<theory> A partial execution of a program which gains information about its semantics (e.g. control structure, flow of information) without performing all the calculations. Abstract interpretation is typically used by compilers to analyse programs in order to decide whether certain optimisations or transformations are applicable. The objects manipulated by the program (typically values and functions) are represented by points in some domain. Each abstract domain point represents some set of real ("concrete") values. For example, we may take the abstract points "+", "0" and "-" to represent positive, zero and negative numbers and then define an abstract version of the multiplication operator, *#, which operates on abstract values: *# | + 0 - ---|------ + | + 0 - 0 | 0 0 0 - | - 0 + An interpretation is "safe" if the result of the abstract operation is a safe approximation to the abstraction of the concrete result. The meaning of "a safe approximation" depends on how we are using the results of the analysis. If, in our example, we assume that smaller values are safer then the "safety condition" for our interpretation (#) is a# *# b# <= (a * b)# where a# is the abstract version of a etc. In general an interpretation is characterised by the domains used to represent the basic types and the abstract values it assigns to constants (where the constants of a language include primitive functions such as *). The interpretation of constructed types (such as user defined functions, sum types and product types) and expressions can be derived systematically from these basic domains and values. A common use of abstract interpretation is {strictness analysis}. See also standard interpretation. (1994-11-08)

In computer science, abstract interpretation is a theory of sound approximation of the semantics of computer programs, based on monotonic functions over ordered sets, especially lattices. It can be viewed as a partial execution of a computer program which gains information about its semantics (e.

An abstract machine is a computer science theoretical model that allows for a detailed and precise analysis of how a computer system functions. It is analogous to a mathematical function in that it receives inputs and produces outputs based on predefined rules. Abstract machines vary from literal machines in that they are expected to perform correctly and independently of hardware. Abstract machines are “machines” because they allow step-by-step execution of programmes; they are “abstract” because they ignore many aspects of actual (hardware) machines. A typical abstract machine consists of a definition in terms of input, output, and the set of allowable operations used to turn the former into the latter. They can be used for purely theoretical reasons as well as models for real-world computer systems. In the theory of computation, abstract machines are often used in thought experiments regarding computability or to analyse the complexity of algorithms. This use of abstract machines is connected to th