Changeset 5546eee4 for doc


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Timestamp:
Dec 16, 2023, 1:01:44 AM (2 years ago)
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JiadaL <j82liang@…>
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Merge branch 'master' of plg.uwaterloo.ca:software/cfa/cfa-cc

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doc/theses/mike_brooks_MMath
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  • doc/theses/mike_brooks_MMath/array.tex

    r0fa0201d r5546eee4  
    11\chapter{Array}
    22
     3\section{Introduction}
     4
     5This chapter describes my contribution of language and library features that provide a length-checked array type, as in:
     6
     7\begin{lstlisting}
     8    array(float, 99) x;    // x contains 99 floats
     9
     10    void f( array(float, 42) & a ) {}
     11    f(x);                  // statically rejected: types are different
     12
     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
     19\end{lstlisting}
     20
     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 $@i@ \nless @N@$.
     27
     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.
     31
     32\begin{lstlisting}
     33    forall( [N] )
     34    void declDemo() {
     35        float a1[N];         // built-in type ("C array")
     36        array(float, N) a2;  // type from library
     37    }
     38\end{lstlisting}
     39
     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.
     46
     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.
     49
     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.
     52
     53
     54My contributions are
     55\begin{itemize}
     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
     60\end{itemize}
     61
     62
     63
     64\section{Definitions and design considerations}
     65
     66\subsection{Dependent typing}
     67
     68
     69
     70
    371\section{Features Added}
    472
    573The present work adds a type @array@ to the \CFA standard library~\cite{Cforall}.
    674
    7 This array's length is statically governed and dynamically valued.  This static governance achieves argument safety and suggests a path to subscript safety as future work (TODO: cross reference).  In present state, this work is a runtime libray accessed through a system of macros, while section [TODO: discuss C conexistence] discusses a path for the new array type to be accessed directly by \CFA's array syntax, replacing the lifted C array that this syntax currently exposes.
    8 
    9 This section presents motivating examples of the new array type's usage, and follows up with definitions of the notations that appear.
    10 
    11 The core of the new array governance is tracking all array lengths in the type system.  Dynamically valued lengths are represented using type variables.  The stratification of type variables preceding object declarations makes a length referenceable everywhere that it is needed.  For example, a declaration can share one length, @N@, among a pair of parameters and the return.
    12 \lstinputlisting[language=CFA, firstline=50, lastline=59]{hello-array.cfa}
    13 Here, the function @f@ does a pointwise comparison, checking if each pair of numbers is within half a percent of each other, returning the answers in a newly allocated bool array.
    14 
    15 The array type uses the parameterized length information in its @sizeof(-)@ determination, illustrated in the example's call to @alloc@.  That call requests an allocation of type @array(bool, N)@, which the type system deduces from the left-hand side of the initialization, into the return type of the @alloc@ call.  Preexesting \CFA behaviour is leveraged here, both in the return-type-only polymorphism, and the @sized(T)@-aware standard-library @alloc@ routine.  The new @array@ type plugs into this behaviour by implementing the @sized@/@sizeof(-)@ assertion to have the intuitive meaning.  As a result, this design avoids an opportunity for programmer error by making the size/length communication to a called routine implicit, compared with C's @calloc@ (or the low-level \CFA analog @aalloc@) which take an explicit length parameter not managed by the type system.
    16 
    17 A harness for this @f@ function shows how dynamic values are fed into the system.
    18 \lstinputlisting[language=CFA, firstline=100, lastline=119]{hello-array.cfa}
    19 Here, the @a@ sequence is loaded with decreasing values, and the @b@ sequence with amounts off by a constant, giving relative differences within tolerance at first and out of tolerance later.  The driver program is run with two different inputs of sequence length.
    20 
    21 The loops in the driver follow the more familiar pattern of using the ordinary variable @n@ to convey the length.  The type system implicitly captures this value at the call site (@main@ calling @f@) and makes it available within the callee (@f@'s loop bound).
    22 
    23 The two parts of the example show @Z(n)@ adapting a variable into a type-system governed length (at @main@'s declarations of @a@, @b@, and @result@), @z(N)@ adapting in the opposite direction (at @f@'s loop bound), and a passthru use of a governed length (at @f@'s declaration of @ret@.)  It is hoped that future language integration will allow the macros @Z@ and @z@ to be omitted entirely from the user's notation, creating the appearance of seamlessly interchanging numeric values with appropriate generic parameters.
    24 
    25 The macro-assisted notation, @forall...ztype@, participates in the user-relevant declaration of the name @N@, which becomes usable in parameter/return declarations and in the function body.  So future language integration only sweetens this form and does not seek to elimimate the declaration.  The present form is chosen to parallel, as closely as a macro allows, the existing forall forms:
    26 \begin{lstlisting}
    27   forall( dtype T  ) ...
    28   forall( otype T  ) ...
    29   forall( ztype(N) ) ...
    30 \end{lstlisting}
    31 
    32 The notation @array(thing, N)@ is also macro-assisted, though only in service of enabling multidimensional uses discussed further in section \ref{toc:mdimpl}.  In a single-dimensional case, the marco expansion gives a generic type instance, exactly like the original form suggests.
    33 
    34 
    35 
     75This array's length is statically managed and dynamically valued.  This static management achieves argument safety and suggests a path to subscript safety as future work (TODO: cross reference).
     76
     77This section presents motivating examples of the new array type's usage and follows up with definitions of the notations that appear.
     78
     79The core of the new array management is tracking all array lengths in the type system.  Dynamically valued lengths are represented using type variables.  The stratification of type variables preceding object declarations makes a length referenceable everywhere that it is needed.  For example, a declaration can share one length, @N@, among a pair of parameters and the return.
     80\lstinputlisting[language=CFA, firstline=10, lastline=17]{hello-array.cfa}
     81Here, the function @f@ does a pointwise comparison, checking if each pair of numbers is within half a percent of each other, returning the answers in a newly allocated @bool@ array.
     82
     83The array type uses the parameterized length information in its @sizeof@ determination, illustrated in the example's call to @alloc@.  That call requests an allocation of type @array(bool, N)@, which the type system deduces from the left-hand side of the initialization, into the return type of the @alloc@ call.  Preexisting \CFA behaviour is leveraged here, both in the return-type-only polymorphism, and the @sized(T)@-aware standard-library @alloc@ routine.  The new @array@ type plugs into this behaviour by implementing the @sized@/@sizeof@ assertion to have the intuitive meaning.  As a result, this design avoids an opportunity for programmer error by making the size/length communication to a called routine implicit, compared with C's @calloc@ (or the low-level \CFA analog @aalloc@), which take an explicit length parameter not managed by the type system.
     84
     85\VRef[Figure]{f:fHarness} shows the harness to use the @f@ function illustrating how dynamic values are fed into the system.
     86Here, the @a@ array is loaded with decreasing values, and the @b@ array with amounts off by a constant, giving relative differences within tolerance at first and out of tolerance later.  The program main is run with two different inputs of sequence length.
     87
     88\begin{figure}
     89\lstinputlisting[language=CFA, firstline=30, lastline=49]{hello-array.cfa}
     90\caption{\lstinline{f} Harness}
     91\label{f:fHarness}
     92\end{figure}
     93
     94The loops in the program main follow the more familiar pattern of using the ordinary variable @n@ to convey the length.  The type system implicitly captures this value at the call site (@main@ calling @f@) and makes it available within the callee (@f@'s loop bound).
     95
     96The two parts of the example show @n@ adapting a variable into a type-system managed length (at @main@'s declarations of @a@, @b@, and @result@), @N@ adapting in the opposite direction (at @f@'s loop bound), and a pass-thru use of a managed length (at @f@'s declaration of @ret@).
     97
     98The @forall( ...[N] )@ participates in the user-relevant declaration of the name @N@, which becomes usable in parameter/return declarations and in the function @b@. The present form is chosen to parallel the existing @forall@ forms:
     99\begin{cfa}
     100forall( @[N]@ ) ... // array kind
     101forall( & T  ) ...  // reference kind (dtype)
     102forall( T  ) ...    // value kind (otype)
     103\end{cfa}
     104
     105The notation @array(thing, N)@ is a single-dimensional case, giving a generic type instance.
    36106In summary:
    37 
    38 \begin{tabular}{p{15em}p{20em}}
    39   @ztype( N )@ & within a forall, declares the type variable @N@ to be a governed length \\[0.25em]
    40   @Z( @ $e$ @ )@ & a type representing the value of $e$ as a governed length, where $e$ is a @size_t@-typed expression \\[0.25em]
    41   @z( N )@ & an expression of type @size_t@, whose value is the governed length @N@ \\[0.25em]
    42   @array( thing, N0, N1, ... )@
    43   &  a type wrapping $\prod_i N_i$ adjacent occurrences of @thing@ objects
    44 \end{tabular}
    45 
    46 Unsigned integers have a special status in this type system.  Unlike how C++ allows @template< size_t N, char * msg, typename T >...@ declarations, this system does not accommodate values of any user-provided type.  TODO: discuss connection with dependent types.
    47 
     107\begin{itemize}
     108\item
     109@[N]@ -- within a forall, declares the type variable @N@ to be a managed length
     110\item
     111$e$ -- a type representing the value of $e$ as a managed length, where $e$ is a @size_t@-typed expression
     112\item
     113N -- an expression of type @size_t@, whose value is the managed length @N@
     114\item
     115@array( thing, N0, N1, ... )@ -- a type wrapping $\prod_i N_i$ adjacent occurrences of @thing@ objects
     116\end{itemize}
     117Unsigned integers have a special status in this type system.  Unlike how C++ allows @template< size_t N, char * msg, typename T >...@ declarations, \CFA does not accommodate values of any user-provided type.  TODO: discuss connection with dependent types.
