Probabilistic Semantics for RoboChart A Weakest Completion Approach

We outline a probabilistic denotational semantics for the RoboChart language, a diagrammatic, domain-specific notation for de- scribing robotic controllers with their hardware platforms and operating environments. We do this using a powerful (but perhaps not so well known) semantic technique: He, Morgan, and McIver’s weakest completion semantics, which is based on Hoare and He’s Unifying Theories of Programming. In this approach, we do the following: (1) start with the standard semantics for a nondeterministic programming language; (2) propose a new probabilistic semantic domain; (3) propose a forgetful function from the probabilistic semantic domain to the standard semantic domain; (4) use the converse of the forgetful function to embed the standard semantic domain in the probabilistic semantic domain; (5) demonstrate that this embedding preserves program structure; (6) define the probabilistic choice operator. Weakest completion semantics guides the semantic definition of new languages by building on existing semantics and, in this case, tackling a notoriously thorny issue: the relationship between demonic and probabilistic choice. Consistency ensures that programming intuitions, development techniques, and proof methods can be carried over from the standard language to the probabilistic one. We largely follow He et al., our contribution being an explication of the technique with meticulous proofs suitable for mechanisation in Isabelle/UTP

Nondeterministic Relational Semantics of a while Program

A relational semantics is a mapping of programs to relations. We consider that the input-output semantics of a program is given by a relation on its set of states; in a nondeterministic context, this relation is calculated by considering the worst behavior of the program (demonic relational semantics). In this paper, we concentrate on while loops. Calculating the relational abstraction (semantics) of a loop is difficult, but showing the correctness of any candidate abstraction is much easier. For functional programs, Mills has described a checking method known as the while statement verification rule. A programming theorem for iterative constructs is proposed, proved, demonstrated and applied for an example. This theorem can be considered as a generalization of the while statement verification to nondeterministic loops.&nbsp

Demonic fixed points

We deal with a relational model for the demonic semantics of programs. The demonic semantics of a while loop is given as a fixed point of a function involving the demonic operators. This motivates us to investigate the fixed points of these functions. We give the expression of the greatest fixed point with respect to the demonic ordering (demonic inclusion) of the semantic function. We prove that this greatest fixed coincides with the least fixed point with respect to the usual ordering (angelic inclusion) of the same function. This is followed by an example of application

Heuristics for constructing while loops

AbstractWe discuss the stepwise construction of iterative programs from specifications, represented by relations. We make an effort to isolate, in the construction of an iterative program, those decisions that are dictated by correctness preservation concerns, from decisions that the programmer is free to make at will

Cell migration within confined sandwich-like nanoenvironments

Aim: We introduced sandwich-like cultures to provide cell migration studies with 4 representative nano-bio-environments where both ventral and dorsal cell receptors are activated. Methods: We have investigated different nano-environmental conditions by changing the protein coating (fibronectin, vitronectin) and/or materials (using polymers that adsorb proteins in qualitatively different conformations) of this sandwich system to show their specific role in cell migration. Results: Here we show that cell migration within sandwich cultures greatly differs from 2D cultures and shares some similarities with migration within 3D environments. Beyond differences in cell morphology and migration, dorsal stimulation promotes cell remodeling of the ECM over simple ventral 12 receptor activation in traditional 2D cultures.</p