2006
DOI: 10.1007/11768173_14
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Modal Design Algebra

Abstract: We give an algebraic model of the designs of UTP based on a variant of modal semirings, hence generalising the original relational model. This is intended to exhibit more clearly the algebraic principles behind UTP and to provide deeper insight into the general properties of designs, the program and specification operators, and refinement. Moreover, we set up a formal connection with general and total correctness of programs as discussed by a number of authors. Finally we show that the designs form a left semi… Show more

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Cited by 13 publications
(25 citation statements)
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“…Since we are going to import some results from the third framework, we will show some connections between variants 1 and 3 (we do not need variant 2 in the present paper, but the treatment for it would be symmetrical). We only give a summary of the necessary theory; a more thorough treatment can be found in [4].…”
Section: The Algebra Of Prescriptionsmentioning
confidence: 99%
See 1 more Smart Citation
“…Since we are going to import some results from the third framework, we will show some connections between variants 1 and 3 (we do not need variant 2 in the present paper, but the treatment for it would be symmetrical). We only give a summary of the necessary theory; a more thorough treatment can be found in [4].…”
Section: The Algebra Of Prescriptionsmentioning
confidence: 99%
“…The identity in algebraic structure is used in the companion paper [4] to give a uniform treatment of normal designs t a and normal prescriptions t a as pairs (a, t) consisting of a transition part a and a termination condition part t.…”
Section: The Algebra Of Prescriptionsmentioning
confidence: 99%
“…In [9] prescriptions were introduced as the general-correctness counterparts of Hoare and He's total-correctness designs, and their properties have since been further explored in [6] and [13]. Let v be the list of state variables of the state space and ok be an additional auxiliary boolean variable with the same interpretation as that already described in Section 3 for designs.…”
Section: A General-correctness Program Calculusmentioning
confidence: 99%
“…The equivalence classes correspond to the designs of the Unifying Theories of Programming of [9] and hence represent a total correctness view. It has been shown in [7] (in the setting of condition semirings that is isomorphic to that of test semirings) that the set of these classes forms again a left semiring and can be made into a weak Kleene and omega algebra by using exactly the same definitions as above (as class representatives). Now top-left-strictness holds, since chaos ≡ loop and loop is a left zero by the definition of command composition.…”
Section: The Demonic Refinement Algebra Of Commandsmentioning
confidence: 99%
“…So these model programs where no miraculous termination can occur; they correspond to the feasible designs of [9]. In [7] it is shown that the set F(S) classes of feasible commands can isomorphically be represented by simple semiring elements. The mediating functions are…”
Section: The Demonic Refinement Algebra Of Commandsmentioning
confidence: 99%