Changeset 40ab446

Dec 11, 2023, 1:48:43 PM (5 months ago)
Michael Brooks <mlbrooks@…>

Recent thesis writing

4 edited


  • doc/theses/mike_brooks_MMath/array.tex

    rdab9fb93 r40ab446  
     5This chapter describes my contribution of language and library features that provide a length-checked array type, as in:
     8    array(float, 99) x;    // x contains 99 floats
     10    void f( array(float, 42) & a ) {}
     11    f(x);                  // statically rejected: types are different
     13    forall( T, [N] )
     14    void g( array(T, N) & a, int i ) {
     15        T elem = a[i];     // dynamically checked: requires 0 <= i < N
     16    }
     17    g(x, 0);               // T is float, N is 99, succeeds
     18    g(x, 1000);            // T is float, N is 99, dynamic check fails
     21This example first declares @x@ a variable, whose type is an instantiation of the generic type named @array@, with arguments @float@ and @99@.
     22Next, it declares @f@ as a function that expects a length-42 array; the type system rejects the call's attempt to pass @x@ to @f@, because the lengths do not match.
     23Next, the @forall@ annotation on function @g@ introduces @T@ as a familiar type parameter and @N@ as a \emph{dimension} parameter, a new feature that represents a count of elements, as managed by the type system.
     24Because @g@ accepts any length of array; the type system accepts the calls' passing @x@ to @g@, inferring that this length is 99.
     25Just as the caller's code does not need to explain that @T@ is @float@, the safe capture and communication of the value @99@ occurs without programmer involvement.
     26In the case of the second call (which passes the value 1000 for @i@), within the body of @g@, the attempt to subscript @a@ by @i@ fails with a runtime error, since $@i@ \nless @N@$.
     28The type @array@, as seen above, comes from my additions to the \CFA standard library.
     29It is very similar to the built-in array type, which \CFA inherits from C.
     30Its runtime characteristics are often identical, and some features are available in both.
     33    forall( [N] )
     34    void declDemo() {
     35        float a1[N];         // built-in type ("C array")
     36        array(float, N) a2;  // type from library
     37    }
     40If a caller instantiates @N@ with 42, then both locally-declared array variables, @a1@ and @a2@, become arrays of 42 elements, each element being a @float@.
     41The two variables have identical size and layout; they both encapsulate 42-float stack allocations, no heap allocations, and no further "bookkeeping" allocations/header.
     42Having the @array@ library type (that of @a2@) is a tactical measure, an early implementation that offers full feature support.
     43A future goal (TODO xref) is to port all of its features into the built-in array type (that of @a1@); then, the library type could be removed, and \CFA would have only one array type.
     44In present state, the built-in array has partial support for the new features.
     45The fully-featured library type is used exclusively in introductory examples; feature support and C compatibility are revisited in sec TODO.
     47Offering the @array@ type, as a distinct alternative from the the C array, is consistent with \CFA's extension philosophy (TODO xref background) to date.
     48A few compatibility-breaking changes to the behaviour of the C array were also made, both as an implementation convenience, and as justified fixes to C's lax treatment.
     50The @array@ type is an opportunity to start from a clean slate and show a cohesive selection of features.
     51A clean slate was an important starting point because it meant not having to deal with every inherited complexity introduced in TODO xref background-array.
     54My contributions are
     56    \item a type system enhancement that lets polymorphic functions and generic types be parameterized by a numeric value: @forall( [N] )@
     57    \item [TODO: general parking...]
     58    \item identify specific abilities brought by @array@
     59    \item Where there is a gap concerning this feature's readiness for prime-time, identification of specific workable improvements that are likely to close the gap
     64\section{Definitions and design considerations}
     66\subsection{Dependent typing}
  • doc/theses/mike_brooks_MMath/background.tex

    rdab9fb93 r40ab446  
    3 \section{Arrays}
    5 \section{Strings}
     3This chapter states facts about the prior work, upon which my contributions build.
