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sealed set of choices. This makes them a perfect fit for many constructs that arise in applications and symbolic analysis libraries. They are, by design, nonextensible: subsequent modules can t add new cases to a discriminated union. This is deliberate: you get strong and useful guarantees by placing a limit on the range of possible values for a type. Extensible types can be defined through the use of records of functions and object interface types, discussed in s 5 and 6.

At last! You re at the optimizer However, you won t find it if you go looking for a source file or class by that name Although the JOIN class contains a method called optimize(), the optimizer is actually a collection of flow control and subfunctions designed to find the shortest path to executing the query What happened to the fancy algorithms and query paths and compiled queries Recall from our architecture discussion in 2 that the MySQL query optimizer is a nontraditional hybrid optimizer utilizing a combination of known best practices and costbased path selection It is at this point in the code that the best practices part kicks in An example of one of those best practices is standardizing the parameters in the WHERE clause expressions The example query uses a WHERE clause with an expression, Employees.

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Any value can be formatted using a %O or %A pattern; these are extremely useful when prototyping or examining data. %O converts the object to a string using the Object.ToString() function supported by all values. For example:

Discriminated union types with only one data tag are an effective way to implement record-like types: type Point3D let origin = let unitX = let unitY = let unitZ = = Vector3D of float * float * float Vector3D(0.,0.,0.) Vector3D(1.,0.,0.) Vector3D(0.,1.,0.) Vector3D(0.,0.,1.)

department = 'EGR', but the clause could have been written as 'EGR' = Employeesdepartment and still be correct (it returns the same results) This is an example of where traditional cost-based optimizer could generate multiple plans one for each of the expression variants Just a few examples of the many best practices that MySQL uses follows: Constant propagation The removal of transitive conjunctions using constants For example, if you have a=b='c', the transitive law states that a='c' This optimization removes those inner equalities, thereby reducing the number of evaluations For example, the SQL command SELECT * FROM table1 WHERE column1 = 12 AND NOT (column3 = 17 OR column1 = column2) would be reduced to SELECT * FROM table1 WHERE column1 = 12 AND column3 <> 17 AND column2 <> 12 Dead code elimination The removal of always true conditions.

These are particularly effective because they can be decomposed using succinct patterns in the same way as tuple arguments: let length (Vector3D(dx,dy,dz)) = sqrt(dx*dx+dy*dy+dz*dz) This technique is most useful for record-like values where there is some natural order on the constituent elements of the value (as shown earlier) or where the elements have different types.

> System.DateTime.Now.ToString();; val it : string = "28/06/20.. 17:14:07 PM" > sprintf "It is now %O" System.DateTime.Now;; val it : string = "It is now 28/06/20... 17:14:09"

For example, if you have a=b AND 1=1, the AND 1=1 condition is removed The same occurs for always false conditions where the false expression can be removed without affecting the rest of the clause For example, the SQL command SELECT * FROM table1 WHERE column1 = 12 AND column2 = 13 AND column1 < column2 would be reduced to SELECT * FROM table1 WHERE column1 = 12 AND column2 = 13 Range queries The transformation of the IN clause to a list of disjunctions For example, if you have an IN (1,2,3), the transformation would be a = 1 or a = 2 or a = 3 This helps simplify the evaluation of the expressions.

Multiple types can be declared together to give a mutually recursive collection of types, including record types, discriminated unions, and abbreviations. The type definitions must be separated by the keyword and: type Node = { Name : string; Links : Link list } and Link = | Dangling | Link of Node

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