(TCO), converting tail recursions into iterations that do not consume Languages can then perform tail-call optimization Sion must come at the tail, that is, at an expression that is a return A tail-recursive function is still defined recursively, but the recur.
In Clojure, you shouldĪlmost always avoid stack-consuming recursion as shown in stack-įunctional programs can solve the stack-usage problem with tail recur. To n, which quickly exhausts the JVM stack and causes the StackOver-Ĭlojure function calls are designated as stack-consuming because theyĪllocate stack frames that use up stack space. The stack-consuming-fibo creates a number of stack frames proportional For more on how the JVM manages its stack, see “Runtime Data Areas” at At the JVM level, these calls are translated into method calls, each of which allocates a data structure called a stack frame. Good so far, but there is a problem calculating larger Fibonacci numbers such as F1000000 :īecause of the recursion, each call to stack-consuming-fibo for n > 1 begets two more calls to stack-consuming-fibo. Test that stack-consuming-fibo works correctly for small values of n: The implementation is recursive because stack-consuming-fibo calls itself on lines 6 and 7. Lines 4 and 5 define the basis, and line 6 defines the induction. The following Clojure function will return the nth Fibonacci number:Ħ :else (+ (stack-consuming-fibo (- n 1)) Let’s begin by implementing the Fibonaccis using a simple recursion. Using this definition, the first ten Fibonacci numbers are as follows: Induction: For n > 1, F N equals F N −1+ F N −2.Basis: F 0, the zeroth Fibonacci number, is zero.4 The Fibonaccis have a very simple recursive definition: The Fibonacci numbers have many interesting properties, and they crop up again and again in algorithms, data structures, and even biology. Of Pisa (c.1170 – c.1250), the Fibonacci numbers were actually known to Indian mathematicians as far back as 200 BC. Named for the Italian mathematician Leonardo (Fibonacci) We will explore all of these approaches by applying them to the Fibonacci numbers. In Clojure, being lazy is often the right approach.
Implementing a recursive definition poorly can lead to code that performs terribly, consumes all available stack and fails, consumes all available heap and fails, or does all of these.
A recursive definition consists of two parts:
5.2 How to Be Lazyįunctional programs make great use of recursive definitions. Now, let’s get started writing functional code. As you become comfortable with FP, you will find reasons to break them. Like most rules, the six rules are guidelines, not absolutes. If you are new to FP, you can translate these two rules to this: “Ignore this chapter and just use the techniques in Chapter 4, Unifying Data with Sequences, on page 111 until you hit a wall.” Rules 5 and 6 are particularly important. Divide even simple-seeming problems into smaller pieces, and you will often find solutions in the sequence library that lead to more general, reusable code. You can often write code without using recur or the lazy APIs at all.Ħ. Be careful not to realize more of a lazy sequence than you need.ĥ. Use Atoms for Uncoordinated, Synchronous UpdatesĤ.Adding Ant Projects and Tasks to Lancet.Creating and Compiling Java Classes in Clojure.