     4Each receives a justification of the extent to which its statement is phrased to provoke controversy or surprise.
     8\subsection{Common knowledge}
     10The reader is assumed to have used C or \CC for the coursework of at least four university-level courses, or have equivalent experience.
     11The current discussion introduces facts, unaware of which, such a functioning novice may be operating.
     13% TODO: decide if I'm also claiming this collection of facts, and test-oriented presentation is a contribution; if so, deal with (not) arguing for its originality
     15\subsection{Convention: C is more touchable than its standard}
     17When it comes to explaining how C works, I like illustrating definite program semantics.
     18I prefer doing so, over a quoting manual's suggested programmer's intuition, or showing how some compiler writers chose to model their problem.
     19To illustrate definite program semantics, I devise a program, whose behaviour exercises the point at issue, and I show its behaviour.
     21This behaviour is typically one of
     23    \item my statement that the compiler accepts or rejects the program
     24    \item the program's printed output, which I show
     25    \item my implied assurance that its assertions do not fail when run
     28The compiler whose program semantics is shown is
     30$ gcc --version
     31gcc (Ubuntu 9.4.0-1ubuntu1~20.04.1) 9.4.0
     33running on Architecture @x86_64@, with the same environment targeted.
     35Unless explicit discussion ensues about differences among compilers or with (versions of) the standard, it is further implied that there exists a second version of GCC and some version of Clang, running on and for the same platform, that give substantially similar behaviour.
     36In this case, I do not argue that my sample of major Linux compilers is doing the right thing with respect to the C standard.
     39\subsection{C reports many ill-typed expressions as warnings}
     41TODO: typeset
     42\lstinputlisting[language=C, firstline=13, lastline=56]{bkgd-c-tyerr.c}
     45\section{C Arrays}
     47\subsection{C has an array type (!)}
     49TODO: typeset
     50\lstinputlisting[language=C, firstline=35, lastline=116]{bkgd-carray-arrty.c}
     52My contribution is enabled by recognizing
     54    \item There is value in using a type that knows how big the whole thing is.
     55    \item The type pointer to (first) element does not.
     56    \item C \emph{has} a type that knows the whole picture: array, e.g. @T[10]@.
     57    \item This type has all the usual derived forms, which also know the whole picture.  A usefully noteworthy example is pointer to array, e.g. @T(*)[10]@.
     60Each of these sections, which introduces another layer of of the C arrays' story,
     61concludes with an \emph{Unfortunate Syntactic Reference}.
     62It shows how to spell the types under discussion,
     63along with interactions with orthogonal (but easily confused) language features.
     64Alterrnate spellings are listed withing a row.
     65The simplest occurrences of types distinguished in the preceding discussion are marked with $\triangleright$.
     66The Type column gives the spelling used in a cast or error message (though note Section TODO points out that some types cannot be casted to).
     67The Declaration column gives the spelling used in an object declaration, such as variable or aggregate member; parameter declarations (section TODO) follow entirely different rules.
     69After all, reading a C array type is easy: just read it from the inside out, and know when to look left and when to look right!
     72\CFA-specific spellings (not yet introduced) are also included here for referenceability; these can be skipped on linear reading.
     73The \CFA-C column gives the, more fortunate, ``new'' syntax of section TODO, for spelling \emph{exactly the same type}.
     74This fortunate syntax does not have different spellings for types vs declarations;
     75a declaration is always the type followed by the declared identifier name;
     76for the example of letting @x@ be a \emph{pointer to array}, the declaration is spelled:
     78[ * [10] T ] x;
     80The \CFA-Full column gives the spelling of a different type, introduced in TODO, which has all of my contributed improvements for safety and ergonomics.
     83\textbf{Unfortunate Syntactic Reference}
     87    & Description & Type & Declaration & \CFA-C  & \CFA-Full \\ \hline
     88    $\triangleright$ & val.