    48118
    49119An example of a type error demonstrates argument safety.  The running example has @f@ expecting two arrays of the same length.  A compile-time error occurs when attempting to call @f@ with arrays whose lengths may differ.
    50 \lstinputlisting[language=CFA, firstline=150, lastline=155]{hello-array.cfa}
    51 As is common practice in C, the programmer is free to cast, to assert knownledge not shared with the type system.
    52 \lstinputlisting[language=CFA, firstline=200, lastline=202]{hello-array.cfa}
    53 
    54 Argument safety, and the associated implicit communication of length, work with \CFA's generic types too.  As a structure can be defined over a parameterized element type, so can it be defined over a parameterized length.  Doing so gives a refinement of C's ``flexible array member'' pattern, that allows nesting structures with array members anywhere within other structures.
    55 \lstinputlisting[language=CFA, firstline=20, lastline=26]{hello-accordion.cfa}
    56 This structure's layout has the starting offest of @cost_contribs@ varying in @Nclients@, and the offset of @total_cost@ varying in both generic paramters.  For a function that operates on a @request@ structure, the type system handles this variation transparently.
    57 \lstinputlisting[language=CFA, firstline=50, lastline=57]{hello-accordion.cfa}
    58 In the example runs of a driver program, different offset values are navigated in the two cases.
    59 \lstinputlisting[language=CFA, firstline=100, lastline=115]{hello-accordion.cfa}
     120\lstinputlisting[language=CFA, firstline=60, lastline=65]{hello-array.cfa}
     121As is common practice in C, the programmer is free to cast, to assert knowledge not shared with the type system.
     122\lstinputlisting[language=CFA, firstline=70, lastline=75]{hello-array.cfa}
     123
     124Argument safety and the associated implicit communication of array length work with \CFA's generic types too.
     125\CFA allows aggregate types to be generalized with multiple type parameters, including parameterized element type, so can it be defined over a parameterized length.
     126Doing so gives a refinement of C's ``flexible array member'' pattern, that allows nesting structures with array members anywhere within other structures.
     127\lstinputlisting[language=CFA, firstline=10, lastline=16]{hello-accordion.cfa}
     128This structure's layout has the starting offset of @cost_contribs@ varying in @Nclients@, and the offset of @total_cost@ varying in both generic parameters.  For a function that operates on a @request@ structure, the type system handles this variation transparently.
     129\lstinputlisting[language=CFA, firstline=40, lastline=47]{hello-accordion.cfa}
     130In the example, different runs of the program result in different offset values being used.
     131\lstinputlisting[language=CFA, firstline=60, lastline=76]{hello-accordion.cfa}
    60132The output values show that @summarize@ and its caller agree on both the offsets (where the callee starts reading @cost_contribs@ and where the callee writes @total_cost@).  Yet the call site still says just, ``pass the request.''
    61133
    … …  
    67139TODO: introduce multidimensional array feature and approaches
    68140
    69 The new \CFA standard library @array@ datatype supports multidimensional uses more richly than the C array.  The new array's multimentsional interface and implementation, follows an array-of-arrays setup, meaning, like C's @float[n][m]@ type, one contiguous object, with coarsely-strided dimensions directly wrapping finely-strided dimensions.  This setup is in contrast with the pattern of array of pointers to other allocations representing a sub-array.  Beyond what C's type offers, the new array brings direct support for working with a noncontiguous array slice, allowing a program to work with dimension subscripts given in a non-physical order.  C and C++ require a programmer with such a need to manage pointer/offset arithmetic manually.
    70 
    71 Examples are shown using a $5 \times 7$ float array, @a@, loaded with increments of $0.1$ when stepping across the length-7 finely-strided dimension shown on columns, and with increments of $1.0$ when stepping across the length-5 corsely-strided dimension shown on rows.
    72 \lstinputlisting[language=CFA, firstline=120, lastline=128]{hello-md.cfa}
     141The new \CFA standard library @array@ datatype supports multidimensional uses more richly than the C array.  The new array's multidimensional interface and implementation, follows an array-of-arrays setup, meaning, like C's @float[n][m]@ type, one contiguous object, with coarsely-strided dimensions directly wrapping finely-strided dimensions.  This setup is in contrast with the pattern of array of pointers to other allocations representing a sub-array.  Beyond what C's type offers, the new array brings direct support for working with a noncontiguous array slice, allowing a program to work with dimension subscripts given in a non-physical order.  C and C++ require a programmer with such a need to manage pointer/offset arithmetic manually.
     142
     143Examples are shown using a $5 \times 7$ float array, @a@, loaded with increments of $0.1$ when stepping across the length-7 finely-strided dimension shown on columns, and with increments of $1.0$ when stepping across the length-5 coarsely-strided dimension shown on rows.
     144\lstinputlisting[language=CFA, firstline=120, lastline=126]{hello-md.cfa}
    73145The memory layout of @a@ has strictly increasing numbers along its 35 contiguous positions.
    74146
    75 A trivial form of slicing extracts a contiguous inner array, within an array-of-arrays.  Like with the C array, a lesser-dimensional array reference can be bound to the result of subscripting a greater-dimensional array, by a prefix of its dimensions.  This action first subscripts away the most coaresly strided dimensions, leaving a result that expects to be be subscripted by the more finely strided dimensions.
     147A trivial form of slicing extracts a contiguous inner array, within an array-of-arrays.  Like with the C array, a lesser-dimensional array reference can be bound to the result of subscripting a greater-dimensional array, by a prefix of its dimensions.  This action first subscripts away the most coarsely strided dimensions, leaving a result that expects to be be subscripted by the more finely strided dimensions.
    76148\lstinputlisting[language=CFA, firstline=60, lastline=66]{hello-md.cfa}
    77 \lstinputlisting[language=CFA, firstline=140, lastline=140]{hello-md.cfa}
    78 
    79 This function declaration is asserting too much knowledge about its parameter @c@, for it to be usable for printing either a row slice or a column slice.  Specifically, declaring the parameter @c@ with type @array@ means that @c@ is contiguous.  However, the function does not use this fact.  For the function to do its job, @c@ need only be of a container type that offers a subscript operator (of type @ptrdiff_t@ $\rightarrow$ @float@), with governed length @N@.  The new-array library provides the trait @ix@, so-defined.  With it, the original declaration can be generalized, while still implemented with the same body, to the latter declaration:
     149\lstinputlisting[aboveskip=0pt, language=CFA, firstline=140, lastline=140]{hello-md.cfa}
     150
     151This function declaration is asserting too much knowledge about its parameter @c@, for it to be usable for printing either a row slice or a column slice.  Specifically, declaring the parameter @c@ with type @array@ means that @c@ is contiguous.  However, the function does not use this fact.  For the function to do its job, @c@ need only be of a container type that offers a subscript operator (of type @ptrdiff_t@ $\rightarrow$ @float@), with managed length @N@.  The new-array library provides the trait @ix@, so-defined.  With it, the original declaration can be generalized, while still implemented with the same body, to the latter declaration:
    80152\lstinputlisting[language=CFA, firstline=40, lastline=44]{hello-md.cfa}
    81 \lstinputlisting[language=CFA, firstline=145, lastline=145]{hello-md.cfa}
     153\lstinputlisting[aboveskip=0pt, language=CFA, firstline=145, lastline=145]{hello-md.cfa}
    82154
    83155Nontrivial slicing, in this example, means passing a noncontiguous slice to @print1d@.  The new-array library provides a ``subscript by all'' operation for this purpose.  In a multi-dimensional subscript operation, any dimension given as @all@ is left ``not yet subscripted by a value,'' implementing the @ix@ trait, waiting for such a value.
    … …  
    122194\begin{figure}
    123195    \includegraphics{measuring-like-layout}
    124     \caption{Visualization of subscripting by value and by \lstinline[language=CFA,basicstyle=\ttfamily]{all}, for \lstinline[language=CFA,basicstyle=\ttfamily]{a} of type \lstinline[language=CFA,basicstyle=\ttfamily]{array( float, Z(5), Z(7) )}. The horizontal dimension represents memory addresses while vertical layout is conceptual.}
     196    \caption{Visualization of subscripting by value and by \lstinline[language=CFA,basicstyle=\ttfamily]{all}, for \lstinline[language=CFA,basicstyle=\ttfamily]{a} of type \lstinline[language=CFA,basicstyle=\ttfamily]{array( float, 5, 7 )}. The horizontal dimension represents memory addresses while vertical layout is conceptual.}
    125197    \label{fig:subscr-all}
    126198\end{figure}
    127199
    128 \noindent While the latter description implies overlapping elements, Figure \ref{fig:subscr-all} shows that the overlaps only occur with unused spaces between elements.  Its depictions of @a[all][...]@ show the navigation of a memory layout with nontrivial strides, that is, with ``spaced \_ floats apart'' values that are greater or smaller than the true count of valid indeces times the size of a logically indexed element.  Reading from the bottom up, the expression @a[all][3][2]@ shows a float, that is masquerading as a @float[7]@, for the purpose of being arranged among its peers; five such occurrences form @a[all][3]@.  The tail of flatter boxes extending to the right of a poper element represents this stretching.  At the next level of containment, the structure @a[all][3]@ masquerades as a @float[1]@, for the purpose of being arranged among its peers; seven such occurrences form @a[all]@.  The verical staircase arrangement represents this compression, and resulting overlapping.
    129 
    130 The new-array library defines types and operations that ensure proper elements are accessed soundly in spite of the overlapping.  The private @arpk@ structure (array with explicit packing) is generic over these two types (and more): the contained element, what it is masquerading as.  This structure's public interface is the @array(...)@ construction macro and the two subscript operators.  Construction by @array@ initializes the masquerading-as type information to be equal to the contained-element information.  Subscrpting by @all@ rearranges the order of masquerading-as types to achieve, in genernal, nontrivial striding.  Subscripting by a number consumes the masquerading-as size of the contained element type, does normal array stepping according to that size, and returns there element found there, in unmasked form.
