因为我写了我之前的答案，我制定了一个声明性属性的新定义，下面引用了它。我还将命令式编程定义为对偶属性。

这个定义比我在之前的回答中提供的定义更优越，因为它更简洁，更普遍。但它可能更难以理解，因为适用于编程和一般生活的不完备定理的含义对人类来说是很难理解的。

引用的定义解释讨论了纯函数式编程在声明式编程中所扮演的角色。

所有外来的编程类型都符合以下声明式和命令式的分类，因为下面的定义声称它们是二元的。

Declarative vs. Imperative The declarative property is weird, obtuse, and difficult to capture in a technically precise definition that remains general and not ambiguous, because it is a naive notion that we can declare the meaning (a.k.a semantics) of the program without incurring unintended side effects. There is an inherent tension between expression of meaning and avoidance of unintended effects, and this tension actually derives from the incompleteness theorems of programming and our universe. It is oversimplification, technically imprecise, and often ambiguous to define declarative as “what to do” and imperative as “how to do”. An ambiguous case is the “what” is the “how” in a program that outputs a program— a compiler. Evidently the unbounded recursion that makes a language Turing complete, is also analogously in the semantics— not only in the syntactical structure of evaluation (a.k.a. operational semantics). This is logically an example analogous to Gödel's theorem— “any complete system of axioms is also inconsistent”. Ponder the contradictory weirdness of that quote! It is also an example that demonstrates how the expression of semantics does not have a provable bound, thus we can't prove2 that a program (and analogously its semantics) halt a.k.a. the Halting theorem. The incompleteness theorems derive from the fundamental nature of our universe, which as stated in the Second Law of Thermodynamics is “the entropy (a.k.a. the # of independent possibilities) is trending to maximum forever”. The coding and design of a program is never finished— it's alive!— because it attempts to address a real world need, and the semantics of the real world are always changing and trending to more possibilities. Humans never stop discovering new things (including errors in programs ;-). To precisely and technically capture this aforementioned desired notion within this weird universe that has no edge (ponder that! there is no “outside” of our universe), requires a terse but deceptively-not-simple definition which will sound incorrect until it is explained deeply. Definition: The declarative property is where there can exist only one possible set of statements that can express each specific modular semantic. The imperative property3 is the dual, where semantics are inconsistent under composition and/or can be expressed with variations of sets of statements. This definition of declarative is distinctively local in semantic scope, meaning that it requires that a modular semantic maintain its consistent meaning regardless where and how it's instantiated and employed in global scope. Thus each declarative modular semantic should be intrinsically orthogonal to all possible others— and not an impossible (due to incompleteness theorems) global algorithm or model for witnessing consistency, which is also the point of “More Is Not Always Better” by Robert Harper, Professor of Computer Science at Carnegie Mellon University, one of the designers of Standard ML. Examples of these modular declarative semantics include category theory functors e.g. the Applicative, nominal typing, namespaces, named fields, and w.r.t. to operational level of semantics then pure functional programming. Thus well designed declarative languages can more clearly express meaning, albeit with some loss of generality in what can be expressed, yet a gain in what can be expressed with intrinsic consistency. An example of the aforementioned definition is the set of formulas in the cells of a spreadsheet program— which are not expected to give the same meaning when moved to different column and row cells, i.e. cell identifiers changed. The cell identifiers are part of and not superfluous to the intended meaning. So each spreadsheet result is unique w.r.t. to the cell identifiers in a set of formulas. The consistent modular semantic in this case is use of cell identifiers as the input and output of pure functions for cells formulas (see below). Hyper Text Markup Language a.k.a. HTML— the language for static web pages— is an example of a highly (but not perfectly3) declarative language that (at least before HTML 5) had no capability to express dynamic behavior. HTML is perhaps the easiest language to learn. For dynamic behavior, an imperative scripting language such as JavaScript was usually combined with HTML. HTML without JavaScript fits the declarative definition because each nominal type (i.e. the tags) maintains its consistent meaning under composition within the rules of the syntax. A competing definition for declarative is the commutative and idempotent properties of the semantic statements, i.e. that statements can be reordered and duplicated without changing the meaning. For example, statements assigning values to named fields can be reordered and duplicated without changed the meaning of the program, if those names are modular w.r.t. to any implied order. Names sometimes imply an order, e.g. cell identifiers include their column and row position— moving a total on spreadsheet changes its meaning. Otherwise, these properties implicitly require global consistency of semantics. It is generally impossible to design the semantics of statements so they remain consistent if randomly ordered or duplicated, because order and duplication are intrinsic to semantics. For example, the statements “Foo exists” (or construction) and “Foo does not exist” (and destruction). If one considers random inconsistency endemical of the intended semantics, then one accepts this definition as general enough for the declarative property. In essence this definition is vacuous as a generalized definition because it attempts to make consistency orthogonal to semantics, i.e. to defy the fact that the universe of semantics is dynamically unbounded and can't be captured in a global coherence paradigm. Requiring the commutative and idempotent properties for the (structural evaluation order of the) lower-level operational semantics converts operational semantics to a declarative localized modular semantic, e.g. pure functional programming (including recursion instead of imperative loops). Then the operational order of the implementation details do not impact (i.e. spread globally into) the consistency of the higher-level semantics. For example, the order of evaluation of (and theoretically also the duplication of) the spreadsheet formulas doesn't matter because the outputs are not copied to the inputs until after all outputs have been computed, i.e. analogous to pure functions. C, Java, C++, C#, PHP, and JavaScript aren't particularly declarative. Copute's syntax and Python's syntax are more declaratively coupled to intended results, i.e. consistent syntactical semantics that eliminate the extraneous so one can readily comprehend code after they've forgotten it. Copute and Haskell enforce determinism of the operational semantics and encourage “don't repeat yourself” (DRY), because they only allow the pure functional paradigm. 2 Even where we can prove the semantics of a program, e.g. with the language Coq, this is limited to the semantics that are expressed in the typing, and typing can never capture all of the semantics of a program— not even for languages that are not Turing complete, e.g. with HTML+CSS it is possible to express inconsistent combinations which thus have undefined semantics. 3 Many explanations incorrectly claim that only imperative programming has syntactically ordered statements. I clarified this confusion between imperative and functional programming. For example, the order of HTML statements does not reduce the consistency of their meaning.