     89        & @T@
     90        & @T x;@
     91        & @[ T ]@
     92        &
     93        \\ \hline
     94    & \pbox{20cm}{ \vspace{2pt} val.\\ \footnotesize{no writing the val.\ in \lstinline{x}}   }\vspace{2pt}
     95        & \pbox{20cm}{ \vspace{2pt} \lstinline{const T} \\ \lstinline{T const}   }
     96        & \pbox{20cm}{ \vspace{2pt} \lstinline{const T x;} \\ \lstinline{T const x;}   }
     97        & @[ const T ]@
     98        &
     99        \\ \hline
     100    $\triangleright$ & ptr.\ to val.
     101        & @T *@
     102        & @T * x;@
     103        & @[ * T ]@
     104        &
     105        \\ \hline
     106    & \pbox{20cm}{ \vspace{2pt} ptr.\ to val.\\ \footnotesize{no writing the ptr.\ in \lstinline{x}}   }\vspace{2pt}
     107        & @T * const@
     108        & @T * const x;@
     109        & @[ const * T ]@
     110        &
     111        \\ \hline
     112    & \pbox{20cm}{ \vspace{2pt} ptr.\ to val.\\ \footnotesize{no writing the val.\ in \lstinline{*x}}   }\vspace{2pt}
     113        & \pbox{20cm}{ \vspace{2pt} \lstinline{const T *} \\ \lstinline{T const *}   }
     114        & \pbox{20cm}{ \vspace{2pt} \lstinline{const T * x;} \\ \lstinline{T const * x;}   }
     115        & @[ * const T ]@
     116        &
     117        \\ \hline
     118    $\triangleright$ & ar.\ of val.
     119        & @T[10]@
     120        & @T x[10];@
     121        & @[ [10] T ]@
     122        & @[ array(T, 10) ]@
     123        \\ \hline
     124    & \pbox{20cm}{ \vspace{2pt} ar.\ of val.\\ \footnotesize{no writing the val.\ in \lstinline{x[5]}}   }\vspace{2pt}
     125        & \pbox{20cm}{ \vspace{2pt} \lstinline{const T[10]} \\ \lstinline{T const[10]}   }
     126        & \pbox{20cm}{ \vspace{2pt} \lstinline{const T x[10];} \\ \lstinline{T const x[10];}   }
     127        & @[ [10] const T ]@
     128        & @[ const array(T, 10) ]@
     129        \\ \hline
     130    & ar.\ of ptr.\ to val.
     131        & @T*[10]@
     132        & @T *x[10];@
     133        & @[ [10] * T ]@
     134        & @[ array(* T, 10) ]@
     135        \\ \hline
     136    & \pbox{20cm}{ \vspace{2pt} ar.\ of ptr.\ to val.\\ \footnotesize{no writing the ptr.\ in \lstinline{x[5]}}   }\vspace{2pt}
     137        & @T * const [10]@
     138        & @T * const x[10];@
     139        & @[ [10] const * T ]@
     140        & @[ array(const * T, 10) ]@
     141        \\ \hline
     142    & \pbox{20cm}{ \vspace{2pt} ar.\ of ptr.\ to val.\\ \footnotesize{no writing the val.\ in \lstinline{*(x[5])}}   }\vspace{2pt}
     143        & \pbox{20cm}{ \vspace{2pt} \lstinline{const T * [10]} \\ \lstinline{T const * [10]}   }
     144        & \pbox{20cm}{ \vspace{2pt} \lstinline{const T * x[10];} \\ \lstinline{T const * x[10];}   }
     145        & @[ [10] * const T ]@
     146        & @[ array(* const T, 10) ]@
     147        \\ \hline
     148    $\triangleright$ & ptr.\ to ar.\ of val.