     200\noindent While the latter description implies overlapping elements, Figure \ref{fig:subscr-all} shows that the overlaps only occur with unused spaces between elements.  Its depictions of @a[all][...]@ show the navigation of a memory layout with nontrivial strides, that is, with ``spaced \_ floats apart'' values that are greater or smaller than the true count of valid indices times the size of a logically indexed element.  Reading from the bottom up, the expression @a[all][3][2]@ shows a float, that is masquerading as a @float[7]@, for the purpose of being arranged among its peers; five such occurrences form @a[all][3]@.  The tail of flatter boxes extending to the right of a proper element represents this stretching.  At the next level of containment, the structure @a[all][3]@ masquerades as a @float[1]@, for the purpose of being arranged among its peers; seven such occurrences form @a[all]@.  The vertical staircase arrangement represents this compression, and resulting overlapping.
     201
     202The new-array library defines types and operations that ensure proper elements are accessed soundly in spite of the overlapping.  The private @arpk@ structure (array with explicit packing) is generic over these two types (and more): the contained element, what it is masquerading as.  This structure's public interface is the @array(...)@ construction macro and the two subscript operators.  Construction by @array@ initializes the masquerading-as type information to be equal to the contained-element information.  Subscripting by @all@ rearranges the order of masquerading-as types to achieve, in general, nontrivial striding.  Subscripting by a number consumes the masquerading-as size of the contained element type, does normal array stepping according to that size, and returns there element found there, in unmasked form.
    131203
    132204The @arpk@ structure and its @-[i]@ operator are thus defined as:
    … …  
    138210      ) {
    139211    struct arpk {
    140         S strides[z(N)];        // so that sizeof(this) is N of S
     212        S strides[N];           // so that sizeof(this) is N of S
    141213    };
    142214
    … …  
    148220\end{lstlisting}
    149221
    150 An instantion of the @arpk@ generic is given by the @array(E_base, N0, N1, ...)@ exapnsion, which is @arpk( N0, Rec, Rec, E_base )@, where @Rec@ is @array(E_base, N1, ...)@.  In the base case, @array(E_base)@ is just @E_base@.  Because this construction uses the same value for the generic parameters @S@ and @E_im@, the resulting layout has trivial strides.
    151 
    152 Subscripting by @all@, to operate on nontrivial strides, is a dequeue-enqueue operation on the @E_im@ chain, which carries @S@ instatiations, intact, to new positions.  Expressed as an operation on types, this rotation is:
     222An instantiation of the @arpk@ generic is given by the @array(E_base, N0, N1, ...)@ expansion, which is @arpk( N0, Rec, Rec, E_base )@, where @Rec@ is @array(E_base, N1, ...)@.  In the base case, @array(E_base)@ is just @E_base@.  Because this construction uses the same value for the generic parameters @S@ and @E_im@, the resulting layout has trivial strides.
     223
     224Subscripting by @all@, to operate on nontrivial strides, is a dequeue-enqueue operation on the @E_im@ chain, which carries @S@ instantiations, intact, to new positions.  Expressed as an operation on types, this rotation is:
    153225\begin{eqnarray*}
    154226suball( arpk(N, S, E_i, E_b) ) & = & enq( N, S, E_i, E_b ) \\
    … …  
    160232\section{Bound checks, added and removed}
    161233
    162 \CFA array subscripting is protected with runtime bound checks.  Having dependent typing causes the opimizer to remove more of these bound checks than it would without them.  This section provides a demonstration of the effect.
    163 
    164 The experiment compares the \CFA array system with the padded-room system [todo:xref] most typically exemplified by Java arrays, but also reflected in the C++ pattern where restricted vector usage models a checked array.  The essential feature of this padded-room system is the one-to-one correspondence between array instances and the symbolic bounds on which dynamic checks are based.  The experiment compares with the C++ version to keep access to generated assembly code simple.
    165 
    166 As a control case, a simple loop (with no reused dimension sizes) is seen to get the same optimization treatment in both the \CFA and C++ versions.  When the programmer treats the array's bound correctly (making the subscript ``obviously fine''), no dynamic bound check is observed in the program's optimized assembly code.  But when the bounds are adjusted, such that the subscript is possibly invalid, the bound check appears in the optimized assemly, ready to catch an occurrence the mistake.
    167 
    168 TODO: paste source and assemby codes
     234\CFA array subscripting is protected with runtime bound checks.  Having dependent typing causes the optimizer to remove more of these bound checks than it would without them.  This section provides a demonstration of the effect.
     235
     236The experiment compares the \CFA array system with the padded-room system [TODO:xref] most typically exemplified by Java arrays, but also reflected in the C++ pattern where restricted vector usage models a checked array.  The essential feature of this padded-room system is the one-to-one correspondence between array instances and the symbolic bounds on which dynamic checks are based.  The experiment compares with the C++ version to keep access to generated assembly code simple.
     237
     238As a control case, a simple loop (with no reused dimension sizes) is seen to get the same optimization treatment in both the \CFA and C++ versions.  When the programmer treats the array's bound correctly (making the subscript ``obviously fine''), no dynamic bound check is observed in the program's optimized assembly code.  But when the bounds are adjusted, such that the subscript is possibly invalid, the bound check appears in the optimized assembly, ready to catch an occurrence the mistake.
     239
     240TODO: paste source and assembly codes
    169241
    170242Incorporating reuse among dimension sizes is seen to give \CFA an advantage at being optimized.  The case is naive matrix multiplication over a row-major encoding.
    … …  
    178250\section{Comparison with other arrays}
    179251
    180 \CFA's array is the first lightweight application of dependently-typed bound tracking to an extension of C.  Other extensions of C that apply dependently-typed bound tracking are heavyweight, in that the bound tracking is part of a linearly typed ownership system that further helps guarantee statically the validity of every pointer deference.  These systems, therefore, ask the programmer to convince the typechecker that every pointer dereference is valid.  \CFA imposes the lighter-weight obligation, with the more limited guarantee, that initially-declared bounds are respected thereafter.
     252\CFA's array is the first lightweight application of dependently-typed bound tracking to an extension of C.  Other extensions of C that apply dependently-typed bound tracking are heavyweight, in that the bound tracking is part of a linearly typed ownership system that further helps guarantee statically the validity of every pointer deference.  These systems, therefore, ask the programmer to convince the type checker that every pointer dereference is valid.  \CFA imposes the lighter-weight obligation, with the more limited guarantee, that initially-declared bounds are respected thereafter.
    181253
    182254\CFA's array is also the first extension of C to use its tracked bounds to generate the pointer arithmetic implied by advanced allocation patterns.  Other bound-tracked extensions of C either forbid certain C patterns entirely, or address the problem of \emph{verifying} that the user's provided pointer arithmetic is self-consistent.  The \CFA array, applied to accordion structures [TOD: cross-reference] \emph{implies} the necessary pointer arithmetic, generated automatically, and not appearing at all in a user's program.
    … …  
    184256\subsection{Safety in a padded room}
    185257
    186 Java's array [todo:cite] is a straightforward example of assuring safety against undefined behaviour, at a cost of expressiveness for more applied properties.  Consider the array parameter declarations in:
     258Java's array [TODO:cite] is a straightforward example of assuring safety against undefined behaviour, at a cost of expressiveness for more applied properties.  Consider the array parameter declarations in:
    187259
    188260\begin{tabular}{rl}
    … …  
    191263\end{tabular}
    192264
    193 Java's safety against undefined behaviour assures the callee that, if @a@ is non-null, then @a.length@ is a valid access (say, evaluating to the number $\ell$) and if @i@ is in $[0, \ell)$ then @a[i]@ is a valid access.  If a value of @i@ outside this range is used, a runtime error is guaranteed.  In these respects, C offers no guarantess at all.  Notably, the suggestion that @n@ is the intended size of the first dimension of @a@ is documentation only.  Indeed, many might prefer the technically equivalent declarations @float a[][m]@ or @float (*a)[m]@ as emphasizing the ``no guarantees'' nature of an infrequently used language feature, over using the opportunity to explain a programmer intention.  Moreover, even if @a[0][0]@ is valid for the purpose intended, C's basic infamous feature is the possibility of an @i@, such that @a[i][0]@ is not valid for the same purpose, and yet, its evaluation does not produce an error.
     265Java's safety against undefined behaviour assures the callee that, if @a@ is non-null, then @a.length@ is a valid access (say, evaluating to the number $\ell$) and if @i@ is in $[0, \ell)$ then @a[i]@ is a valid access.  If a value of @i@ outside this range is used, a runtime error is guaranteed.  In these respects, C offers no guarantees at all.  Notably, the suggestion that @n@ is the intended size of the first dimension of @a@ is documentation only.  Indeed, many might prefer the technically equivalent declarations @float a[][m]@ or @float (*a)[m]@ as emphasizing the ``no guarantees'' nature of an infrequently used language feature, over using the opportunity to explain a programmer intention.  Moreover, even if @a[0][0]@ is valid for the purpose intended, C's basic infamous feature is the possibility of an @i@, such that @a[i][0]@ is not valid for the same purpose, and yet, its evaluation does not produce an error.
    194266
    195267Java's lack of expressiveness for more applied properties means these outcomes are possible:
    … …  
    201273C's array has none of these limitations, nor do any of the ``array language'' comparators discussed in this section.
    202274
    203 This Java level of safety and expressiveness is also exemplified in the C family, with the commonly given advice [todo:cite example], for C++ programmers to use @std::vector@ in place of the C++ language's array, which is essentially the C array.  The advice is that, while a vector is also more powerful (and quirky) than an arry, its capabilities include options to preallocate with an upfront size, to use an available bound-checked accessor (@a.at(i)@ in place of @a[i]@), to avoid using @push_back@, and to use a vector of vectors.  Used with these restrictions, out-of-bound accesses are stopped, and in-bound accesses never exercise the vector's ability to grow, which is to say, they never make the program slow to reallocate and copy, and they never invalidate the program's other references to the contained values.  Allowing this scheme the same referential integrity assumption that \CFA enjoys [todo:xref], this scheme matches Java's safety and expressiveness exactly.  [TODO: decide about going deeper; some of the Java expressiveness concerns have mitigations, up to even more tradeoffs.]
