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CHAPTER 8 MA STERING F#: C OMM ON TE CHNIQUE S
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an internal library type called BigNat along with a sign field that is 1 or -1. When implementing the BigInt type, it turns out to be convenient to have two different representations of the number zero, one with sign 1 and one with sign -1. Of course, these should be equal as far as generic equality and comparison are concerned. Listing 8-1 shows how to customize generic comparison for the BigInt type so that it respects this desired behavior. The type definition of BigInt includes overrides of Object.Equals and an implementation of the interface System. IComparable. Listing 8-1. Customizing Generic Comparison for a New Type Definition open Microsoft.FSharp.Math.Primitives type BigInt = { sign : int; v : BigNat } override x.Equals(yobj:obj) = let y = unbox<BigInt>(yobj) (x.sign = y.sign) && (x.v = y.v) || BigNat.isZero(x.v) && BigNat.isZero(y.v) interface System.IComparable with override x.CompareTo(yobj:obj) = let y = unbox<BigInt>(yobj) match x.sign,y.sign with | 1, 1 -> compare x.v y.v | -1,-1 -> compare y.v x.v | _ when BigNat.IsZero(x.v) && BigNat.IsZero(y.v) -> 0 | 1, -1 -> 1 | -1, 1 -> -1 | _ -> invalid_arg "BigInt signs should be +/- 1" The System.IComparable interface is defined in the .NET libraries: namespace System type IComparable = abstract CompareTo : obj -> int An unbox is necessary when implementing both IComparable and Object.Equals; this operation is relatively cheap. Recursive calls to compare subterms should use the following function:
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val compare : 'a -> 'a -> int
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Listing 8-1 defined the implementations of the overrides and interfaces immediately at the point of the type definition. However, it is also common to define the implementations of these as an extension to the type later in the same file. This lets you define a complete set of operations for the type starting with appropriate primitives and building up the set of operations until all are correctly defined. Listing 8-2 shows how to do this for the case of BigInt.
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C HAPTE R 8 MAS TE RING F#: COMMON TEC HN IQUES
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Listing 8-2. Customizing Generic Hashing and Comparison Using an Extension open Microsoft.FSharp.Math.Primitives type BigInt = { sign : int; v : BigNat } interface System.IComparable module BigIntOps = let equal x y = (x.sign = y.sign) && (x.v = y.v) || BigNat.isZero(x.v) && BigNat.isZero(y.v) let hashBigInt x = if BigNat.IsZero(x.v) then 0 else hash x.sign + hash x.v let compareBigInt x y = match x.sign,y.sign with | 1, 1 -> compare x.v y.v | -1,-1 -> compare y.v x.v | _ when BigNat.IsZero(x.v) && BigNat.IsZero(y.v) -> 0 | 1, -1 -> 1 | -1, 1 -> -1 | _ -> invalid_arg "BigInt signs should be +/- 1" // OK, let's augment the type with generic hash/compare/print behavior type BigInt with override x.GetHashCode() = BigIntOps.hashBigInt(x) override x.Equals(y:obj) = BigIntOps.equal x (unbox y) override x.ToString() = sprintf "%s%A" (if x.sign < 0 && not (BigNat.IsZero(x.v)) then "-" else "") x.v interface System.IComparable with member x.CompareTo(y:obj) = BigIntOps.compareBigInt x (unbox y) Listing 8-2 also shows how to implement the System.Object method GetHashCode, the F# technique to implement generic hashing, and the method ToString for generic printing. These follow the same pattern as generic comparison. If needed, you can implement more advanced interfaces such as Microsoft.FSharp.Core.IStructuralHash and Microsoft.FSharp.Text. StructuredFormat.IFormattable to give more control over the processing of hashing and formatting large structured terms. (See http://www.expert-fsharp.com/Topics/GenericHashing.)
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Note You should be very careful about using generic comparison and hashing on recursive data structures
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(including ones using pointers) or data you mutate. Changing the value of a field may change the value of the hash or the results of comparison! Floating-point NaN values also have surprising behavior in comparison. When uses of the operators <, >, <=, >=, =, and <> are applied to two floating-point values, the IEEE rules for NaNs apply. In other words, if either argument is a NaN, then the result is false (true for <>).
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