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type AttemptBuilder() = /// Wraps an ordinary value into an Attempt value. /// Used to de-sugar uses of 'return' inside computation expressions. member b.Return(x) = succeed x /// Composes two attempt values. If the first returns Some(x) then the result /// is the result of running rest(x). /// Used to de-sugar uses of 'let!' inside computation expressions. member b.Bind(p,rest) = bind p rest /// Delays the construction of an attempt until just before it is executed member b.Delay(f) = delay f /// Used to de-sugar uses of 'let' inside computation expressions. member b.Let(p,rest) : Attempt<'T> = rest p let attempt = new AttemptBuilder()

These methods must return either a key not found or end-of-file return code Take care to code these return statements correctly or you could encounter some strange query results The first method is the index_read() method This method sets the row buffer to the row in the file that matches the key passed in If the key passed in is null, then the method should return the first key value in the file Locate the index_read() method and add the code to get the file position from the index and read the corresponding row from the data file Listing 7-49 shows the method with the changes Listing 7-49 Changes to the index_read() Method in ha_spartan.

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member g.Build(f) = match f with | And(x,y) -> g.And(g.Build x, g.Build y) | Var(p) -> g.Var(p) | Not(x) -> g.Not(g.Build x) | False -> g.False | Exists(v,p) -> failwith "Exists node" member g.Equiv p1 p2 = (g.Build(p1) = g.Build(p2)) You can now install a pretty-printer and inspect the BDDs for some simple formulae: > let bddBuilder = BddBuilder(compare);; val bddBuilder: BddBuilder > fsi.AddPrinter(fun bdd -> bddBuilder.ToString(bdd));; val it: unit = () > bddBuilder.Build(var "x");; val it : Bdd = (x => T | F) > bddBuilder.Build(var "x" &&& var "x");; val it : Bdd = (x => T | F) > bddBuilder.Build(var "x") = bddBuilder.Build(var "x" &&& var "x");; val it : bool = true > (var "x") = (var "x" &&& var "x");; val it : bool = false > bddBuilder.Build(var "x" &&& var "y");; val it : Bdd = (x => (y => T | F) | F) > bddBuilder.Equiv (var "x") (var "x" &&& var "x");; val it : bool = true Note that the BDD representations of x and x AND x are identical, while the Prop representations are not. The Prop representation is an abstract syntax representation, while the BDD representation is more of a semantic or computational representation. The BDD representation incorporates all the logic necessary to prove propositional formula equivalent; in other words, this logic is built into the representation itself.

The inferred types here are as follows: type AttemptBuilder = new : unit -> AttemptBuilder member Bind : Attempt<'T> * ('T -> Attempt<'U>) -> Attempt<'U> member Delay : (unit -> Attempt<'T>) -> Attempt<'T> member Let : 'T * ('T -> Attempt<'U>) -> Attempt<'U> member Return : 'T -> Attempt<'T> val attempt : AttemptBuilder F# implements workflows by de-sugaring computation expressions using a builder. For example, given the previous AttemptBuilder, the following workflow attempt { let! n1 = failIfBig inp1 let! n2 = failIfBig inp2 let sum = n1 + n2 return sum };; de-sugars to this: attempt.Bind( failIfBig inp1,(fun n1 -> attempt.Bind(failIfBig inp2,(fun n2 -> attempt.Return sum))))) One purpose of the F# workflow syntax is to make sure you don t have to write this sort of thing by hand. The de-sugaring of the workflow syntax is implemented by the F# compiler. Table 9-3 shows some of the typical signatures that a workflow builder needs to implement. Table 9-3. Some Typical Workflow Builder Members as Required by the F# Compiler

cc int ha_spartan::index_read(byte * buf, const byte * key, uint key_len __attribute__((unused)), enum ha_rkey_function find_flag __attribute__((unused))) { long long pos; DBUG_ENTER("ha_spartan::index_read"); if (key == NULL) pos = share->index_class->get_first_pos(); else pos = share->index_class->get_index_pos((byte *)key, key_len); if (pos == -1) DBUG_RETURN(HA_ERR_KEY_NOT_FOUND); current_position = pos + share->data_class->row_size(table->s->rec_buff_length); share->data_class->read_row(buf, table->s->rec_buff_length, pos); share->index_class->get_next_key(); DBUG_RETURN(0); }.

You can now use BDDs to perform circuit verification. For example, the following verifies that you can swap the x and y inputs to an 8-bit adder:

Used to de-sugar let! and do! within computation expressions. Used to de-sugar return within computation expressions. Used to de-sugar return! within computation expressions. Used to ensure that side effects within a computation expression are performed when expected. Used to de-sugar for ... do ... within computation expressions. M<'U> can optionally be M<unit>.

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