Context Navigation

-                      r566cc33
+                      r314c9d8
 (In \CFA, the primary constants @0@ and @1@ can be overloaded for any type.)
 Hence, each primary constant has a symbolic name referring to its internal representation, and these names are dictated by language syntax related to types.
 In theory, there are an infinite set of primary names per type.
 \Newterm{Secondary naming} is a common practice in mathematics, engineering and computer science, \eg $\pi$, $\tau$ (2$\pi$), $\phi$ (golden ratio), MB (mega byte, 1E6), and in general situations, \eg specific times (noon, New Years), cities (Big Apple), flowers (Lily), \etc.
+In theory, there are an infinite set of primary constant names per type.
+\Newterm{Secondary naming} is a common practice in mathematics, engineering and computer science, \eg $\pi$, $\tau$ (2$\pi$), $\phi$ (golden ratio), MB (megabyte, 1E6), and in general situations, \eg specific times (noon, New Years), cities (Big Apple), flowers (Lily), \etc.
 Many programming languages capture this important software-engineering capability through a mechanism called \Newterm{constant} or \Newterm{literal} naming, where a secondary name is aliased to a primary name.
+Its common purpose is to eliminate duplication of the primary constant throughout a program.
+For example, the secondary name replaces its primary name, thereafter changing the binding of the secondary to primary name automatically distributes the rebinding throughout the program.
+Its purpose is for readability and to eliminate duplication of the primary constant throughout a program.
+For example, a meaningful secondary name replaces a primary name throughout a program;
+thereafter, changing the binding of the secondary to primary name automatically distributes the rebinding, preventing errors.
 In some cases, secondary naming is \Newterm{opaque}, where the matching internal representation can be chosen arbitrarily, and only equality operations are available, \eg @O_RDONLY@, @O_WRONLY@, @O_CREAT@, @O_TRUNC@, @O_APPEND@.
 Because a secondary name is a constant, it cannot appear in a mutable context, \eg \mbox{$\pi$ \lstinline{= 42}} is meaningless, and a constant has no address, \ie it is an \Newterm{rvalue}\footnote{
 The term rvalue defines an expression that can only appear on the right-hand side of an assignment expression.}.
 Secondary names can form an (ordered) set, \eg days of the week, months of a year, floors of a building (basement, ground, 1st), colours in a rainbow, \etc.
+Secondary names can form an (ordered) set, \eg days of a week, months of a year, floors of a building (basement, ground, 1st), colours in a rainbow, \etc.
 Many programming languages capture these groupings through a mechanism called an \Newterm{enumeration}.
 \begin{quote}
 …
 This independence from internal representation allows multiple names to have the same representation (eighth note, quaver), giving synonyms.
 A set can have a partial or total ordering, making it possible to compare set elements, \eg Monday is before Friday and Friday is after.
 Ordering allows iterating among the enumeration set using relational operators and advancement, \eg
+Ordering allows iterating among the enumeration set using relational operators and advancement, \eg:
 \begin{cfa}
 for ( cursor = Monday; cursor @<=@ Friday; cursor = @succ@( cursor ) ) ...
 \end{cfa}
 Here the internal representations for the secondary names are logically \emph{generated} rather than listing a subset of names.
+Here the internal representation for the secondary names are logically \emph{generated} rather than listing a subset of names.
 Hence, the fundamental aspects of an enumeration are:
 \begin{enumerate}
 \item
+It defines a type from which instants can be generated.
+\item
+The type lists a finite set of secondary names, which become its primary constants.
+This differentiates an enumeration from general types with an infinite number of primary constants.
+\item
+An enumeration's secondary names represent constants, which follows from their binding (aliasing) to primary names, which are constants.
+\item
+For safety, an enumeration instance is restricted to hold only its type's secondary names.
+\begin{sloppypar}
+It provides a finite set of secondary names, which become its primary constants.
+This differentiates an enumeration from general types with an infinite set
+of primary constants.
+\end{sloppypar}
+\item
+The secondary names are constants, which follows transitively from their binding (aliasing) to primary names, which are constants.
+\item
+Defines a type for generating instants (variables).
