| 词汇 | example_english_recursion |
| 释义 | Examples of recursionThese examples are from corpora and from sources on the web. Any opinions in the examples do not represent the opinion of the Cambridge Dictionary editors or of Cambridge University Press or its licensors. Here, applying simple recursions, h1t u ! The recursions describing the time path of bt are the same for both models, except for the value of the positive definite matrix modifying the forecast error. The semantics of the language is based on a translation, and it exploits abstract data types rather than polymorphic types and recursion. The structural aspect of recursion is almost ignored and certainly never presented as the bridge to object-oriented programming. The programmer sees only recursion equations, but the machine performs normal order graph reduction using those equations as rules. The recursion equations above can be regarded as defining functions over type expressions. Three aspects of the region calculus are highlighted as essential features: region polymorphism, region polymorphic recursion, and effect polymorphism. In this way, semantically, the linear recursion can be reduced to recursion with ground result type and substitution of parameters. As another illustration of action constructs, we consider how countable nondeterminism can be approximated by means of binary choice and recursion. In general, if we allow functional result type in a safe recursion then we can define exponentiation. However, implementations of lazy functional languages generally express recursion by a back-pointer in the function graph. I am not entirely convinced, though, that the objective to eliminate recursion is fully successful. Section 8 discusses the semantics of recursion, and section 9 discusses refinement laws and presents a small example. Since we want to be able to define recursive expressions of any type, there is no specific type construct associated with recursion. Though they couldn't be listed individually, they could result from a constructional idiom containing variables that permit recursion. The two interpretations are defined by mutual recursion. Remarkably, the recursion operators in the language have continuous interpretations in the denotational model. Also, to interpret recursion we will use domains in place of sets in the target category. The latter follows from domain-theoretic generalizations of two theorems from elementary recursion theory. The second is that structural recursion has too much expressive power because it can express queries that require exponential time and space. The functional programs we consider in this article are simply typed -terms extended by pairs, projections, if-then-else, and least fixed point recursion. However, at this point the process may continue to a next recursion or iteration cycle depending on the results obtained. In imperative languages, iteration can be introduced first as a simpler, more specialised form of repetition, and recursion can be delayed until trees are covered. The paper only presented two example constructions that illustrate recursion by bidirectional optimization. Not enough programmers are familiar with functional languages, and some experienced programmers find it hard to learn concepts such as recursion and polymorphism. The parsers for infix and prefix operators embody the grammar transformations required to remove left-recursion. The latter permits recursion on any constructor-guarded subterm (cf. the previous section) of the argument it addresses. To see that (ii) is not a reasonable choice, let rec be a candidate for a recursion operator. When present, the optional guard expression imposes additional constraints on the matching of the input subform prior to any structural recursion specified by the subpattern. In this paper, we derive the recursion equations for one- and two-locus identity probabilities in an infinite island model. Contrast this with s i cp's treatment of recursion. The recipes also introduce a new distinction into program design: structural versus generative recursion. Our language allows recursion both for dynamic and for static functions. Structural recursion thus delivers more functions than primitive recursion (in its original first-order sense). Therefore, higher levels of recursion are rarely used. Technically, since mov eone is free in the body of the procedure, we cannot use the restricted rule for recursion to type it. Intuitively, this can be viewed as a kind of backpatching semantics for recursion at the level of types. When using a fold, the behavior for each constructor is specified, and the recursion is done by the fold operator. They also establish variable bindings that may be used in output expressions to refer to input subforms or the results of structural recursion. Before starting the loop, we push a prompt on the stack to mark the point at which the recursion will eventually return. Once (58) is given, we apply the proof rules for abstraction and recursion to obtain the required assertion (57). In section 4 we define a notion of recursion operator and give two examples. We may also consider adding recursion to this system. Then the program passes the test if and only if it is defined by recursion on the left argument first. However, this is not the case, since the direct implementation of addition makes no use of dependent types, proof arguments or well-founded recursion. However, they do not define this recursion operator in their paper, only an iteration operator. We memoize the result only with respect to the pair of states; we ignore the depth of recursion. A -graph