Making Temporal Logic Calculational: A Tool for Unification and Discovery

Boute, Raymond

doi:10.1007/978-3-642-05089-3_25

Cited by 1 publication

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References 25 publications

(36 reference statements)

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“…In fact, this part of formula (3) expresses function compatibility, written f ∩ = g ("equality on the domain intersection"). Note: ∩ = is reflexive; therefore this symmetric symbol replaces the older compatibility operator © [23][24][25]28] at the suggestion of a reviewer.…”

Section: Functionsmentioning

confidence: 99%

“…The first batch are formulas formerly derived in [28] by getting rid of the variable β along the way, but now derived by pointfree calculation from the start.…”

Section: Illustration: Deriving Pointfree Theorems In Ftcmentioning

confidence: 99%

“…In particular, one reviewer prompted the author to rewrite several derivations that were still partially pointwise in [28] in fully pointfree form and also provided extensive worked-out examples of alternative formulations in a categorical style as represented in the Algebra of Programming [1, 13,69].…”

Section: Acknowledgementsmentioning

confidence: 99%

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Pointfree expression and calculation: from quantification to temporal logic

Boute

2010

Form Methods Syst Des

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Pointfree formulation means suppressing domain variables to focus on higherlevel objects (functions, relations). Advantages are algebraic-style calculation and abstraction as formal logics pursue by axiomatization. Various specific uses are considered, starting with quantification in the wider sense (∀, ∃, , etc.). Pointfree style is achieved by suitable functionals that prove superior to pointwise conventions such as the Eindhoven notation. Pointwise calculations from the literature are reworked in pointfree form. The second use considered is in describing systems, with generic functionals capturing signal flow patterns. An illustration is the mathematics behind a neat magician's trick, whose implementation allows comparing the pointfree style in Funmath, LabVIEW, TLA + , Haskell and Maple. The third use is making temporal logic calculational, with a simple generic Functional Temporal Calculus (FTC) for unification. Specific temporal logics are then captured via endosemantic functions. The example is TLA + . Calculation is illustrated by deriving various theorems, most related to liveness issues, and discovering results by calculation rather than proving them afterwards. To conclude, various ramifications, style and abstraction issues are discussed, in relation to engineering mathematics in general and to categorical formulations.

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Section: Functionsmentioning

confidence: 99%

“…The first batch are formulas formerly derived in [28] by getting rid of the variable β along the way, but now derived by pointfree calculation from the start.…”

Section: Illustration: Deriving Pointfree Theorems In Ftcmentioning

confidence: 99%