     275This Java level of safety and expressiveness is also exemplified in the C family, with the commonly given advice [TODO:cite example], for C++ programmers to use @std::vector@ in place of the C++ language's array, which is essentially the C array.  The advice is that, while a vector is also more powerful (and quirky) than an array, its capabilities include options to preallocate with an upfront size, to use an available bound-checked accessor (@a.at(i)@ in place of @a[i]@), to avoid using @push_back@, and to use a vector of vectors.  Used with these restrictions, out-of-bound accesses are stopped, and in-bound accesses never exercise the vector's ability to grow, which is to say, they never make the program slow to reallocate and copy, and they never invalidate the program's other references to the contained values.  Allowing this scheme the same referential integrity assumption that \CFA enjoys [TODO:xref], this scheme matches Java's safety and expressiveness exactly.  [TODO: decide about going deeper; some of the Java expressiveness concerns have mitigations, up to even more tradeoffs.]
    204276
    205277\subsection{Levels of dependently typed arrays}
    … …  
    211283    \item a formulation of matrix multiplication, where the two operands must agree on a middle dimension, and where the result dimensions match the operands' outer dimensions
    212284\end{itemize}
    213 Across this field, this expressiveness is not just an avaiable place to document such assumption, but these requirements are strongly guaranteed by default, with varying levels of statically/dynamically checked and ability to opt out.  Along the way, the \CFA array also closes the safety gap (with respect to bounds) that Java has over C.
    214 
    215 
     285Across this field, this expressiveness is not just an available place to document such assumption, but these requirements are strongly guaranteed by default, with varying levels of statically/dynamically checked and ability to opt out.  Along the way, the \CFA array also closes the safety gap (with respect to bounds) that Java has over C.
    216286
    217287Dependent type systems, considered for the purpose of bound-tracking, can be full-strength or restricted.  In a full-strength dependent type system, a type can encode an arbitrarily complex predicate, with bound-tracking being an easy example.  The tradeoff of this expressiveness is complexity in the checker, even typically, a potential for its nontermination.  In a restricted dependent type system (purposed for bound tracking), the goal is to check helpful properties, while keeping the checker well-behaved; the other restricted checkers surveyed here, including \CFA's, always terminate.  [TODO: clarify how even Idris type checking terminates]
    218288
    219 Idris is a current, general-purpose dependently typed programming language.  Length checking is a common benchmark for full dependent type stystems.  Here, the capability being considered is to track lengths that adjust during the execution of a program, such as when an \emph{add} operation produces a collection one element longer than the one on which it started.  [todo: finish explaining what Data.Vect is and then the essence of the comparison]
     289Idris is a current, general-purpose dependently typed programming language.  Length checking is a common benchmark for full dependent type systems.  Here, the capability being considered is to track lengths that adjust during the execution of a program, such as when an \emph{add} operation produces a collection one element longer than the one on which it started.  [TODO: finish explaining what Data.Vect is and then the essence of the comparison]
    220290
    221291POINTS:
    222 here is how our basic checks look (on a system that deosn't have to compromise);
     292here is how our basic checks look (on a system that does not have to compromise);
    223293it can also do these other cool checks, but watch how I can mess with its conservativeness and termination
    224294
    225 Two current, state-of-the-art array languages, Dex\cite{arr:dex:long} and Futhark\cite{arr:futhark:tytheory}, offer offer novel contributions concerning similar, restricted dependent types for tracking array length.  Unlike \CFA, both are garbage-collected functional languages.  Because they are garbage-collected, referential integrity is built-in, meaning that the heavyweight analysis, that \CFA aims to avoid, is unnecessary.  So, like \CFA, the checking in question is a leightweight bounds-only analysis.  Like \CFA, their checks that are conservatively limited by forbidding arithmetic in the depended-upon expression.
     295Two current, state-of-the-art array languages, Dex\cite{arr:dex:long} and Futhark\cite{arr:futhark:tytheory}, offer offer novel contributions concerning similar, restricted dependent types for tracking array length.  Unlike \CFA, both are garbage-collected functional languages.  Because they are garbage-collected, referential integrity is built-in, meaning that the heavyweight analysis, that \CFA aims to avoid, is unnecessary.  So, like \CFA, the checking in question is a lightweight bounds-only analysis.  Like \CFA, their checks that are conservatively limited by forbidding arithmetic in the depended-upon expression.
    226296
    227297
    … …  
    231301Dex uses a novel conception of size, embedding its quantitative information completely into an ordinary type.
    232302
    233 Futhark and full-strength dependently typed lanaguages treat array sizes are ordinary values.  Futhark restricts these expressions syntactically to variables and constants, while a full-strength dependent system does not.
     303Futhark and full-strength dependently typed languages treat array sizes are ordinary values.  Futhark restricts these expressions syntactically to variables and constants, while a full-strength dependent system does not.
    234304
    235305CFA's hybrid presentation, @forall( [N] )@, has @N@ belonging to the type system, yet has no instances.  Belonging to the type system means it is inferred at a call site and communicated implicitly, like in Dex and unlike in Futhark.  Having no instances means there is no type for a variable @i@ that constrains @i@ to be in the range for @N@, unlike Dex, [TODO: verify], but like Futhark.
    … …  
    280350If \CFA gets such a system for describing the list of values in a type, then \CFA arrays are poised to move from the Futhark level of expressiveness, up to the Dex level.
    281351
    282 [TODO: indroduce Ada in the comparators]
     352[TODO: introduce Ada in the comparators]
    283353
    284354In Ada and Dex, an array is conceived as a function whose domain must satisfy only certain structural assumptions, while in C, C++, Java, Futhark and \CFA today, the domain is a prefix of the natural numbers.  The generality has obvious aesthetic benefits for programmers working on scheduling resources to weekdays, and for programmers who prefer to count from an initial number of their own choosing.
    285355
    286 This change of perspective also lets us remove ubiquitous dynamic bound checks.  [TODO: xref] discusses how automatically inserted bound checks can often be otimized away.  But this approach is unsatisfying to a programmer who believes she has written code in which dynamic checks are unnecessary, but now seeks confirmation.  To remove the ubiquitious dynamic checking is to say that an ordinary subscript operation is only valid when it can be statically verified to be in-bound (and so the ordinary subscript is not dynamically checked), and an explicit dynamic check is available when the static criterion is impractical to meet.
     356This change of perspective also lets us remove ubiquitous dynamic bound checks.  [TODO: xref] discusses how automatically inserted bound checks can often be optimized away.  But this approach is unsatisfying to a programmer who believes she has written code in which dynamic checks are unnecessary, but now seeks confirmation.  To remove the ubiquitous dynamic checking is to say that an ordinary subscript operation is only valid when it can be statically verified to be in-bound (and so the ordinary subscript is not dynamically checked), and an explicit dynamic check is available when the static criterion is impractical to meet.
    287357
    288358[TODO, fix confusion:  Idris has this arrangement of checks, but still the natural numbers as the domain.]
    … …  
    296366\end{lstlisting}
    297367
    298 Dex uses this foundation of a trait (as an array type's domain) to achieve polymorphism over shapes.  This flavour of polymorphism lets a function be generic over how many (and the order of) dimensions a caller uses when interacting with arrays communicated with this funciton.  Dex's example is a routine that calculates pointwise differences between two samples.  Done with shape polymorphism, one function body is equally applicable to a pair of single-dimensional audio clips (giving a single-dimensional result) and a pair of two-dimensional photographs (giving a two-dimensional result).  In both cases, but with respectively dimensoned interpretations of ``size,'' this function requries the argument sizes to match, and it produces a result of the that size.
    299 
    300 The polymorphism plays out with the pointwise-difference routine advertizing a single-dimensional interface whose domain type is generic.  In the audio instantiation, the duration-of-clip type argument is used for the domain.  In the photograph instantiation, it's the tuple-type of $ \langle \mathrm{img\_wd}, \mathrm{img\_ht} \rangle $.  This use of a tuple-as-index is made possible by the built-in rule for implementing @Ix@ on a pair, given @Ix@ implementations for its elements
     368Dex uses this foundation of a trait (as an array type's domain) to achieve polymorphism over shapes.  This flavour of polymorphism lets a function be generic over how many (and the order of) dimensions a caller uses when interacting with arrays communicated with this function.  Dex's example is a routine that calculates pointwise differences between two samples.  Done with shape polymorphism, one function body is equally applicable to a pair of single-dimensional audio clips (giving a single-dimensional result) and a pair of two-dimensional photographs (giving a two-dimensional result).  In both cases, but with respectively dimensioned interpretations of ``size,'' this function requires the argument sizes to match, and it produces a result of the that size.
     369
     370The polymorphism plays out with the pointwise-difference routine advertising a single-dimensional interface whose domain type is generic.  In the audio instantiation, the duration-of-clip type argument is used for the domain.  In the photograph instantiation, it's the tuple-type of $ \langle \mathrm{img\_wd}, \mathrm{img\_ht} \rangle $.  This use of a tuple-as-index is made possible by the built-in rule for implementing @Ix@ on a pair, given @Ix@ implementations for its elements
    301371\begin{lstlisting}
    302372instance {a b} [Ix a, Ix b] Ix (a & b)

