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Let s now take a look at the propositional formula for a halfAdder with variable inputs and outputs: > halfAdder (var "x") (var "y") (var "sum") (var "carry");; > val it : Prop = And(Not And (Not And (Var "sum", Not Not And (Not And (Var "x",Var "y"),Not And (Not Var "x",Not Var "y"))), Not And (Not Var "sum", Not Not Not And (Not And (Var "x",Var "y"),Not And (Not Var "x",Not Var "y")))), Not And (Not And (Var "carry",And (Var "x",Var "y")), Not And (Not Var "carry",Not And (Var "x",Var "y")))) Clearly, you don t want to be doing too much of that! You will see better ways of inspecting circuits and the symbolic values of bit vectors in the section Representing Propositional Formulae Efficiently Using BDDs.

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All of the configured Managed Providers are available through the services of the Provider Factory. To get a list of installed providers on a system, you can use the GetFactoryClasses method on the DbProviderFactory type (see Default.aspx in Web10). protected void Page_Load(object sender, EventArgs e) { GridView gv = new GridView(); gv.DataSource = DbProviderFactories.GetFactoryClasses(); gv.DataBind(); form1.Controls.Add(gv); } By binding this DataTable to a grid, you can see the information it returns, and a list of the installed providers on the machine, shown here in Figure 10-4.

Performing DML on a Table Containing a Column of the Nested Table Type Let s now look at how to carry out DML operations on a table containing a nested table column. We can insert a row in the table components_nt as follows: benchmark@ORA10G> insert into components_nt values 2 ( 1, 'component 1', 3 part_type_tab( (part_type(1,1, 'part1', 'part1 description')), 4 (part_type(1,2, 'part2', 'part2 description') ) 5 ) 6 ); 1 row created. The syntax should be familiar to you by now: It uses nested table constructors, which we have already covered. The following example runs a simple select on table components_nt: benchmark@ORA10G> select * from components_nt; COMPONENT_ID COMPONENT_NAME PARTS(COMPONENT_ID, PART_ID, PART_NAME, PART_DESC) ------------ ---------------------------------------------1 component 1 PART_TYPE_TAB(PART_TYPE(1, 1, 'part1', 'part1 description'), PART_TYPE(1, 2, 'part2', 'part2 description'))

In passing, we note that the twoBitAdder uses an internal wire. You could model this using an existential formula: let twoBitAdderWithHiding (x1,x2) (y1,y2) (sum1,sum2) carry = let carryInnerVar = fresh "carry" let carryInner = var(carryInnerVar) Exists(carryInnerVar, halfAdder x1 y1 sum1 carryInner &&& fullAdder x2 y2 carryInner sum2 carry) However, this brings up issues beyond the scope of this chapter, and instead we take an approach to modeling where there are no boundaries to the circuits and where all internal wires are exposed.

If we want to unnest the nested table contents, we can run the following select using the table construct to join the nested table with its parent table (very similar to the case of varrays): benchmark@ORA10G> select p.* 2 from components_nt c, TABLE( c.parts ) p; COMPONENT_ID PART_ID PART_NA ------------ ---------- ------1 1 part1 1 2 part2 PART_DESC -------------------part1 description part2 description

Figure 10-4. The data returned by GetProviderFactories, listing the installed Managed Providers on the system In Figure 10-4, you can see the data contained in the DataTable returned by GetObjectFactories, including all of the invariant names of the providers, which you can use to create instances of the factory for a specific provider. All of the installed providers are registered in the machine.config under a new element named DbProviderFactories. <system.data> <DbProviderFactories> <add name="Odbc Data Provider" invariant="System.Data.Odbc" description=".Net Framework Data Provider for Odbc" type="System.Data.Odbc.OdbcFactory, System.Data, Version=..." /> <add name="OleDb Data Provider" invariant="System.Data.OleDb" description=".Net Framework Data Provider for OleDb" type="System.Data.OleDb.OleDbFactory, System.Data, Version=..." /> <add name="OracleClient Data Provider" invariant="System.Data.OracleClient" description=".Net Framework Data Provider for Oracle" type="System.Data.OracleClient.OracleClientFactory, System.Data..." /> <add name="SqlClient Data Provider" invariant="System.Data.SqlClient" description=".Net Framework Data Provider for SqlServer" type="System.Data.SqlClient.SqlClientFactory, System.Data, Version=..." /> <add name="SQL Server CE Data Provider" invariant="Microsoft.SqlServerCe.Client" support="3F7"

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