     149        & @T(*)[10]@
     150        & @T (*x)[10];@
     151        & @[ * [10] T ]@
     152        & @[ * array(T, 10) ]@
     153        \\ \hline
     154    & \pbox{20cm}{ \vspace{2pt} ptr.\ to ar.\ of val.\\ \footnotesize{no writing the ptr.\ in \lstinline{x}}   }\vspace{2pt}
     155        & @T(* const)[10]@
     156        & @T (* const x)[10];@
     157        & @[ const * [10] T ]@
     158        & @[ const * array(T, 10) ]@
     159        \\ \hline
     160    & \pbox{20cm}{ \vspace{2pt} ptr.\ to ar.\ of val.\\ \footnotesize{no writing the val.\ in \lstinline{(*x)[5]}}   }\vspace{2pt}
     161        & \pbox{20cm}{ \vspace{2pt} \lstinline{const T(*)[10]} \\ \lstinline{T const (*) [10]}   }
     162        & \pbox{20cm}{ \vspace{2pt} \lstinline{const T (*x)[10];} \\ \lstinline{T const (*x)[10];}   }
     163        & @[ * [10] const T ]@
     164        & @[ * const array(T, 10) ]@
     165        \\ \hline
     166    & ptr.\ to ar.\ of ptr.\ to val.
     167        & @T*(*)[10]@
     168        & @T *(*x)[10];@
     169        & @[ * [10] * T ]@
     170        & @[ * array(* T, 10) ]@
     171        \\ \hline
     175\subsection{Arrays decay and pointers diffract}
     177TODO: typeset
     178\lstinputlisting[language=C, firstline=4, lastline=26]{bkgd-carray-decay.c}
     181So, C provides an implicit conversion from @float[10]@ to @float*@, as described in ARM-
     184    Except when it is the operand of the @sizeof@ operator, or the unary @&@ operator, or is a
     185    string literal used to initialize an array
     186    an expression that has type ``array of type'' is
     187    converted to an expression with type ``pointer to type'' that points to the initial element of
     188    the array object
     191This phenomenon is the famous ``pointer decay,'' which is a decay of an array-typed expression into a pointer-typed one.
     193It is worthy to note that the list of exception cases does not feature the occurrence of @a@ in @a[i]@.
     194Thus, subscripting happens on pointers, not arrays.
     196Subscripting proceeds first with pointer decay, if needed.  Next, ARM- explains that @a[i]@ is treated as if it were @(*((a)+(i)))@.
     197ARM- explains that the addition, of a pointer with an integer type,  is defined only when the pointer refers to an element that is in an array, with a meaning of ``@i@ elements away from,'' which is valid if @a@ is big enough and @i@ is small enough.
     198Finally, ARM- explains that the @*@ operator's result is the referenced element.
     200Taken together, these rules also happen to illustrate that @a[i]@ and @i[a]@ mean the same thing.
     202Subscripting a pointer when the target is standard-inappropriate is still practically well-defined.
     203While the standard affords a C compiler freedom about the meaning of an out-of-bound access,
     204or of subscripting a pointer that does not refer to an array element at all,
     205the fact that C is famously both generally high-performance, and specifically not bound-checked,
     206leads to an expectation that the runtime handling is uniform across legal and illegal accesses.
     207Moreover, consider the common pattern of subscripting on a malloc result:
     209    float * fs = malloc( 10 * sizeof(float) );
     210    fs[5] = 3.14;
     212The @malloc@ behaviour is specified as returning a pointer to ``space for an object whose size is'' as requested (ARM-
     213But program says \emph{nothing} more about this pointer value, that might cause its referent to \emph{be} an array, before doing the subscript.
     215Under this assumption, a pointer being subscripted (or added to, then dereferenced)
     216by any value (positive, zero, or negative), gives a view of the program's entire address space,
     217centred around the @p@ address, divided into adjacent @sizeof(*p)@ chunks,
     218each potentially (re)interpreted as @typeof(*p)@.
     220I call this phenomenon ``array diffraction,''  which is a diffraction of a single-element pointer
     221into the assumption that its target is in the middle of an array whose size is unlimited in both directions.
     223No pointer is exempt from array diffraction.
     225No array shows its elements without pointer decay.
