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In practice, circuits are defined largely with respect to vectors of wires, not just individual wires. You can model these using arrays of propositions, and since it s now clear we re modeling bits via propositions, we make an appropriate type abbreviation for them as well: type bit = Prop type bitvec = bit[] let Lo : bit = False let Hi : bit = True let vec n nm : bitvec = Array.init n (fun i -> var (sprintf "%s%d" nm i)) let bitEq (b1:bit) (b2:bit) = (b1 <=> b2) let AndL l = Seq.fold1 (fun x y-> And(x,y)) l let vecEq (v1:bitvec) (v2:bitvec) = AndL (Array.map2 bitEq v1 v2) These functions have types as follows: type bit = Prop type bitvec = bit [] val Lo : bit val Hi : bit val vec : int -> string -> bitvec val bitEq : bit -> bit -> Prop val AndL : #seq<Prop> -> Prop val vecEq : bitvec -> bitvec -> Prop You can now proceed to define larger circuits. For example: let fourBitAdder (x:bitvec) (y:bitvec) (sum:bitvec) (carry:bitvec) = halfAdder x.[0] y.[0] sum.[0] carry.[0] &&& fullAdder x.[1] y.[1] carry.[0] sum.[1] carry.[1] &&& fullAdder x.[2] y.[2] carry.[1] sum.[2] carry.[2] &&& fullAdder x.[3] y.[3] carry.[2] sum.[3] carry.[3]

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We also create an index on the foreign key column in the child table parts_rel. Almost always, this index is required in real-life applications to speed up the access to queries on child tables and to avoid unnecessary locking and even deadlocks during a delete cascade operation (see http://asktom.oracle.com/~tkyte/unindex/index.html for more details). benchmark@ORA10G> create index parts_id_rel_idx on parts_rel(component_id );

Or, more generally, you can chain an arbitrary series of adders to form an N-bit adder. First you define an abbreviation for the AndL function to represent the composition of multiple circuit blocks: let Blocks l = AndL l And here is the definition of an N-bit adder with a halfAdder at one end: let nBitCarryRippleAdder (n:int) (x:bitvec) (y:bitvec) (sum:bitvec) (carry:bitvec) = Blocks [ for i in 0 .. n-1 -> if i = 0 then halfAdder x.[i] y.[i] sum.[i] carry.[i] else fullAdder x.[i] y.[i] carry.[i-1] sum.[i] carry.[i] ] Using a similar approach, you get the following satisfying specification of a symmetric N-bit adder that accepts a carry as input and also gives a carry as output: let rippleAdder (n:int) (x:bitvec) (y:bitvec) (sum:bitvec) (carry:bitvec) Blocks [ for i in 0 .. n-1 -> fullAdder x.[i] y.[i] carry.[i] sum.[i] carry.[i+1] ] =

Let s now look at an alternative solution that uses nested tables to store the same data. Using nested tables to store data involves the following steps: 1. Create the nested table type. 2. Create the table containing a column of the nested table type. 3. Perform DMLs on the table containing a column of the nested table type. Let s look at each of these steps separately. Creating a Nested Table Type The first step is to create an object type, part_type, to represent the child table columns: benchmark@ORA10G> create or replace type part_type as object 2 ( 3 component_id number, 4 part_id number, 5 part_name varchar2(50), 6 part_desc varchar2(500) 7 ); 8 / Type created. Then we can create the nested table type, part_type_tab, representing a collection of part_type objects: benchmark@ORA10G> create or replace type part_type_tab as table of part_type; 2 / Type created. Creating a Table Containing a Column of the Nested Table Type Finally, we create the components table called components_nt, wherein we have the parts column of the nested table type representing the parts of a component. Thus the child table is embedded or nested within the parent table in this approach. The nested table column data is actually stored in a real, physical table called parts_nt, as specified by the nested table parts stored as parts_nt clause:

This method returns a DataTable with metadata about all of the installed providers on the system. This method returns an instance of a DbProviderFactory type. It accepts an argument that describes the factory either a DataRow from the DataTable returned by GetFactoryClasses, or an invariant name of the provider, which is a column returned in the DataTable.

benchmark@ORA10G> create table components_nt 2 ( 3 component_id number primary key, 4 component_name varchar2(50), 5 parts part_type_tab 6 ) 7 nested table parts store as parts_nt; Table created. Attempting to create a foreign key constraint on the nested table does not work because nested tables do not allow referential integrity constraints, as shown in the following code. We will address this issue shortly. benchmark@ORA10G> alter table parts_nt add constraint parts_nt_fk foreign key(component_id) 2 references components_nt(component_id); alter table parts_nt add constraint parts_nt_fk foreign key(component_id) * ERROR at line 1: ORA-30730: referential constraint not allowed on nested table column