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F# includes matrix and column vector types, which are generic and called Matrix<'a> and Vector<'a>, respectively. For symmetry a type of row vectors, RowVector<'a>, is also included. Most commonly, the element types are instantiated to be double (that is, float), so the following abbreviations are used: type vector = Vector<float> type matrix = Matrix<float> type rowvec = RowVector<float> The modules Matrix, Vector, and RowVector in the Microsoft.FSharp.Math namespace have many further functions for creating and working with these types. The functions are specialized for use with floating-point matrices, but versions to work with generic types are available at Microsoft.FSharp.Math.Matrix.Generic and Microsoft.FSharp.Math.Vector. Generic. The functions vector and matrix are also available for creating literal values. Here are some examples of the uses of these types and functions: > open Microsoft.Fsharp.Math;; > vector [ 1.0; 2.0 ; 3.0 ] + vector [ 1.0; 2.0 ; 3.0 ];; val it : Vector<float> = vector [2.0; 4.0; 6.0] > matrix [ [ 1.0; 2.0 ]; [ 1.0; 3.0 ] ] * matrix [ [ 1.0; -2.0 ]; [ 0.5; 3.0 ] ];; val it : Math.matrix = matrix [[1.0; -4.0]; [0.5; 9.0];] Table 10-11 summarizes the primary properties of these types.

One subtlety with programming with on-demand or lazy values like sequences is that side effects such as reading and writing from an external store shouldn t in general happen until the lazy sequence value is consumed. For example, the previous allFiles function reads the top-level directory C:\ as soon as allFiles is applied to its argument. This may not be appropriate if the contents of C:\ are changing. You can delay the computation of the sequence by using the library function Seq.delay or by using a sequence expression, covered in the next section, where delays are inserted automatically by the F# compiler.

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/* list of all tables in query */ TABLE_LIST *all_tables; /* most outer SELECT_LEX_UNIT of query */ SELECT_LEX_UNIT *unit= &lex->unit; /* Saved variable value */ DBUG_ENTER("mysql_execute_command"); thd->net.no_send_error= 0; ... switch (lex->sql_command) { case SQLCOM_SELECT: { ... select_result *result=lex->result; ... res= check_access(thd, lex->exchange SELECT_ACL | FILE_ACL : SELECT_ACL, any_db, 0, 0, 0, 0); ... if (!(res= open_and_lock_tables(thd, all_tables))) { if (lex->describe) { /* We always use select_send for EXPLAIN, even if it's an EXPLAIN for SELECT ... INTO OUTFILE: a user application should be able to prepend EXPLAIN to any query and receive output for it, even if the query itself redirects the output. */ ... query_cache_store_query(thd, all_tables); res= handle_select(thd, lex, result, 0); ... } There are a number of interesting things happening in this function. You will notice another switch statement that has as its cases the SQLCOM keywords. In the case of the example query, you saw the parser set the lex->sql_command member variable to SQLCOM_SELECT. I have included a

Exceptions may also be processed using the try ... finally ... construct. This guarantees to run the finally clause both when an exception is thrown and when the expression evaluates normally. This allows the programmer to ensure that resources are disposed after the completion

Aggregate operators are a powerful way of working with seq<type> values. However, F# also provides a convenient and compact syntax called sequence expressions for specifying sequence values that can be built using operations such as choose, map, filter, and concat. You can also use sequence expressions to specify the shapes of lists and arrays. It s valuable to learn how to use sequence expressions: They re a compact way of specifying interesting data and generative processes. They re used to specify database queries when using data-access layers such as Microsoft s Language Integrated Queries (LINQ). See 15 for examples of using sequence expressions this way. They re one particular use of computation expressions, a more general concept that has several uses in F# programming. 9 discusses computation expressions, and we show how to use them for asynchronous and parallel programming in 13.

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