+\item
+For safety, an enumeration instance should be restricted to hold only its type's secondary names.
 \item
 There is a mechanism for \emph{enumerating} over the secondary names, where the ordering can be implicit from the type, explicitly listed, or generated arithmetically.
 …
 \label{s:Terminology}
 The term \Newterm{enumeration} defines a type with a set of secondary names, and the term \Newterm{enumerator} represents an arbitrary secondary name \see{\VRef{s:CEnumeration}}.
 As well, an enumerated type has three fundamental properties, \Newterm{label}, \Newterm{order}, and \Newterm{value}.
+The term \Newterm{enumeration} defines a type with a set of secondary names, and the term \Newterm{enumerator} represents an arbitrary secondary name \see{\VRef{s:CEnumeration} for the name derivation}.
+As well, an enumerated type can have three fundamental properties, \Newterm{label}, \Newterm{order}, and \Newterm{value}.
 \begin{cquote}
 \sf\setlength{\tabcolsep}{3pt}
 \begin{tabular}{rcccccccr}
 \it\color{red}enumeration       & \multicolumn{8}{c}{\it\color{red}enumerators} \\
 $\downarrow$\hspace*{25pt}      & \multicolumn{8}{c}{$\downarrow$}                              \\
 @enum@ Week \{                          & Mon,  & Tue,  & Wed,  & Thu,  & Fri,  & Sat,  & Sun = 42      & \};   \\
+$\downarrow$\hspace*{15pt}      & \multicolumn{8}{c}{$\downarrow$}                              \\
+@enum@ Week \{                          & Mon,  & Tue,  & Wed,  & Thu,  & Fri,  & Sat,  & Sun {\color{red}= 42} & \};   \\
 \it\color{red}label                     & Mon   & Tue   & Wed   & Thu   & Fri   & Sat   & Sun           &               \\
 \it\color{red}order                     & 0             & 1             & 2             & 3             & 4             & 5             & 6                     &               \\
 \it\color{red}value                     & 0             & 1             & 2             & 3             & 4             & 5             & 42            &
+\it\color{red}value                     & 0             & 1             & 2             & 3             & 4             & 5             & {\color{red}42}               &
 \end{tabular}
 \end{cquote}
 …
 \section{Motivation}
+Some programming languages only provide direct secondary renaming.
+Many programming languages provide an enumeration-like mechanism, which may or may not cover the previous five fundamental enumeration aspects.
+Hence, the term \emph{enumeration} can be confusing and misunderstood.
+Furthermore, some languages conjoin the enumeration with other type features, making it difficult to tease apart which featuring is being used.
+This section discusses some language features that are sometimes called an enumeration but do not provide all enumeration aspects.
+\subsection{Aliasing}
+Some languages provide simple secondary aliasing (renaming), \eg:
 \begin{cfa}
 const Size = 20, Pi = 3.14159, Name = "Jane";
 \end{cfa}
+Here, it is possible to compare the secondary names, \eg @Size < Pi@, if that is meaningful.
+Secondary renaming can simulate an enumeration, but with extra effort.
+The secondary name is logically replaced in the program text by its corresponding primary name.
+Therefore, it is possible to compare the secondary names, \eg @Size < Pi@, only because the primary constants allow it, whereas \eg @Pi < Name@ might be disallowed depending on the language.
+Aliasing is not macro substitution, \eg @#define Size 20@, where a name is replaced by its value \emph{before} compilation, so the name is invisible to the programming language.
+With aliasing, each secondary name is part of the language, and hence, participates fully, such as name overloading in the type system.
+Aliasing is not an immutable variable, \eg:
+\begin{cfa}
+extern @const@ int Size = 20;
+extern void foo( @const@ int @&@ size );
+foo( Size ); // take the address of (reference) Size
+\end{cfa}
+Taking the address of an immutable variable makes it an \Newterm{lvalue}, which implies it has storage.
+With separate compilation, it is necessary to choose one translation unit to perform the initialization.
+If aliasing does require storage, its address and initialization are opaque (compiler only), similar to \CC rvalue reference @&&@.