     227A further pointer--array confusion, closely related to decay, occurs in parameter declarations.
     228ARM- explains that when an array type is written for a parameter,
     229the parameter's type becomes a type that I summarize as being the array-decayed type.
     230The respective handlings of the following two parameter spellings shows that the array-spelled one is really, like the other, a pointer.
     231\lstinputlisting[language=C, firstline=40, lastline=44]{bkgd-carray-decay.c}
     232As the @sizeof(x)@ meaning changed, compared with when run on a similarly-spelled local variariable declaration,
     233GCC also gives this code the warning: ```sizeof' on array function parameter `x' will return size of `float *'.''
     235The caller of such a function is left with the reality that a pointer parameter is a pointer, no matter how it's spelled:
     236\lstinputlisting[language=C, firstline=60, lastline=63]{bkgd-carray-decay.c}
     237This fragment gives no warnings.
     239The shortened parameter syntax @T x[]@ is a further way to spell ``pointer.''
     240Note the opposite meaning of this spelling now, compared with its use in local variable declarations.
     241This point of confusion is illustrated in:
     242\lstinputlisting[language=C, firstline=80, lastline=87]{bkgd-carray-decay.c}
     243The basic two meanings, with a syntactic difference helping to distinguish,
     244are illustrated in the declarations of @ca@ vs.\ @cp@,
     245whose subsequent @edit@ calls behave differently.
     246The syntax-caused confusion is in the comparison of the first and last lines,
     247both of which use a literal to initialze an object decalared with spelling @T x[]@.
     248But these initialized declarations get opposite meanings,
     249depending on whether the object is a local variable or a parameter.
     252In sumary, when a funciton is written with an array-typed parameter,
     254    \item an appearance of passing an array by value is always an incorrect understanding
     255    \item a dimension value, if any is present, is ignorred
     256    \item pointer decay is forced at the call site and the callee sees the parameter having the decayed type
     259Pointer decay does not affect pointer-to-array types, because these are already pointers, not arrays.
     260As a result, a function with a pointer-to-array parameter sees the parameter exactly as the caller does:
     261\lstinputlisting[language=C, firstline=100, lastline=110]{bkgd-carray-decay.c}
     265\textbf{Unfortunate Syntactic Reference}
     268(Parameter declaration; ``no writing'' refers to the callee's ability)
     272    & Description & Type & Param. Decl & \CFA-C  \\ \hline
     273    $\triangleright$ & ptr.\ to val.
     274        & @T *@
     275        & \pbox{20cm}{ \vspace{2pt} \lstinline{T * x,} \\ \lstinline{T x[10],} \\ \lstinline{T x[],}   }\vspace{2pt}
     276        & \pbox{20cm}{ \vspace{2pt} \lstinline{[ * T ]} \\ \lstinline{[ [10] T ]} \\ \lstinline{[ [] T  ]}   }
     277        \\ \hline
     278    & \pbox{20cm}{ \vspace{2pt} ptr.\ to val.\\ \footnotesize{no writing the ptr.\ in \lstinline{x}}   }\vspace{2pt}
     279        & @T * const@
     280        & \pbox{20cm}{ \vspace{2pt} \lstinline{T * const x,} \\ \lstinline{T x[const 10],} \\ \lstinline{T x[const],}   }\vspace{2pt}
     281        & \pbox{20cm}{ \vspace{2pt} \lstinline{[ const * T ]} \\ \lstinline{[ [const 10] T ]} \\ \lstinline{[ [const] T  ]}   }
     282        \\ \hline
     283    & \pbox{20cm}{ \vspace{2pt} ptr.\ to val.\\ \footnotesize{no writing the val.\ in \lstinline{*x}}   }\vspace{2pt}
     284        & \pbox{20cm}{ \vspace{2pt} \lstinline{const T *} \\ \lstinline{T const *}   }
     285        & \pbox{20cm}{ \vspace{2pt} \lstinline{const T * x,} \\ \lstinline{T const * x,} \\ \lstinline{const T x[10],} \\ \lstinline{T const x[10],} \\ \lstinline{const T x[],} \\ \lstinline{T const x[],}   }\vspace{2pt}
     286        & \pbox{20cm}{ \vspace{2pt} \lstinline{[* const T]} \\ \lstinline{[ [10] const T ]} \\ \lstinline{[ [] const T  ]}   }
     287        \\ \hline
     288    $\triangleright$ & ptr.\ to ar.\ of val.