编辑:我在Robert Harper的博客上发表了以下评论:

in functional programming ... the range of variation of a variable is a type Depending on how one distinguishes functional from imperative programming, your ‘assignable’ in an imperative program also may have a type placing a bound on its variability. The only non-muddled definition I currently appreciate for functional programming is a) functions as first-class objects and types, b) preference for recursion over loops, and/or c) pure functions— i.e. those functions which do not impact the desired semantics of the program when memoized (thus perfectly pure functional programming doesn't exist in a general purpose denotational semantics due to impacts of operational semantics, e.g. memory allocation). The idempotent property of a pure function means the function call on its variables can be substituted by its value, which is not generally the case for the arguments of an imperative procedure. Pure functions seem to be declarative w.r.t. to the uncomposed state transitions between the input and result types. But the composition of pure functions does not maintain any such consistency, because it is possible to model a side-effect (global state) imperative process in a pure functional programming language, e.g. Haskell's IOMonad and moreover it is entirely impossible to prevent doing such in any Turing complete pure functional programming language. As I wrote in 2012 which seems to the similar consensus of comments in your recent blog, that declarative programming is an attempt to capture the notion that the intended semantics are never opaque. Examples of opaque semantics are dependence on order, dependence on erasure of higher-level semantics at the operational semantics layer (e.g. casts are not conversions and reified generics limit higher-level semantics), and dependence on variable values which can not be checked (proved correct) by the programming language. Thus I have concluded that only non-Turing complete languages can be declarative. Thus one unambiguous and distinct attribute of a declarative language could be that its output can be proven to obey some enumerable set of generative rules. For example, for any specific HTML program (ignoring differences in the ways interpreters diverge) that is not scripted (i.e. is not Turing complete) then its output variability can be enumerable. Or more succinctly an HTML program is a pure function of its variability. Ditto a spreadsheet program is a pure function of its input variables. So it seems to me that declarative languages are the antithesis of unbounded recursion, i.e. per Gödel's second incompleteness theorem self-referential theorems can't be proven. Lesie Lamport wrote a fairytale about how Euclid might have worked around Gödel's incompleteness theorems applied to math proofs in the programming language context by to congruence between types and logic (Curry-Howard correspondence, etc).