+Aliasing does provide readability and automatic resubstitution.
+It also provides simple enumeration properties, but with extra effort.
 \begin{cfa}
 const Mon = 1, Tue = 2, Wed = 3, Thu = 4, Fri = 5, Sat = 6, Sun = 7;
 …
 const Sun = 1, Mon = 2, Tue = 3, Wed = 4, Thu = 5, Fri = 6, Sat = 7;
 \end{cfa}
+Finally, there is no type to create a type-checked instance or iterator cursor.
+Hence, there is only a weak equivalence between secondary naming and enumerations, justifying a seperate enumeration type in a programming language.
+A variant (algebraic) type is often promoted as a kind of enumeration, \ie a variant type can simulate an enumeration.
+Fundamentally, a variant type is a tagged-union, where the tag is normally opaque and the types are usually heterogeneous.
+\begin{cfa}[morekeywords={variant}]
+@variant@ Variant {
+        @int tag;@  // optional/implicit: 0 => int, 1 => double, 2 => S
+        @union {@ // implicit
+                case int i;
+                case double d;
+                case struct S { int i, j; } s;
+        @};@
+};
+\end{cfa}
+Crucially, the union implies instance storage is shared by all the variant types, and therefore, before a variant type can be used in a statically-typed expression, it must be dynamically discriminated to its current contained type.
+Hence, knowing which type is in a variant instance is crucial for correctness.
+Occasionally, it is possible to statically determine all regions where each variant type is used, so a tag and runtime checking is unnecessary.
+Otherwise, a tag is required to denote the particular type in the variant, and the tag is discriminated at runtime using some form of type pattern-matching, after which the value can be used in a statically-typed expression.
+A less frequent variant case is multiple variants with the same type, which normally requires explicit naming of the tag to disambiguate among the common types.
+For these reasons, aliasing is sometimes called an enumeration.
+However, there is no type to create a type-checked instance or iterator cursor, so there is no ability for enumerating.
+Hence, there are multiple enumeration aspects not provided by aliasing, justifying a separate enumeration type in a programming language.
+\subsection{Algebraic Data Type}
+An algebraic data type (ADT)\footnote{ADT is overloaded with abstract data type.} is another language feature often linked with enumeration, where an ADT conjoins an arbitrary type, possibly a \lstinline[language=C++]{class} or @union@, and a named constructor.
+For example, in Haskell:
+\begin{haskell}
+data S = S { i::Int, d::Double }                $\C{// structure}$
+data @Foo@ = A Int | B Double | C S             $\C{// ADT, composed of three types}$
+foo = A 3;                                                              $\C{// type Foo is inferred}$
+bar = B 3.5
+baz = C S{ i = 7, d = 7.5 }
+\end{haskell}
+the ADT has three variants (constructors), @A@, @B@, @C@ with associated types @Int@, @Double@, and @S@.
+The constructors create an initialized value of the specific type that is bound to the immutable variables @foo@, @bar@, and @baz@.
+Hence, the ADT @Foo@ is like a union containing values of the associated types, and a constructor name is used to access the value using dynamic pattern-matching.
 \begin{cquote}
+\begin{tabular}{@{}l@{\hspace{30pt}}l@{}}
+\begin{cfa}[morekeywords={variant}]
+variant VariantCT {
+        case @car@: int i;  // explicitly typed
+        case @boat@: int i;
+        case @bridge@: int i;
+};
+\end{cfa}
+\setlength{\tabcolsep}{15pt}
+\begin{tabular}{@{}ll@{}}
+\begin{haskell}
+prtfoo val = -- function
+    -- pattern match on constructor
+    case val of
+      @A@ a -> print a
+      @B@ b -> print b
+      @C@ (S i d) -> do
+          print i
+          print d
+\end{haskell}
+&
+\begin{cfa}[morekeywords={variant}]
+variant VariantCU {
+        case @car@: ;  // empty or unit type
+        case @boat@: ;
+        case @bridge@: ;
+};
+\end{cfa}
+\begin{haskell}
+main = do
+    prtfoo foo
+    prtfoo bar
+    prtfoo baz
+.5
+.5
+\end{haskell}
 \end{tabular}
 \end{cquote}
+Here, the explicit tag name is used to give different meaning to the values in the common @int@ type, \eg the value 3 has different interpretations depending on the tag name.
