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Subtracting a vector means going in the opposite direction the vector is pointing. If soldier Alpha was forced to retreat from a well-armed droid, he might calculate a vector to his adversary and then subtract it from his current position to find a point directly behind him. The math for vector subtraction is very similar to addition, but we subtract from the components rather than add. Listing 5-11 shows a method to subtract a vector from another vector, which you can add to the Vector2 class. Listing 5-11. Vector Subtraction Method def __sub__(self, rhs): return Vector2(self.x rhs.x, self.y rhs.y)

An AST is a representation of the construct that makes up the program; it s intended to be easy for the programmer to use. One reason F# is good for this kind of development is its union type. This type is great for representing languages because you can use it to represent items that are related yet do not share the same structure. The following example shows how to use an AST: type Ast = | Ident of string | Val of System.Double | Multi of Ast * Ast | Div of Ast * Ast | Plus of Ast * Ast | Minus of Ast * Ast The tree consists of only one type because it is quite simple. A complicated tree would contain many more types, but it would still follow this basic pattern. Here you can see that the tree, which is of the type Expr, will consist of either identifiers (the Ident type); the names of the identifiers represented by a string; or values (the Val type), which will be values represented by a System.Double. The type Expr consists of four more types (Multi, Div, Plus, and Minus) that represent the arithmetic operations. They use recursion, so they are composed of other expressions.

During the iteration, the coach is paying close attention to the daily activities of the team. When the coach notices any member of the team straying from the XP practices (not pairing or switching pairs, not testing first, and so on), he intervenes and corrects the action. Sometimes, when there is a difficult problem or a shortage of pairs, the coach needs to jump in and pair with a developer.

Let s suppose soldier Alpha arrived at point B, only to find he had forgotten his spare batteries; how could he calculate a vector back to A (i.e., Vector BA) He could do the math given the points again, but an alternative is to negate vector AB, which has already been calculated. Negating a vector creates a vector of the same length that points in the opposite direction. So AB is the same as BA. To negate a vector, simply negate the components. Listing 5-12 is a member function that does negation, which you can add to the Vector2 class. Listing 5-12. Vector Negation def __neg__(self): return Vector2( self.x, self.y)

Once you create your AST, you have two choices: you can either interpret it or compile it. Interpreting it simply means walking the tree and performing actions as you go. Compiling it means changing it into some other form that is easier, or more typically faster, for the machine to execute. This section will examine how to interpret the results; the next section will look at the options for compiling them; finally, you will look at when you should use interpretation and when you should use compilation. The following example shows a short interpreter for your program. The main work of interpreting the AST is done by the function interpret, which walks the tree, performing the necessary actions as it goes. The logic is quite simple. If you find a literal value or an identifier, you return the appropriate value: | Ident (s) -> variableDict.[s] | Val (v) -> v

If you find an operand, you recursively evaluate the expressions it contains to obtain its values and then perform the operation: | Multi (e1, e2) -> (interpretInner e1) * (interpretInner e2) You can see the complete interpreter in Listing 12-6. Listing 12-6. Interpreting an AST Generated from Command-Line Input open System open System.Collections.Generic open Strangelights.Expression // requesting a value for variable from the user let getVariableValues e = let rec getVariableValuesInner input (variables : Map<string, float>) = match input with | Ident (s) -> match variables.TryFind(s) with | Some _ -> variables | None -> printf "%s: " s let v = float(Console.ReadLine()) variables.Add(s,v) | Multi (e1, e2) -> variables |> getVariableValuesInner e1 |> getVariableValuesInner e2 | Div (e1, e2) -> variables |> getVariableValuesInner e1 |> getVariableValuesInner e2 | Plus (e1, e2) -> variables |> getVariableValuesInner e1 |> getVariableValuesInner e2 | Minus (e1, e2) -> variables |> getVariableValuesInner e1 |> getVariableValuesInner e2 | _ -> variables getVariableValuesInner e (Map.empty)