     289        & @T(*)[10]@
     290        & \pbox{20cm}{ \vspace{2pt} \lstinline{T (*x)[10],} \\ \lstinline{T x[3][10],} \\ \lstinline{T x[][10],}   }\vspace{2pt}
     291        & \pbox{20cm}{ \vspace{2pt} \lstinline{[* [10] T]} \\ \lstinline{[ [3] [10] T ]} \\ \lstinline{[ [] [10] T  ]}   }
     292        \\ \hline
     293    & ptr.\ to ptr.\ to val.
     294        & @T **@
     295        & \pbox{20cm}{ \vspace{2pt} \lstinline{T ** x,} \\ \lstinline{T *x[10],} \\ \lstinline{T *x[],}   }\vspace{2pt}
     296        & \pbox{20cm}{ \vspace{2pt} \lstinline{[ * * T ]} \\ \lstinline{[ [10] * T ]} \\ \lstinline{[ [] * T  ]}   }
     297        \\ \hline
     298    & \pbox{20cm}{ \vspace{2pt} ptr.\ to ptr.\ to val.\\ \footnotesize{no writing the val.\ in \lstinline{**argv}}   }\vspace{2pt}
     299        & @const char **@
     300        & \pbox{20cm}{ \vspace{2pt} \lstinline{const char *argv[],} \\ \footnotesize{(others elided)}   }\vspace{2pt}
     301        & \pbox{20cm}{ \vspace{2pt} \lstinline{[ [] * const char ]} \\ \footnotesize{(others elided)}   }
     302        \\ \hline
     307\subsection{Lengths may vary, checking does not}
     309When the desired number of elements is unknown at compile time,
     310a variable-length array is a solution:
     312    int main( int argc, const char *argv[] ) {
     314        assert( argc == 2 );
     315        size_t n = atol( argv[1] );
     316        assert( 0 < n && n < 1000 );
     318        float a[n];
     319        float b[10];
     321        // ... discussion continues here
     322    }
     324This arrangement allocates @n@ elements on the @main@ stack frame for @a@,
     325just as it puts 10 elements on the @main@ stack frame for @b@.
     326The variable-sized allocation of @a@ is provided by @alloca@.
     328In a situation where the array sizes are not known to be small enough
     329for stack allocation to be sensible,
     330corresponding heap allocations are achievable as:
     332    float *ax1 = malloc( sizeof( float[n] ) );
     333    float *ax2 = malloc( n * sizeof( float ) );
     334    float *bx1 = malloc( sizeof( float[1000000] ) );
     335    float *bx2 = malloc( 1000000 * sizeof( float ) );
     341Parameter dependency
     343Checking is best-effort / unsound
     345Limited special handling to get the dimension value checked (static)
     349\subsection{C has full-service, dynamically sized, multidimensional arrays (and \CC does not)}
     351In C and \CC, ``multidimensional array'' means ``array of arrays.''  Other meanings are discussed in TODO.
     353Just as an array's element type can be @float@, so can it be @float[10]@.
     355While any of @float*@, @float[10]@ and @float(*)[10]@ are easy to tell apart from @float@,
     356telling them apart from each other may need occasional reference back to TODO intro section.
     357The sentence derived by wrapping each type in @-[3]@ follows.
     359While any of @float*[3]@, @float[3][10]@ and @float(*)[3][10]@ are easy to tell apart from @float[3]@,
     360telling them apart from each other is what it takes to know what ``array of arrays'' really means.