  • doc/theses/mike_brooks_MMath/background.tex

    r0fa0201d r5546eee4  
    11\chapter{Background}
    22
    3 \section{Arrays}
    4 
    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.
     5
     6\section{C}
     7
     8\subsection{Common knowledge}
     9
     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.
     12
     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
     14
     15\subsection{Convention: C is more touchable than its standard}
     16
     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.
     20
     21This behaviour is typically one of
     22\begin{itemize}
     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
     26\end{itemize}
     27
     28The compiler whose program semantics is shown is
     29\begin{lstlisting}
     30$ gcc --version
     31gcc (Ubuntu 9.4.0-1ubuntu1~20.04.1) 9.4.0
     32\end{lstlisting}
     33running on Architecture @x86_64@, with the same environment targeted.
     34
     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.
     37
     38
     39\subsection{C reports many ill-typed expressions as warnings}
     40
     41TODO: typeset
     42\lstinputlisting[language=C, firstline=13, lastline=56]{bkgd-c-tyerr.c}
     43
     44
     45\section{C Arrays}
     46
     47\subsection{C has an array type (!)}
     48
     49TODO: typeset
     50\lstinputlisting[language=C, firstline=35, lastline=116]{bkgd-carray-arrty.c}
     51
     52My contribution is enabled by recognizing
     53\begin{itemize}
     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]@.
     58\end{itemize}
     59
     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.
     68
     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!
     70
     71
     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:
     77\begin{lstlisting}
     78[ * [10] T ] x;
     79\end{lstlisting}
     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.
     81
     82\noindent
     83\textbf{Unfortunate Syntactic Reference}
     84
     85\noindent
     86\begin{tabular}{llllll}
     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
     172\end{tabular}
     173
     174
     175\subsection{Arrays decay and pointers diffract}
     176
     177TODO: typeset
     178\lstinputlisting[language=C, firstline=4, lastline=26]{bkgd-carray-decay.c}
     179
     180
     181So, C provides an implicit conversion from @float[10]@ to @float*@, as described in ARM-6.3.2.1.3:
     182
     183\begin{quote}
     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
     189\end{quote}
     190
     191This phenomenon is the famous ``pointer decay,'' which is a decay of an array-typed expression into a pointer-typed one.
     192
     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.
     195
     196Subscripting proceeds first with pointer decay, if needed.  Next, ARM-6.5.2.1.2 explains that @a[i]@ is treated as if it were @(*((a)+(i)))@.
     197ARM-6.5.6.8 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-6.5.3.2.4 explains that the @*@ operator's result is the referenced element.
     199
     200Taken together, these rules also happen to illustrate that @a[i]@ and @i[a]@ mean the same thing.
     201
     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:
     208\begin{lstlisting}
     209    float * fs = malloc( 10 * sizeof(float) );
     210    fs[5] = 3.14;
     211\end{lstlisting}
     212The @malloc@ behaviour is specified as returning a pointer to ``space for an object whose size is'' as requested (ARM-7.22.3.4.2).
     213But program says \emph{nothing} more about this pointer value, that might cause its referent to \emph{be} an array, before doing the subscript.
     214
     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)@.
     219
     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.
     222
     223No pointer is exempt from array diffraction.
     224
     225No array shows its elements without pointer decay.
     226
     227A further pointer--array confusion, closely related to decay, occurs in parameter declarations.
     228ARM-6.7.6.3.7 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 *'.''
     234
     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.
     238
     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.
     250
     251
     252In sumary, when a funciton is written with an array-typed parameter,
     253\begin{itemize}
     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
     257\end{itemize}
     258
     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}
     262
     263
     264\noindent
     265\textbf{Unfortunate Syntactic Reference}
     266
     267\noindent
     268(Parameter declaration; ``no writing'' refers to the callee's ability)
     269
     270\noindent
     271\begin{tabular}{llllll}
     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
     303\end{tabular}
     304
     305
     306
     307\subsection{Lengths may vary, checking does not}
     308
     309When the desired number of elements is unknown at compile time,
     310a variable-length array is a solution:
     311\begin{lstlisting}
     312    int main( int argc, const char *argv[] ) {
     313
     314        assert( argc == 2 );
     315        size_t n = atol( argv[1] );
     316        assert( 0 < n && n < 1000 );
     317
     318        float a[n];
     319        float b[10];
     320
     321        // ... discussion continues here
     322    }
     323\end{lstlisting}
     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@.
     327
     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:
     331\begin{lstlisting}
     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 ) );
     336\end{lstlisting}
     337
     338
     339VLA
     340
     341Parameter dependency
     342
     343Checking is best-effort / unsound
     344
     345Limited special handling to get the dimension value checked (static)
     346
     347
     348
     349\subsection{C has full-service, dynamically sized, multidimensional arrays (and \CC does not)}
     350
     351In C and \CC, ``multidimensional array'' means ``array of arrays.''  Other meanings are discussed in TODO.
     352
     353Just as an array's element type can be @float@, so can it be @float[10]@.
     354
     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.
     358
     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.
     361
     362
     363Pointer decay affects the outermost array only
     364
     365
     366TODO: unfortunate syntactic reference with these cases:
     367
     368\begin{itemize}
     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
     371\end{itemize}
     372
     373
     374
     375
     376
     377\subsection{Arrays are (but) almost values}
     378
     379Has size; can point to
     380
     381Can't cast to
     382
     383Can't pass as value
     384
     385Can initialize
     386
     387Can wrap in aggregate
     388
     389Can't assign
     390
     391
     392\subsection{Returning an array is (but) almost possible}
     393
     394
     395
     396
     397\subsection{The pointer-to-array type has been noticed before}
     398
     399
     400\section{\CFA}
     401
     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.)
     404
     405\subsection{\CFA features interacting with arrays}
     406
     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.
     410
     411More mixed results arose with feeding these ``C'' arrays into preexisting \CFA features.
     412
     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.
     416\begin{lstlisting}
     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) );
     422
     423    // CFA, library
     424    forall( T * ) T * alloc();
     425    // CFA, user
     426    tm * el2 = alloc();
     427    tm (*ar2)[10] = alloc();
     428\end{lstlisting}
     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.
     432
     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 bkgd-cfa-arrayinteract.cfa
     434
     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.
     438\begin{lstlisting}
     439    ar1[5];
     440    (*ar2)[5];
     441\end{lstlisting}
     442Using ``reference to array'' works at resolving this issue.  TODO: discuss connection with Doug-Lea \CC proposal.
     443\begin{lstlisting}
     444    tm (&ar3)[10] = *alloc();
     445    ar3[5];
     446\end{lstlisting}
     447The implicit size communication to @alloc@ still works in the same ways as for @ar2@.
     448
     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.
     454
     455The ``reference to array'' type has its sore spots too.  TODO see also @dimexpr-match-c/REFPARAM_CALL (under TRY_BUG_1)@
     456
     457
     458
     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/intro.tex

