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CHAPTER 15 WORKING WITH DATA
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Accumulating Using Folding Operators
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Some of the most general operators supported by most F# data structures are the fold, fold_left, and fold_right operators. These apply a function to each element of a collection and accumulate a result. For fold_left and fold_right, the function is applied in left-to-right or right-toleft order, respectively. If the name fold is used, then typically the ordering is left to right. Both functions also take an initial value for the accumulator. For example: > List.fold_left (fun acc x -> acc + x) 0 [4; 5; 6];; val it : int = 15 > Seq.fold (fun acc x -> acc + x) 0.0 [4.0; 5.0; 6.0];; val it : float = 15.0 > List.fold_right (fun x acc -> min x acc) [4; 5; 6; 3; 5] System.Int32.MaxValue;; val it : int = 3 The following are equivalent, but no explicit anonymous function values have been used: > List.fold_left (+) 0 [4; 5; 6];; val it : int = 15 > Seq.fold (+) 0.0 [4.0; 5.0; 6.0];; val it : float = 15.0 > List.fold_right min [4; 5; 6; 3; 5] System.Int32.MaxValue;; val it : int = 3 If used carefully, the various fold_right operators are pleasantly compositional, because they let you apply a selection function as part of the accumulating function: > List.fold_right (fst >> min) [(3, "three"); (5, "five")] System.Int32.MaxValue;; val it : int = 3 At the time of writing, the F# library also includes more direct accumulation functions such as Seq.sumByFloat and Seq.sumByInt. These use a fixed accumulation function (addition) with a fixed initial value (zero).
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Caution Folding operators are very powerful and can help you avoid many explicit uses of recursion or
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loops in your code. However, they are sometimes overused in functional programming and can be hard for novice users to read and understand. Take the time to document uses of these operators, or consider using them to build simpler operators that apply a particular accumulation function.
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C HA PTER 15 WO RK ING WI T H D A TA
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Expressing Some Queries Using Sequence Expressions
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Using aggregate operators to form queries is closely related to the sequence expression notation described in 3 and is used frequently in this book. For example, namesSalesOver30 defined previously can also be defined as follows: seq { for (name, age, dept) in people do if (age >= 30 && dept = "Sales") then yield name } This is simply a different notation for the same computation. For very simple queries, F# sequence expressions also support an even more compact form where if/then clauses are replaced by when, the final do is dropped from the for statement, and yield is replaced by ->: seq { for (name, age, dept) in people when (age >= 30 && dept = "Sales") -> name } There is no difference between these two sequence expressions it s just a matter of syntax. You can use sequence expressions in conjunction with the |> operator. For example: seq { for i in numbers do if i % 2 = 0 then yield (i, i*i) } |> Seq.truncate 3 |> sortBy revOrder There are pros and cons to using sequence expression syntax for some parts of queries: Sequence expressions are very good for the subset of queries expressed using iteration (for), mapping (select/yield), and filtering (if/then/when/where). They are particularly good for queries containing multiple nested for statements. Other query constructs such as ordering, truncating, grouping, and aggregating must be expressed directly using aggregate operators such as Seq.orderBy and Seq.groupBy. Some queries depend on the index position of an item within a stream. These are best expressed directly using aggregate operators such as Seq.mapi. Many queries are often part of a longer series of transformations chained by |> operators. Often the type of the data being transformed at each step varies substantially through the chain of operators. These queries are best expressed using aggregate operator chains.
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Note It is likely that in the future the F# sequence expression syntax will include support for specifying
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grouping and aggregation operations within the expression syntax. However, at the time of writing, it was necessary to explicitly use operators such as Seq.orderBy and Seq.groupBy for these operations.
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