxN->Z, /:NxN->Q, ...).
type cluster/supervision models:
#coordinated:
. the set of polymorphic subtypes is fixed,
and the supertype knows how to convert between them;
because,
it knows the data formats of all its subtypes .
# translated:
. the supertype provides an all-inclusive
universal data format;
eg, numbers -> complex .
. all subtypes convert between that format
and their own .
type cluster/subtypes must include range constraints:
. range constraints are essential for efficiency
as well as stronger static typing;
because, range limits are what allow
direct use of native numeric types .
. typical native types include
{N,Z,R}{8,16,32,64,128} .
# type classing (Subtype polymorphism):
. declaring a type is a member of a class,
and is compatable with that class
by inheriting its interface;
the new type is then usable
anywhere the inherited class is . [12.31:
. the type class is defined by its interface;
any type following that interface
is considered a member of that class .
. it's not about sharing code by extension;
it's organizing hierarchies of compatability .]
# type cluster combined with type classing:
. the subtypes of a type cluster
can be type classed; eg,
a dimensioned number could inherit from int;
and then to coordinate with the numeric supertype
it uses functionality from int.type
to deal with these messages:
{ what is your numeric subtype?
, your numeric value?
, replace your numeric value with this one
} .
. with just that interface,
any subclass of any numeric subtype
can be used in any numeric operation . [12.31:
. all self-modifying operations ( x`f)
can be translated as assignments (x`= f(x));
so then the inherited subtype
provides all the transform code .]
#type classing without clustering:
11.20:
. without type clustering;
what does type classing do then?
are biop's supported? polymorphism?
. historical reasons for inheritance:
# polymorphism
# type compatability
# reuse of work .
. you want to extend a type's
structure and functionality,
not interfere with its code base,
and still be useful everywhere your ancestors are .
. in the popular oop model,
the inherited work is reused by
adding to an inherited type's
functionality and instance var'space
(creating a polymorphism in the type).
. there's type compatability because
the obj' can handle all the ancestor's
unary and self-modifying functions;
but, popular oop approaches differ on
how biop's are handled .
. the classic, math'al oop uses clusters, [12.31:
which can handle biop's because the supertype
has limited membership to its type class
and can thus know in advance
what combinations of subtypes to expect
among a biop's pair of arg's .
. in a system without clustering's
closed class of subtypes
then there is no particular type to handle
the coordination of mixed biop arg's .
(that mix can consist of any types in
one arg's ancestors, or their descendents).]
. if subtypes can redefine a biop,
then a biop's method might be arbitrated by:
# nearest common ancestor:
the arg' set's nearest common ancestor type;
# popular:
the first arg determines the method;
# translation:
. an inheritable type has a universal format
which inheritors convert to,
in order to use the root's biop method .]
# incremental composition:
. it can be simplifying to describe a type
in terms of how it differs from other types;
this case includes anything not considered to be
type clustering or subclassing .
. revisions such as removing inherited parts
can preclude type compatability;
in such cases, compatability could be declared
with the use of a conversion map .
. incremental composition provides
module operators for building in ways
familiar to lisp users:
code can read other code, modify it,
and then use it as a module definition .
[11.20:
. with incremental composition,
any inheritance behaviors should be possible;
but the built-in inheritance should be
simple, classic type clustering and classing
as described above .
. the directions of popular oop
are not helping either readability or reuse;
esp'y unrewarding is the ability to
inherit multiple implementations
that have overlapping interfaces .]
#frameworks:
11.15:
. generic types can implement frameworks:
a type is an interface with all code supplied;
a generic type
leaves some of its interface undefined
or optionally redefinable,
with the intent that parameter instantiations
are customizing the framework;
eg,
a typical gui framework would be impl'd as
a generic task type;
so that creating an obj' of that type
initiates a thread of execution
that captures all user input
and responds to these events by
calling functions supplied by the
framework's customizing init's .]
adda/oop/value types:
11.16:
. the classic use of oop is type clustering
as is done for numerics:
it provides users of the numeric library
with an effortless, automated way
to use a variety of numeric subtypes
while also employing static typing,
and enjoying any enhanced readability or safety
that may be provided by that .
. coercions and range checks can all be
tucked under the hood,
without requiring compliance from clients .
. this automation is possible because
the designer of a type cluster's supertype
is using subtype tags to determine
each value's data format .
. the supertype module is also
the only place to coordinate
multiple param's having unmatched subtypes;
after one param' is coerced to match the other,
operations involving matched binary subtypes
are then relegated to subtype modules .
11.19: intro to value`type:
. static typing generally means
that a var's allowed values are confined to
one declared type,
and perhaps also constrained;
eg, limited to a range of values,
or a specific subtype .