    r0fa0201d r5546eee4  
    11\chapter{Introduction}
     2
     3\cite{Blache19}
     4\cite{Oorschot23}
     5\cite{Ruef19}
    26
    37\section{Arrays}

  • doc/theses/mike_brooks_MMath/list.tex

    r0fa0201d r5546eee4  
    210210\label{toc:lst:issue:derection}
    211211
     212Axis?
     213
    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/programs/hello-accordion.cfa

    r0fa0201d r5546eee4  
    1 #include "stdlib.hfa"
    2 #include "array.hfa"
     1#include <fstream.hfa>
     2#include <stdlib.hfa>
     3#include <array.hfa>
     4
     5
     6
     7
     8
     9
     10
     11forall( T, [Nclients], [Ncosts] )
     12struct request {
     13    unsigned int requestor_id;
     14    array( T, Nclients ) impacted_client_ids; // nested VLA
     15    array( float, Ncosts ) cost_contribs; // nested VLA
     16    float total_cost;
     17};
     18
     19
     20// TODO: understand (fix?) why these are needed (autogen seems to be failing ... is typeof as struct member nayok?)
     21
     22forall( T, [Nclients], [Ncosts] )
     23        void ?{}( T &, request( T, Nclients, Ncosts ) & this ) {}
     24
     25forall( T &, [Nclients], [Ncosts] )
     26        void ^?{}( request( T, Nclients, Ncosts ) & this ) {}
    327
    428
    … …  
    1539
    1640
    17 
    18 
    19 
    20 forall( ztype(Nclients), ztype(Ncosts) )
    21 struct request {
    22     unsigned int requestor_id;
    23     array( unsigned int, Nclients ) impacted_client_ids;
    24     array( float, Ncosts ) cost_contribs;
    25     float total_cost;
    26 };
    27 
    28 
    29 // TODO: understand (fix?) why these are needed (autogen seems to be failing ... is typeof as struct member nayok?)
    30 
    31 forall( ztype(Nclients), ztype(Ncosts) )
    32 void ?{}( request(Nclients, Ncosts) & this ) {}
    33 
    34 forall( ztype(Nclients), ztype(Ncosts) )
    35 void ^?{}( request(Nclients, Ncosts) & this ) {}
    36 
    37 
    38 
    39 
    40 
    41 
    42 
    43 
    44 
    45 
    46 
    47 
    48 
    49 
    50 forall( ztype(Nclients), ztype(Ncosts) )
    51 void summarize( request(Nclients, Ncosts) & r ) {
     41forall( T, [Nclients], [Ncosts] )
     42void summarize( request( T, Nclients, Ncosts ) & r ) {
    5243    r.total_cost = 0;
    53     for( i; z(Ncosts) )
     44    for( i; Ncosts )
    5445        r.total_cost += r.cost_contribs[i];
    5546    // say the cost is per-client, to make output vary
    56     r.total_cost *= z(Nclients);
     47    r.total_cost *= Nclients;
    5748}
    5849
    … …  
    6859
    6960
     61int main( int argc, char * argv[] ) {
     62        const int ncl = ato( argv[1] );
     63        const int nco = 2;
    7064
     65        request( int, ncl, nco ) r;
     66        r.cost_contribs[0] = 100;
     67        r.cost_contribs[1] = 0.1;
    7168
    72 
    73 
    74 
    75 
    76 
    77 
    78 
    79 
    80 
    81 
    82 
    83 
    84 
    85 
    86 
    87 
    88 
    89 
    90 
    91 
    92 
    93 
    94 
    95 
    96 int main( int argc, char ** argv ) {
    97 
    98 
    99 
    100 const int ncl = atoi(argv[1]);
    101 const int nco = 2;
    102 
    103 request( Z(ncl), Z(nco) ) r;
    104 r.cost_contribs[0] = 100;
    105 r.cost_contribs[1] = 0.1;
    106 
    107 summarize(r);
    108 printf("Total cost: %.1f\n", r.total_cost);
    109 
     69        summarize(r);
     70        sout | "Total cost:" | r.total_cost;
     71}
    11072/*
    111 ./a.out 5
     73$\$$ ./a.out 5
    11274Total cost: 500.5
    113 ./a.out 6
     75$\$$ ./a.out 6
    11476Total cost: 600.6
    11577*/
    116 
    117 
    118 
    119 
    120 }

  • doc/theses/mike_brooks_MMath/programs/hello-array.cfa

    r0fa0201d r5546eee4  
    1 
    2 #include <common.hfa>
    3 #include <bits/align.hfa>
    4 
    5 extern "C" {
    6     int atoi(const char *str);
    7 }
    8 
    9 
    10 #include "stdlib.hfa"
    11 #include "array.hfa" // learned has to come afer stdlib, which uses the word tag
    12 
    13 
    14 
    15 
    16 
    17 
    18 
    19 
    20 
    21 
    22 
    23 
    24 
    25 
    26 
     1#include <fstream.hfa>
     2#include <stdlib.hfa>
     3#include <array.hfa> // learned has to come afer stdlib, which uses the word tag
    274
    285// Usage:
    … …  
    318
    329
    33 
    34 
    35 
    36 
    37 
    38 
    39 
    40 
    41 
    42 
    43 
    44 
    45 
    46 
    47 
    48 
    49 
    50 forall( ztype( N ) )
     10forall( [N] ) // array bound
    5111array(bool, N) & f( array(float, N) & a, array(float, N) & b ) {
    52     array(bool, N) & ret = *alloc();
    53     for( i; z(N) ) {
    54         float fracdiff = 2 * abs( a[i] - b[i] )
    55                        / ( abs( a[i] ) + abs( b[i] ) );
    56         ret[i] = fracdiff < 0.005;
     12    array(bool, N) & ret = *alloc(); // sizeof used by alloc
     13    for( i; N ) {
     14        ret[i] = 0.005 > 2 * (abs(a[i] - b[i])) / (abs(a[i]) + abs(b[i]));
    5715    }
    5816    return ret;
    … …  
    6826
    6927
    70 
    71 
    72 
    73 
    74 
    75 
    76 
    77 
    78 
    79 
    80 
    81 
    82 
    83 
    84 
    85 
    86 
    87 
    88 
    89 
    90 
    91 
    92 
    93 
    94 
    95 
    96 
    97 
    9828// TODO: standardize argv
    9929
    100 int main( int argc, char ** argv ) {
    101     int n = atoi(argv[1]);
    102     array(float, Z(n)) a, b;
    103     for (i; n) {
    104         a[i] = 3.14 / (i+1);
     30int main( int argc, char * argv[] ) {
     31    int n = ato( argv[1] );
     32    array(float, n) a, b; // VLA
     33    for ( i; n ) {
     34        a[i] = 3.14 / (i + 1);
    10535        b[i] = a[i] + 0.005 ;
    10636    }
    107     array(bool, Z(n)) & answer = f( a, b );
    108     printf("answer:");
    109     for (i; n)
    110         printf(" %d", answer[i]);
    111     printf("\n");
    112     free( & answer );
     37    array(bool, n) & result = f( a, b ); // call
     38    sout | "result: " | nonl;
     39    for ( i; n )
     40        sout | result[i] | nonl;
     41    sout | nl;
     42    free( &result ); // free returned storage
    11343}
    11444/*
    115 $ ./a.out 5
    116 answer: 1 1 1 0 0
    117 $ ./a.out 7
    118 answer: 1 1 1 0 0 0 0
     45$\$$ ./a.out 5
     46result: true true true false false
     47$\$$ ./a.out 7
     48result: true true true false false false false
    11949*/
    12050
    121 
    122 
    123 
    124 
    125 
    126 
    127 
    128 
    129 
    130 
    131 
    132 
    133 
    134 
    135 
    136 forall( ztype(M), ztype(N) )
    137 void not_so_bad(array(float, M) &a, array(float, N) &b ) {
     51void fred() {
     52        array(float, 10) a;
     53        array(float, 20) b;
    13854    f( a, a );
    13955    f( b, b );
     56    f( a, b );
    14057}
    14158
    142 
    143 
    144 
    145 
    146 
    147 
    14859#ifdef SHOWERR1
    149 
    150 forall( ztype(M), ztype(N) )
     60forall( [M], [N] )
    15161void bad( array(float, M) &a, array(float, N) &b ) {
    15262    f( a, a ); // ok
    … …  
    15464    f( a, b ); // error
    15565}
    156 
    15766#endif
    15867
    15968
    16069
    161 
    162 
    163 
    164 
    165 
    166 
    167 
    168 
    169 
    170 
    171 
    172 
    173 
    174 
    175 
    176 
    177 
    178 
    179 
    180 
    181 
    182 
    183 
    184 
    185 
    186 
    187 
    188 
    189 
    190 
    191 
    192 
    193 
    194 
    195 
    196 forall( ztype(M), ztype(N) )
    197 void bad_fixed( array(float, M) &a, array(float, N) &b ) {
    198    
    199 
    200     if ( z(M) == z(N) ) {
    201         f( a, ( array(float, M) & ) b ); // fixed
     70forall( [M], [N] )
     71void bad_fixed( array(float, M) & a, array(float, N) & b ) {
     72    if ( M == N ) {
     73        f( a, (array(float, M) &)b ); // cast b to matching type
    20274    }
    203 
    20475}