声明性编程是通过在输入和输出之间表达一些永恒的逻辑来编程，例如，在伪代码中，下面的例子将是声明性的:

def factorial(n):
  if n < 2:
    return 1
  else:
    return factorial(n-1)

output = factorial(argvec[0])

We just define a relationship called the 'factorial' here, and defined the relationship between the output and the input as the that relationship. As should be evident here, about any structured language allows declarative programming to some extend. A central idea of declarative programming is immutable data, if you assign to a variable, you only do so once, and then never again. Other, stricter definitions entail that there may be no side-effects at all, these languages are some times called 'purely declarative'.

在命令式风格中，同样的结果将是:

a = 1
b = argvec[0]
while(b < 2):
  a * b--

output = a

在这个例子中，我们没有在输入和输出之间表达永恒的静态逻辑关系，我们手动更改内存地址，直到其中一个保存所需的结果。很明显，所有语言在某种程度上都允许声明性语义，但并非所有语言都允许命令式语义，一些“纯”声明性语言允许副作用和突变。

Declarative languages are often said to specify 'what must be done', as opposed to 'how to do it', I think that is a misnomer, declarative programs still specify how one must get from input to output, but in another way, the relationship you specify must be effectively computable (important term, look it up if you don't know it). Another approach is nondeterministic programming, that really just specifies what conditions a result much meet, before your implementation just goes to exhaust all paths on trial and error until it succeeds.

纯声明性语言包括Haskell和Pure Prolog。从一种到另一种的比例可以是:Pure Prolog, Haskell, OCaml, Scheme/Lisp, Python, Javascript, C——，Perl, PHP, c++， Pascall, C, Fortran, Assembly

我认为你的分类是不正确的。有两种相反的类型，命令式和声明式。函数式只是声明式的一个子类型。顺便说一句，维基百科也说了同样的事实。

命令式——表达式描述要执行的动作序列(关联的)

声明性——表达式是对程序行为做出贡献的声明(关联、交换、幂等、单调)

函数式表达式的值仅为效果;语义支持等式推理

命令式编程是指任何一种编程风格，其中你的程序是由描述计算机执行的操作如何发生的指令构成的。

声明式编程是指任何一种编程风格，其中你的程序是对问题或解决方案的描述，但没有显式地说明如何完成工作。

函数式编程是通过计算函数和函数的函数来编程。函数式编程(严格定义)是指通过定义无副作用的数学函数来编程，因此它是一种声明式编程，但它不是唯一的声明式编程。

逻辑编程(例如在Prolog中)是另一种形式的声明式编程。它包括通过决定一个逻辑语句是否为真(或是否可以满足它)来计算。程序通常是一系列事实和规则——即描述，而不是一系列指令。

术语重写(例如CASL)是声明式编程的另一种形式。它涉及代数项的符号变换。它完全不同于逻辑编程和函数式编程。

对于这些并没有明确客观的定义。以下是我对它们的定义:

命令式——重点是计算机应该采取什么步骤，而不是计算机将会做什么(例如C, c++， Java)。

声明性——重点是计算机应该做什么，而不是它应该如何做(例如SQL)。

函数式——声明性语言的子集，非常注重递归