. if that declared type is a type cluster,
it's values will include a type tag
for use by the supertype module,
to indicate which of its subtype modules
is responsible for that data format .
. type.tags are sometimes seen as a way to
replace Static typing with ducktyping
(where the tag is used at run-time
to check that the given value has a type
that is compatible with the requested operation).
. type clustering, in contrast to ducktyping,
is static typing with polymorphism
(statically bound to the cluster's supertype);
and there, the purpose of the type.tag
is merely to allow the supertype module
to support a variety of subtypes,
usually for the efficiency to be gained
from supporting a variety of data formats;
eg,
if huge complex numbers won't be used,
then a real.tag can indicate there is
no mem' allocated for the imaginary component;
or,
if only int's within a certain range will be used,
then the format can be that of a native int,
which is considerably faster than non-native formats .
. the value's subtype (or value`type)
is contrasted with a var's subtype
to remind us that they need not be equal
as long as they are compatable;
eg,
a var' of type"real may contain
a value of type"integer;
because they are both subtypes of number,
and the integer values are a
subset of the real values
(independent of format).
. the obj's subtype puts a limit on
the value`types it can support;
eg,
while a var' of subtype"R16 (16bit float)
can coerce any ints to float,
it raises an exception if that float
can't fit in a 16-bit storage .
. another possibly interesting distinction
between var' types and value`types
is that value`types have no concept of
operating on self; [11.19:
a unary operation over a value`type
doesn't involve any addresses,
and there is nothing being modified .
. while popular oop has a var`address
modify itself with a msg,
eg, x`f;
classic oop would say that was an
assignment stmt plus a unary operation:
x`= x`type`f(x) -- shown here fully qualified
to indicate how modularity is preserved:
the function belongs to x's type .]
. adda can also enforce typing between
unrelated types like {pure number, Meters},
but the system depends on supertype designers
to correctly handle their own subtypes .
. in addition to the distinction between
{library, application} programmers,
there is also kernel mode:
the adda run-time manages all native types
so that any code that
could be responsible for system crashes
is all in one module .
10.23: news.adda/compositional modularity:
11.14: Bracha, Lindstrom 1992`Modularity meets Inheritance
We "unbundle" the roles of classes10.23: Banavar 1995`compositional modularity app framework:
by providing a suite of operators
independently controlling such effects as
combination, modification, encapsulation,
name resolution, and sharing,
all on the single notion of module.
All module operators are forms of inheritance.
Thus, inheritance not only is
not in conflict with modularity in our system,
but is its foundation.
This allows a previously unobtainable
spectrum of features
to be combined in a cohesive manner,
including multiple inheritance, mixins,
encapsulation and strong typing.
We demonstrate our approach in a language:
Jigsaw is modular in two senses:
# it manipulates modules,
# it is highly modular in its own conception,
permitting various module combinators to be
included, omitted, or newly constructed
in various realizations .
11.14:
. it provides not only decomposition and encapsulation
but also module recomposition .
. the model of compositional modularity is itself
realized as a generic, reusable software arch',
an oo-app framework" Etyma
that borrows meta module operators
from the module manipulation lang, Jigsaw
-- Bracha 1992`modularity meets inheritance .
. it efficiently builds completions;
ie, tools for compositionally modular system .
. it uses the unix toolbox approach:
each module does just one thing well,
but has sophisticated and reliable mechanisms
for massive recomposition .
. forms of composition:
#functional: returns are piped to param's;
#data-flow: data filters piped;
#conventional modules: lib api calls;
# compositional modularity:
. interfaces and module impl's
operated on to obtain new modules .
. oop inheritance is a form of recomposition;
it's a linguistic mechanism that supports
reuse via incremental programming;
ie, describing a system in terms of
how it differs from another system .
. compositional modularity evolves
traditional modules beyond oop .
. that compositional modularity
sounds interesting,
what's the author been up to recently?
reflective cap'based security lang's!
Bracha 2010`Modules as Objects in Newspeak:
. a module can exist as several instances;--. this is the equivalent of SOA:
they can be mutually recursive .
. Newspeak, a msg-based lang has no globals,
and all names are late-bound (obj' msg's).
. programming to an interface (msg's vs methods)
is central to modularity .
. it features cap'based security:
# obj's can hide internals
even from other instances of the same class;
# obj's have no access to globals
thus avoiding [ambient authority]
(being modified by external agents) .
# unlike E-lang, Newspeak supports reflection .
Newspeak handles foreign functions
by wrapping them in an alien obj,
rather than let safe code
call unsafe functions directly .
whatever you foreigners want to do,
do it on your own box (thread, module)
and send me the neat results .
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