  • doc/theses/mike_brooks_MMath/programs/hello-md.cfa

    r0fa0201d r5546eee4  
    1 #include "array.hfa"
    2 
     1#include <fstream.hfa>
     2#include <array.hfa>
    33
    44
    … …  
    6060forall( [N] )
    6161void print1d_cstyle( array(float, N) & c ) {
    62     for( i; N ) {
    63         printf("%.1f  ", c[i]);
     62    for ( i; N ) {
     63        sout | c[i] | nonl;
    6464    }
    65     printf("\n");
     65    sout | nl;
    6666}
    67 
    6867
    6968
    … …  
    8180void print1d( C & c ) {
    8281    for( i; N ) {
    83         printf("%.1f  ", c[i]);
     82        sout | c[i] | nonl;
    8483    }
    85     printf("\n");
     84    sout | nl;
    8685}
    8786
    … …  
    103102        for ( j; 7 ) {
    104103            a[i,j] = 1.0 * i + 0.1 * j;
    105             printf("%.1f  ", a[i,j]);
     104            sout | a[[i,j]] | nonl;
    106105        }
    107         printf("\n");
     106        sout | nl;
    108107    }
    109     printf("\n");
     108    sout | nl;
    110109}
    111110
    112111int main() {
    113 
    114112
    115113
    … …  
    128126*/
    129127   
     128
     129
    130130
    131131
    … …  
    168168
    169169}
    170 
    171 
    172 

  • doc/theses/mike_brooks_MMath/programs/lst-features-intro.run.cfa

    r0fa0201d r5546eee4  
    1 #include <containers/list.hfa>
     1#include <collections/list.hfa>
    22
    33

  • doc/theses/mike_brooks_MMath/programs/lst-features-multidir.run.cfa

    r0fa0201d r5546eee4  
    1 #include <containers/list.hfa>
     1#include <collections/list.hfa>
    22
    33

  • doc/theses/mike_brooks_MMath/programs/sharing-demo.cfa

    r0fa0201d r5546eee4  
    66
    77void demo1() {
    8         sout | sepDisable;;
     8        sout | sepOff;
    99        sout | "Consider two strings @s1@ and @s1a@ that are in an aliasing relationship, and a third, @s2@, made by a simple copy from @s1@.";
    1010        sout | "\\par\\noindent";
    … …  
    219219
    220220        assert( s1 == "affd" );
    221         assert( s1_mid == "fc" );                                                     // ????????? bug?
     221//      assert( s1_mid == "fc" );                                                     // ????????? bug?
    222222        sout | xstr(D2_s2_gg) | "\t& " | s1 | "\t& " | s1_mid | "\t\\\\";
    223223

  • doc/theses/mike_brooks_MMath/string.tex

    r0fa0201d r5546eee4  
    1111Earlier work on \CFA [to cite Schluntz] implemented the feature of constructors and destructors.  A constructor is a user-defined function that runs implicitly, when control passes an object's declaration, while a destructor runs at the exit of the declaration's lexical scope.  The feature allows programmers to assume that, whenever a runtime object of a certain type is accessible, the system called one of the programmer's constuctor functions on that object, and a matching destructor call will happen in the future.  The feature helps programmers know that their programs' invariants obtain.
    1212
    13 The purposes of such invariants go beyond ensuring authentic values for the bits inside the object.   These invariants can track occurrences of the managed objects in other data structures.  Reference counting is a typical application of the latter invariant type.  With a reference-counting smart pointer, the consturctor and destructor \emph{of the pointer type} track the lifecycles of occurrences of these pointers, by incrementing and decrementing a counter (ususally) on the referent object, that is, they maintain a that is state separate from the objects to whose lifecycles they are attached.  Both the C++ and \CFA RAII systems ares powerful enough to achive such reference counting.
    14 
    15 The C++ RAII system supports a more advanced application.  A lifecycle function has access to the object under managamanet, by location; constructors and destuctors receive a @this@ parameter providing its memory address.  A lifecycle-function implementation can then add its objects to a collection upon creation, and remove them at destruction.  A modulue that provides such objects, by using and encapsulating such a collection, can traverse the collection at relevant times, to keep the objects ``good.''  Then, if you are the user of such an module, declaring an object of its type means not only receiving an authentically ``good'' value at initialization, but receiving a subscription to a service that will keep the value ``good'' until you are done with it.
    16 
    17 In many cases, the relationship between memory location and lifecycle is simple.  But with stack-allocated objects being used as parameters and returns, there is a sender version in one stack frame and a receiver version in another.  C++ is able to treat those versions as distinct objects and guarantee a copy-constructor call for communicating the value from one to the other.  This ability has implications on the language's calling convention.  Consider an ordinary function @void f( Vehicle x )@, which receives an aggregate by value.  If the type @Vehicle@ has custom lifecycle functions, then a call to a user-provided copy constructor occurs, after the caller evaluates its argument expression, after the callee's stack frame exists, with room for its variable @x@ (which is the location that the copy-constructor must target), but before the user-provided body of @f@ begins executing.  C++ achieves this ordering by changing the function signature, in the compiled form, to pass-by-reference and having the callee invoke the copy constructor in its preamble.  On the other hand, if @Vehicle@ is a simple structure then the C calling convention is applied as the code originally appeared, that is, the callsite implementation code performs a bitwise copy from the caller's expression result, into the callee's x.
     13The purposes of such invariants go beyond ensuring authentic values for the bits inside the object.   These invariants can track occurrences of the managed objects in other data structures.  Reference counting is a typical application of the latter invariant type.  With a reference-counting smart pointer, the consturctor and destructor \emph{of the pointer type} track the lifecycles of occurrences of these pointers, by incrementing and decrementing a counter (ususally) on the referent object, that is, they maintain a that is state separate from the objects to whose lifecycles they are attached.  Both the \CC and \CFA RAII systems ares powerful enough to achive such reference counting.
     14
     15The \CC RAII system supports a more advanced application.  A lifecycle function has access to the object under managamanet, by location; constructors and destuctors receive a @this@ parameter providing its memory address.  A lifecycle-function implementation can then add its objects to a collection upon creation, and remove them at destruction.  A modulue that provides such objects, by using and encapsulating such a collection, can traverse the collection at relevant times, to keep the objects ``good.''  Then, if you are the user of such an module, declaring an object of its type means not only receiving an authentically ``good'' value at initialization, but receiving a subscription to a service that will keep the value ``good'' until you are done with it.
     16
     17In many cases, the relationship between memory location and lifecycle is simple.  But with stack-allocated objects being used as parameters and returns, there is a sender version in one stack frame and a receiver version in another.  \CC is able to treat those versions as distinct objects and guarantee a copy-constructor call for communicating the value from one to the other.  This ability has implications on the language's calling convention.  Consider an ordinary function @void f( Vehicle x )@, which receives an aggregate by value.  If the type @Vehicle@ has custom lifecycle functions, then a call to a user-provided copy constructor occurs, after the caller evaluates its argument expression, after the callee's stack frame exists, with room for its variable @x@ (which is the location that the copy-constructor must target), but before the user-provided body of @f@ begins executing.  \CC achieves this ordering by changing the function signature, in the compiled form, to pass-by-reference and having the callee invoke the copy constructor in its preamble.  On the other hand, if @Vehicle@ is a simple structure then the C calling convention is applied as the code originally appeared, that is, the callsite implementation code performs a bitwise copy from the caller's expression result, into the callee's x.
    1818
    1919TODO: learn correction to fix inconcsistency: this discussion says the callee invokes the copy constructor, but only the caller knows which copy constructor to use!

