Theories
The semantic foundation of the UTP is the first-order predicate calculus, augmented with fixed point constructs from second-order logic. Following the tradition of Eric Hehner, programs are predicates in the UTP, and there is no distinction between programs and specifications at the semantic level. In the words of Hoare:
A computer program is identified with the strongest predicate describing every relevant observation that can be made of the behaviour of a computer executing that program.
In UTP parlance, a theory is a model of a particular programming paradigm. A UTP theory is composed of three ingredients:
- an alphabet, which is a set of variable names denoting the attributes of the paradigm that can be observed by an external entity;
- a signature, which is the set of programming language constructs intrinsic to the paradigm; and
- a collection of healthiness conditions, which define the space of programs that fit within the paradigm. These healthiness conditions are typically expressed as monotonic idempotent predicate transformers.
Program refinement is an important concept in the UTP. A program is refined by if and only if every observation that can be made of is also an observation of . The definition of refinement is common across UTP theories:
where denotes the universal closure of all variables in the alphabet.
Read more about this topic: Unifying Theories Of Programming
Famous quotes containing the word theories:
“The egoism which enters into our theories does not affect their sincerity; rather, the more our egoism is satisfied, the more robust is our belief.”
—George Eliot [Mary Ann (or Marian)
“Philosophers of science constantly discuss theories and representation of reality, but say almost nothing about experiment, technology, or the use of knowledge to alter the world. This is odd, because ‘experimental method’ used to be just another name for scientific method.... I hope [to] initiate a Back-to-Bacon movement, in which we attend more seriously to experimental science. Experimentation has a life of its own.”
—Ian Hacking (b. 1936)
“It takes twenty or so years before a mother can know with any certainty how effective her theories have been—and even then there are surprises. The daily newspapers raise the most frightening questions of all for a mother of sons: Could my once sweet babes ever become violent men? Are my sons really who I think they are?”
—Mary Kay Blakely (20th century)