Elements of Programming

Only by reading the code, proving the lemmas, and doing the exercises can readers gain understanding of the material.

##Chapter 1 Foundations == Structure == Chapter 1 作为全书的领头羊，具有画龙点睛之功效。 也是我人为这本书，值得一度的根本原因。 本章内容是其他内容的最高抽象，也就是其余内容都是作为第一章的延伸。你可以理解为金字塔的塔尖。 Categories of ideas and it's incarnation. == Understand == Catefories of ideas =========== Entity: 物质可灭，精神永存 抽象存在：不可变，永恒的。 具体存在：会生，会灭。 attribute：具体与抽象之间对应，或者说共享、共同存在的内容。只有通过attribute抽象的存在才能以具体存在，特定的等价联系。来自具体存在。 Identity：指存在的根本内容，作者没有给出具体定义。 Species:类别 An abstract species describes common properties of essentially equivalent abstract entities.抽象属性集合 A concrete species describes the set of attributes of essentially equivalent concrete entities. 具体属性集合 Genus:类属 An abstract genus describes different abstract species that are similar in some respect. A concrete genus describes different concrete species similar in some respect. entity属于一个类别，类别提供了entity，产生，存在的规则。 entity可以属于多个类属，每个类属描述一些属性。 Objects and values属于entities，types属于species， concepts是Genus。 计算机处理的都是抽象内容。 Incarnation ======= Function: is a rule that associates one or more abstract entities, called arguments, from corresponding species with an abstract entity, called the result, from another species.函数是抽象存在到抽象存在的转化的规则，就是小学学到的函数定义。 Values: A datum is a finite sequence of 0s and 1s.计算机数据就是0 1 的序列。 A datum corresponding to a particular entity is called a representation of the entity; the entity is called the interpretation of the datum. 数据是作为entity，如object，value的（原始）表示，长什么样，一个鼻子俩个眼。 而entity是作为数据的一种解释，好看呀还是俊俏。 We refer to a datum together with its interpretation as a value. 那么value包括两方面：entity和datum。 我们可以形成这样非严格的逻辑关系： datum -> entity(value, object) ->species->genura 101 -> 5 -> int -> number 这有点 类似高中课本上那条咬住自己尾巴的snake。 A value type is a correspondence between a species and a set of datums. 那么vlaue type是datum和species联系的纽带。表示这种关系的一个实例！所以说value type本质上是代表一个二元关系，而不是某个实体。 这很重要，可以说是颠覆式的。二元关系，在算术中是大小，几何中是相似，集合中是包含。而value type 这种二元关系涉及到的两个主题就是value 和entity。 A value type is properly partial if its values represent a proper subset of the abstract entities in the corresponding species; otherwise it is total. For example, the type int is properly partial, while the type bool is total. 很自然，我们就会对关系加以分类。上面这段话理解很费劲。我理解成boundary！ 整型值无法被完全表述entities，只能partial。可以把boudary理解为genus。 A value type is uniquely represented if and only if at most one value corresponds to each abstract entity. Two values of a value type are equal if and only if they represent the same abstract entity. They are representationally equal if and only if their datums are identical sequences of 0s and 1s.相同值表述不一定相同，如负数的补码和普通形式。 If a value type is uniquely represented, equality implies representational equality.在同一种表述格式的前提下，当然值也相同。 Object An object is a representation of a concrete entity as a value in memory. object 对应具体存在在内存的值形态。 An object type is a pattern for storing and modifying values in memory. Values and objects play complementary roles. Describing the states of objects in terms of values allows us to abstract from the particular implementations of the objects when discussing equality. Functional programming deals with values; imperative programming deals with objects. Since values are unchanging, they can represent abstract entities. Sequences of values can also represent sequences of snapshots of concrete entities. Objects hold values representing entities. Since objects are changeable, they can represent concrete entities by taking on a new value to represent a change in the entity. Objects can also represent abstract entities: staying constant or taking on different approximations to the abstract. 讨论抽象具体entities与其表述方式value object的关系。 We use objects in the computer for the following three reasons. 1. Objects model changeable concrete entities, such as employee records in a payroll application. 2. Objects provide a powerful way to implement functions on values, such as a procedure implementing the square root of a floating-point number using an iterative algorithm.迭代过程改变object的值， 理解对吗？ 3. Computers with memory constitute the only available realization of a universal computational device 2、3 理解不能。 Some properties of value types carry through to object types. Since concrete entities have identities, objects representing them need a corresponding notion of identity. Procedures A procedure is a sequence of instructions that modifies the state of some objects; it may also construct or destroy objects. ##Chapter 2. Transformations and Their Orbits