+It is even possible to remove the type or use the empty @unit@ type (@struct unit {}@).
+It is this tag naming that is used to simulate an enumeration.
+Normally, the variant tag is implicitly set by the compiler based on type, but with common types, a tag name is required to resolve type ambiguity.
+\begin{cfa}
+Variant v = 3;                                                  $\C{// implicitly set tag to 0 based on type of 3}$
+VariantCT ve = boats.3;                                 $\C{// explicitly set tag to 1 using tag name}$
+\end{cfa}
+Type pattern-matching is then used to dynamically test the tag and branch to a section of statically-typed code to safely manipulate the value, \eg:
+For safety, most languages require all assocaited types to be listed or a default case with no field accesses.
+A less frequent case is multiple constructors with the same type.
+\begin{haskell}
+data Bar = X Int | Y Int | Z Int;
+foo = X 3;
+bar = Y 3;
+baz = Z 5;
+\end{haskell}
+Here, the constructor name gives different meaning to the values in the common \lstinline[language=Haskell]{Int} type, \eg the value @3@ has different interpretations depending on the constructor name in the pattern matching.
+Note, the term \Newterm{variant} is often associated with ADTs.
+However, there are multiple languages with a @variant@ type that is not an ADT \see{Algol68~\cite{Algol68} or \CC \lstinline{variant}}.
+In these languages, the variant is often a union using RTTI tags, which cannot be used to simulate an enumeration.
+Hence, in this work the term variant is not a synonym for ADT.
+% https://downloads.haskell.org/ghc/latest/docs/libraries/base-4.19.1.0-179c/GHC-Enum.html
+% https://hackage.haskell.org/package/base-4.19.1.0/docs/GHC-Enum.html
+The association between ADT and enumeration occurs if all the constructors have a unit (empty) type, \eg @struct unit {}@.
+Note, the unit type is not the same as \lstinline{void}, \eg:
+\begin{cfa}
+void foo( void );
+struct unit {} u;  // empty type
+unit bar( unit );
+foo( foo() );        // void argument does not match with void parameter
+bar( bar( u ) );   // unit argument does match with unit parameter
+\end{cfa}
+For example, in the Haskell ADT:
+\begin{haskell}
+data Week = Mon | Tue | Wed | Thu | Fri | Sat | Sun deriving(Enum, Eq, Show)
+\end{haskell}
+the default type for each constructor is the unit type, and deriving from @Enum@ enforces no other type, @Eq@ allows equality comparison, and @Show@ is for printing.
+The nullary constructors for the unit types are numbered left-to-right from $0$ to @maxBound@$- 1$, and provides enumerating operations @succ@, @pred@, @enumFrom@ @enumFromTo@.
+\VRef[Figure]{f:HaskellEnumeration} shows enumeration comparison and iterating (enumerating).
+\begin{figure}
 \begin{cquote}
+\begin{tabular}{@{}l@{\hspace{30pt}}l@{}}
+\begin{cfa}[morekeywords={match}]
+@match@( v ) { // know type implicitly or test tag
+        case int { /* only access i field */ }
+        case double { /* only access d field */ }
+        case S { /* only access s field */ }
+}
+\end{cfa}
+\setlength{\tabcolsep}{15pt}
+\begin{tabular}{@{}ll@{}}
+\begin{haskell}
+day = Tue
+main = do
+    if day == Tue then
+        print day
+    else
+        putStr "not Tue"
+    print (enumFrom Mon)            -- week
+    print (enumFromTo Mon Fri)   -- weekday
+    print (enumFromTo Sat Sun)  -- weekend
+\end{haskell}
+&
+\begin{cfa}[morekeywords={match}]
+@match@( ve ) {
+        case car: int { /* car interpretation */ }
+        case boat: int { /* boat interpretation */ }
+        case bridge: int { /* bridge interpretation */ }
+}
+\end{cfa}
+\begin{haskell}
+Tue
+[Mon,Tue,Wed,Thu,Fri,Sat,Sun]
+[Mon,Tue,Wed,Thu,Fri]
+[Sat,Sun]
+\end{haskell}
 \end{tabular}
 \end{cquote}
+For safety, some languages require all variant types to be listed or a @default@ case with no field accesses.