is treated as a system of recursion equations involving -terms, and rewriting is described as a sequence of equational transformations. The main difference between 0 and the g -calculus is the restriction of the list of constraints to a list of recursion equations. We present a type-based flow analysis for simply typed lambda calculus with booleans, data-structures and recursion. The authors restore it by controlling the operations on the recursion equations. The type-theoretic version of the algorithm is then defined by structural recursion on the proof that the input values satisfy this predicate. We generalise the bisimulation proof method by relaxing the bare recursion in (). The simplest restriction that will ensure this is to require that nesting of subnetworks (and hence recursion) is limited to some small depth. Instead, such results about recursion can be proved, rather primitively, by the finite restriction characterisation. Together with pairs, this gives tools that are as close as possible to primitive recursion. In particular, we have a look at recursion, prefix iteration, projection, renamings, parallel composition and silent step. In addition, the language supports a restriction operator and includes (unguarded) recursion. The fold operator is not the only useful recursion operator. Technically, the standard definition of primitive recursion requires that the argument y is a finite sequence of arguments. Dealing with this complication would be truly difficult using a single recursion equation. Red rats eater exposes recursion in children's word formation. We now apply the inductive step using recursion. While it is difficult to give an explicit formula for the recursion, the coefficients are easily determined via symbolic computation. In the early stochastic stages of increase, the exact recursion (8) is multiplied by a factor (1k)#. The examples in (8a, b) also demonstrate more complex utterances which may involve recursion. The only complication, as shown in the example, is that default values for recursion have to be replaced by explicit initialisation of variables. The depth of a recursion may be interpreted as either time or space (hardware complexity). Interpreting the depth of recursion as time allows the computation to occupy a variable number of clock cycles on a fixed amount of hardware. However, some very typical cases are caught this way, for instance the 'counter problem' where some counter is maintained in a recursion. Repeatedly halving that sequence at successive levels of recursion leads to shorter and shorter sequences at deeper nodes in the tree. Using the weak form of extensionality we establish that recursion operators compute the least fixed point (with respect to operational approximation) of functional. The library function foldr captures a common pattern of recursion over lists. To describe this multiset we employ recursion equations involving finite multisets, multiset union, addition and multiplication lifted to multisets. The meaning of higher-order recursion equations is given by the usual least-fixpoints semantics. As in our approach, polymorphic recursion on abstracted region variables plays a critical role. Thus, the construction can be done without recursion. Although our system is just a prototype, it is already quite useful in its limited domain of lists and primitive recursion. In the present setting, we need to extend this notion to patterns with choices, as-patterns, and recursion. We avoid having to introduce and analyze a type theory with recursors but consider structural recursion as a primitive principle. Explicit recursion can be added either through explicit fixed point operators or some other syntax (for instance, a letrec operator). We extended our results to some cases involving negation and recursion. The language also supports parametrised procedures and recursion. Also, for some predicates, there are two sources of recursion, requiring three cases of the predicate. The (letrec) rule is similar to (abs) except that it must allow for mutual recursion. The number of recursions is referred to as the number of "poles". The bound on the number of recursions is set on the initial call and remains static throughout the computation for that call. Also, recursions were replaced with loops wherever possible. Such structural recursions are worth investigating, but that is the subject for another paper. The following recursions come from the structure of pruning the infinite tree. The recursions describing the agents' estimators can now be reported. The exact forward and backward lengths of similar segments of arbitrary length can be determined from these recursions. In contrast, our own approach will obtain direct algebraic recursions for the quantile functions themselves, which are readily adapted for computation. When a specification contains many explicit recursions, it is possible to carry out a preliminary transformation phase, by folding the recursions with higher-order functions to hide the recursions. Analysis of such a model with decreasing variance has proven difficult because the form of the resulting recursions is not addressed by the stochastic approximation literature. The first sound example is with two recursions, the second with three recursions and the third with all five, illustrating the way the structure evolves over time. These examples are from corpora and from sources on the web. Any opinions in the examples do not represent the opinion of the Cambridge Dictionary editors or of Cambridge University Press or its licensors. |
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