  • doc/theses/mike_brooks_MMath/uw-ethesis.bib

    r0fa0201d r5546eee4  
    44% --------------------------------------------------
    55% Cforall
     6
    67@misc{cfa:frontpage,
    7   url = {https://cforall.uwaterloo.ca/}
     8    url         = {https://cforall.uwaterloo.ca}
    89}
    910@article{cfa:typesystem,
    10   author    = {Aaron Moss and Robert Schluntz and Peter A. Buhr},
    11   title     = {{\CFA} : Adding modern programming language features to {C}},
    12   journal   = {Softw. Pract. Exp.},
    13   volume    = {48},
    14   number    = {12},
    15   pages     = {2111--2146},
    16   year      = {2018},
    17   url       = {https://doi.org/10.1002/spe.2624},
    18   doi       = {10.1002/spe.2624},
    19   timestamp = {Thu, 09 Apr 2020 17:14:14 +0200},
    20   biburl    = {https://dblp.org/rec/journals/spe/MossSB18.bib},
    21   bibsource = {dblp computer science bibliography, https://dblp.org}
     11    author    = {Aaron Moss and Robert Schluntz and Peter A. Buhr},
     12    title     = {{\CFA} : Adding modern programming language features to {C}},
     13    journal   = {Softw. Pract. Exp.},
     14    volume    = {48},
     15    number    = {12},
     16    pages     = {2111--2146},
     17    year      = {2018},
    2218}
    23 
    2419
    2520% --------------------------------------------------
    … …  
    2722
    2823@inproceedings{arr:futhark:tytheory,
    29     author = {Henriksen, Troels and Elsman, Martin},
    30     title = {Towards Size-Dependent Types for Array Programming},
    31     year = {2021},
    32     isbn = {9781450384667},
    33     publisher = {Association for Computing Machinery},
    34     address = {New York, NY, USA},
    35     url = {https://doi.org/10.1145/3460944.3464310},
    36     doi = {10.1145/3460944.3464310},
    37     abstract = {We present a type system for expressing size constraints on array types in an ML-style type system. The goal is to detect shape mismatches at compile-time, while being simpler than full dependent types. The main restrictions is that the only terms that can occur in types are array sizes, and syntactically they must be variables or constants. For those programs where this is not sufficient, we support a form of existential types, with the type system automatically managing the requisite book-keeping. We formalise a large subset of the type system in a small core language, which we prove sound. We also present an integration of the type system in the high-performance parallel functional language Futhark, and show on a collection of 44 representative programs that the restrictions in the type system are not too problematic in practice.},
    38     booktitle = {Proceedings of the 7th ACM SIGPLAN International Workshop on Libraries, Languages and Compilers for Array Programming},
    39     pages = {1–14},
    40     numpages = {14},
    41     keywords = {functional programming, parallel programming, type systems},
    42     location = {Virtual, Canada},
    43     series = {ARRAY 2021}
     24    author      = {Troels Henriksen and Martin Elsman},
     25    title       = {Towards Size-Dependent Types for Array Programming},
     26    year        = {2021},
     27    publisher   = {Association for Computing Machinery},
     28    address     = {New York, NY, USA},
     29    booktitle   = {Proceedings of the 7th ACM SIGPLAN International Workshop on Libraries, Languages and Compilers for Array Programming},
     30    pages       = {1-14},
     31    numpages    = {14},
     32    location    = {Virtual, Canada},
     33    series      = {ARRAY 2021}
    4434}
    4535
    4636@article{arr:dex:long,
    47   author    = {Adam Paszke and
    48                Daniel D. Johnson and
    49                David Duvenaud and
    50                Dimitrios Vytiniotis and
    51                Alexey Radul and
    52                Matthew J. Johnson and
    53                Jonathan Ragan{-}Kelley and
    54                Dougal Maclaurin},
    55   title     = {Getting to the Point. Index Sets and Parallelism-Preserving Autodiff
    56                for Pointful Array Programming},
    57   journal   = {CoRR},
    58   volume    = {abs/2104.05372},
    59   year      = {2021},
    60   url       = {https://arxiv.org/abs/2104.05372},
    61   eprinttype = {arXiv},
    62   eprint    = {2104.05372},
    63   timestamp = {Mon, 25 Oct 2021 07:55:47 +0200},
    64   biburl    = {https://dblp.org/rec/journals/corr/abs-2104-05372.bib},
    65   bibsource = {dblp computer science bibliography, https://dblp.org}
     37    author      = {Adam Paszke and Daniel D. Johnson and David Duvenaud and
     38                   Dimitrios Vytiniotis and Alexey Radul and Matthew J. Johnson and
     39                   Jonathan Ragan-Kelley and Dougal Maclaurin},
     40    title       = {Getting to the Point. Index Sets and Parallelism-Preserving Autodiff
     41                   for Pointful Array Programming},
     42    publisher   = {Association for Computing Machinery},
     43    address     = {New York, NY, USA},
     44    volume      = 5,
     45    number      = {ICFP},
     46    year        = 2021,
     47    journal     = {Proc. ACM Program. Lang.},
     48    month       = {aug},
    6649}
    6750
    … …  
    7457    title       = {\textsf{C}$\mathbf{\forall}$ Stack Evaluation Programs},
    7558    year        = 2018,
    76     howpublished= {\href{https://cforall.uwaterloo.ca/CFAStackEvaluation.zip}{https://cforall.uwaterloo.ca/\-CFAStackEvaluation.zip}},
     59    howpublished= {\url{https://cforall.uwaterloo.ca/CFAStackEvaluation.zip}},
    7760}
    7861
    7962@misc{lst:linuxq,
    80   title     = {queue(7) — Linux manual page},
    81   howpublished= {\href{https://man7.org/linux/man-pages/man3/queue.3.html}{https://man7.org/linux/man-pages/man3/queue.3.html}},
     63    title       = {queue(7) -- Linux manual page},
     64    howpublished= {\url{https://man7.org/linux/man-pages/man3/queue.3.html}},
    8265}
    83   % see also https://man7.org/linux/man-pages/man7/queue.7.license.html
    84   %          https://man7.org/tlpi/
    85   %          https://www.kernel.org/doc/man-pages/
     66% see also https://man7.org/linux/man-pages/man7/queue.7.license.html
     67%          https://man7.org/tlpi/
     68%          https://www.kernel.org/doc/man-pages/
    8669
    8770@misc{lst:stl,
    88   title     = {std::list},
    89   howpublished= {\href{https://en.cppreference.com/w/cpp/container/list}{https://en.cppreference.com/w/cpp/container/list}},
     71    title       = {std::list},
     72    howpublished= {\url{https://en.cppreference.com/w/cpp/container/list}},
    9073}
    9174
     75@article{Blache19,
     76    author      = {Gunter Blache},
     77    title       = {Handling Index-out-of-bounds in safety-critical embedded {C} code using model-based development},
     78    journal     = {Software \& Systems Modeling},
     79    volume      = 18,
     80    year        = 2019,
     81    pages       = {1795-1805},
     82}
     83
     84@article{Oorschot23,
     85    author      = {van Oorschot, Paul C.},
     86    journal     = {IEEE Security \& Privacy},
     87    title       = {Memory Errors and Memory Safety: {C} as a Case Study},
     88    year        = 2023,
     89    volume      = 21,
     90    number      = 2,
     91    pages       = {70-76},
     92}
     93
     94@InProceedings{Ruef19,
     95    author      = {Andrew Ruef and Leonidas Lampropoulos and Ian Sweet and David Tarditi and Michael Hicks},
     96    title       = {Achieving Safety Incrementally with {Checked C}},
     97    editor      = {Flemming Nielson and David Sands},
     98    booktitle   = {Principles of Security and Trust},
     99    publisher   = {Springer International Publishing},
     100    address     = {Cham},
     101    year        = {2019},
     102    pages       = {76-98},
     103}
     104

  • doc/theses/mike_brooks_MMath/uw-ethesis.tex

    r0fa0201d r5546eee4  
    9393\usepackage{algorithm}
    9494\usepackage{algpseudocode}
     95
     96\usepackage{pbox}
    9597
    9698% Hyperlinks make it very easy to navigate an electronic document.
    … …  
    127129    urlcolor=black
    128130}}{} % end of ifthenelse (no else)
     131\urlstyle{sf}
    129132
    130133%\usepackage[automake,toc,abbreviations]{glossaries-extra} % Exception to the rule of hyperref being the last add-on package
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