+To further strengthen the simulate for an enumeration with different values, each variant type can be a @const@ type or the tag becomes non-opaque, possibly taking advantage of the opaque auto-numbering.
+\begin{cquote}
+\begin{tabular}{@{}l@{\hspace{30pt}}l@{}}
+\begin{cfa}
+variant Week {
+        case Mon: const int = 0;
+        ...
+        case Sat: const int = 5;
+        case Sun: const int = 10;
+};
+\end{cfa}
+&
+\begin{cfa}
+variant Week {
+        case Mon: ;  // tag auto-numbering
+        ...
+        case Sat: ;
+        case @Sun = 10@: ; // directly set tag value
+};
+\end{cfa}
+\end{tabular}
+\end{cquote}
+Directly setting the tag implies restrictions, like unique values.
+In both cases, instances of @Week@ are @const@ (immutable).
+However, usage between these two types becomes complex.
+\begin{cfa}
+Week day = Week.Mon;  // sets value or tag depending on type
+if ( day == Week.Mon )   // dereference value or tag ?
+\end{cfa}
+Here, the dereference of @day@ should return the value of the type stored in the variant, never the tag.
+If it does return the tag, some special meaning must be given to the empty/unit type, especially if a variant contains both regular and unit types.
+In general, the enumeration simulation and the variant extensions to support it, are deviating from the normal use of a variant (union) type.
+As well, the enumeration operations are limited to the available tag operations, \eg pattern matching.
+While enumerating among tag names is possible:
+\begin{cfa}[morekeywords={in}]
+for ( cursor in Week.Mon, Week.Wed, Week.Fri, Week.Sun ) ...
+\end{cfa}
+what is the type of @cursor@?
+If it the tag type (@int@), how is this value used?
+If it is the variant type, where is the instance variable, which only contains one value.
+Hence, either enumerating with a variant enumeration is disallowed or some unusual typing rule must be invented to make it work but only in restricted contexts.
+While functional programming systems regularly re-purposing variant types into enumeration types, this process seems contrived and confusing.
+A variant tag is not an enumeration, it is a discriminant among a restricted set of types stored in a storage block.
+Hence, there is only a weak equivalence between an enumeration and variant type, justifying a seperate enumeration type in a programming language.
+\caption{Haskell Enumeration}
+\label{f:HaskellEnumeration}
+\end{figure}
+The key observation is the dichotomy between an ADT and enumeration: the ADT uses the associated type resulting in a union-like data structure, and the enumeration does not use the associated type, and hence, is not a union.
+While the enumeration is constructed using the ADT mechanism, it is so restricted it is not really an ADT.
+Furthermore, a general ADT cannot be an enumeration because the constructors generate different values making enumerating meaningless.
+While functional programming languages regularly repurpose the ADT type into an enumeration type, this process seems contrived and confusing.
+Hence, there is only a weak equivalence between an enumeration and ADT, justifying a separate enumeration type in a programming language.
 \section{Contributions}
 The goal of this work is to to extend the simple and unsafe enumeration type in the C programming-language into a sophisticated and safe type in the \CFA programming-language, while maintain backwards compatibility with C.
+The goal of this work is to to extend the simple and unsafe enumeration type in the C programming-language into a complex and safe enumeration type in the \CFA programming-language, while maintaining backwards compatibility with C.
 On the surface, enumerations seem like a simple type.
 However, when extended with advanced features, enumerations become complex for both the type system and the runtime implementation.
+The contribution of this work are:
 \begin{enumerate}
 \item
 …
 typing
 \item
 subset
+subseting
 \item
 inheritance

Note: See TracChangeset for help on using the changeset viewer.

Context Navigation

Changeset 314c9d8 for doc

Legend:

doc/theses/jiada_liang_MMath/intro.tex

Download in other formats: