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Improve Your Breathing For More Power
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  Improve Your Breathing For More PowerThe fundamental problem addressed by a type theory is to ensure that programs have meaning. The fundamental problem caused by a type theory is that meaningful programs may not have meanings ascribed to them. The quest for richer type systems results from this tension.ssigning a data type, termed typing, gives meaning to a sequence of bits such as a value in memory or some object such as a variable. The hardware of a general purpose computer is unable to discriminate between for example a memory address and an instruction code, or between a character, an integer, or a floating-point number, because it makes no intrinsic distinction between any of the possible values that a sequence of bits might mean./note // Associating a sequence of bits with a type 
 conveys that meaning to the programmable hardware to form a symbolic system composed of that hardware and some program.A program associates each value with at least one specific type, but it also can occur that one value is associated with many subtypes. Other entities, such as objects, modules, communication channels, dependencies can become associated with a type. Even a type can become associated with a type. An implementation of a type system could in theory associate identifications called data type (a type of a value), class (a type of an object), and kind (a type of a type, or metatype). These are the abstractions that typing can go through, on a hierarchy of levels contained in a system.When a programming language evolves a more elaborate type system, it gains a more finely grain
 ed rule set than basic type checking, but this comes at a price when the type inferences (and other properties) become undecidable, and when more attention must be paid by the programmer to annotate code or to consider computer-related operations and functioning. It is challenging to find a sufficiently expressive type system that satisfies all programming practices in a type safe manner.The more type restrictions that are imposed by the compiler, the more strongly typed a programming language is. Strongly typed languages often require the programmer to make explicit conversions in contexts where an implicit conversion would cause no harm. Pascal's type system has been described as "too strong" because, for example, the size of an array or string is part of its type, making some programm
 ing tasks difficult.////// Haskell is also strongly typed but its types are automatically inferred so that explicit conversions are often (but not always) unnecessary.

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