     363Pointer decay affects the outermost array only
     366TODO: unfortunate syntactic reference with these cases:
     369    \item ar. of ar. of val (be sure about ordering of dimensions when the declaration is dropped)
     370    \item ptr. to ar. of ar. of val
     377\subsection{Arrays are (but) almost values}
     379Has size; can point to
     381Can't cast to
     383Can't pass as value
     385Can initialize
     387Can wrap in aggregate
     389Can't assign
     392\subsection{Returning an array is (but) almost possible}
     397\subsection{The pointer-to-array type has been noticed before}
     402Traditionally, fixing C meant leaving the C-ism alone, while providing a better alternative beside it.
     403(For later:  That's what I offer with array.hfa, but in the future-work vision for arrays, the fix includes helping programmers stop accidentally using a broken C-ism.)
     405\subsection{\CFA features interacting with arrays}
     407Prior work on \CFA included making C arrays, as used in C code from the wild,
     408work, if this code is fed into @cfacc@.
     409The quality of this this treatment was fine, with no more or fewer bugs than is typical.
     411More mixed results arose with feeding these ``C'' arrays into preexisting \CFA features.
     413A notable success was with the \CFA @alloc@ function,
     414which type information associated with a polymorphic return type
     415replaces @malloc@'s use of programmer-supplied size information.
     417    // C, library
     418    void * malloc( size_t );
     419    // C, user
     420    struct tm * el1 = malloc(      sizeof(struct tm) );
     421    struct tm * ar1 = malloc( 10 * sizeof(struct tm) );
     423    // CFA, library
     424    forall( T * ) T * alloc();
     425    // CFA, user
     426    tm * el2 = alloc();
     427    tm (*ar2)[10] = alloc();
     429The alloc polymorphic return compiles into a hidden parameter, which receives a compiler-generated argument.
     430This compiler's argument generation uses type information from the left-hand side of the initialization to obtain the intended type.
     431Using a compiler-produced value eliminates an opportunity for user error.
     433TODO: fix in following: even the alloc call gives bad code gen: verify it was always this way; walk back the wording about things just working here; assignment (rebind) seems to offer workaround, as in
     435Bringing in another \CFA feature, reference types, both resolves a sore spot of the last example, and gives a first example of an array-interaction bug.
     436In the last example, the choice of ``pointer to array'' @ar2@ breaks a parallel with @ar1@.
     437They are not subscripted in the same way.
     439    ar1[5];
     440    (*ar2)[5];
     442Using ``reference to array'' works at resolving this issue.  TODO: discuss connection with Doug-Lea \CC proposal.
     444    tm (&ar3)[10] = *alloc();
     445    ar3[5];
     447The implicit size communication to @alloc@ still works in the same ways as for @ar2@.
     449Using proper array types (@ar2@ and @ar3@) addresses a concern about using raw element pointers (@ar1), albeit a theoretical one.
     450TODO xref C standard does not claim that @ar1@ may be subscripted,
     451because no stage of interpreting the construction of @ar1@ has it be that ``there is an \emph{array object} here.''
     452But both @*ar2@ and the referent of @ar3@ are the results of \emph{typed} @alloc@ calls,
     453where the type requested is an array, making the result, much more obviously, an array object.
     455The ``reference to array'' type has its sore spots too.  TODO see also dimexpr-match-c/REFPARAM_CALL (under TRY_BUG_1)
     459TODO: I fixed a bug associated with using an array as a T.  I think.  Did I really?  What was the bug?
  • doc/theses/mike_brooks_MMath/list.tex

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    212214\PAB{I'm not sure about the term \newterm{Directionality}. Directionality to me, means going forward or backwards through a list.
    213215Would \newterm{dimensionality} work? Think of each list containing the node as a different dimension in which the node sits.}
  • doc/theses/mike_brooks_MMath/uw-ethesis.tex

    rdab9fb93 r40ab446  
    9698% Hyperlinks make it very easy to navigate an electronic document.
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