Investigations on a Pedagogical Calculus of Constructions

In the last few years appeared pedagogical propositional natural deduction systems. In these systems, one must satisfy the pedagogical constraint: the user must give an example of any introduced notion. First we expose the reasons of such a constraint and properties of these "pedagogical" calculi: the absence of negation at logical side, and the "usefulness" feature of terms at computational side (through the Curry-Howard correspondence). Then we construct a simple pedagogical restriction of the calculus of constructions (CC) called CCr. We establish logical limitations of this system, and compare its computational expressiveness to Godel system T. Finally, guided by the logical limitations of CCr, we propose a formal and general definition of what a pedagogical calculus of constructions should be.Comment: 18 page

Localized approach to galvanic coupling in an aluminum–magnesium system

The corrosion behavior of a pure aluminum/pure magnesium couple in a weakly conductive sodium sulfate solution was investigated. Potential and current distributions on the surface of the model couple at the beginning of immersion were obtained by solving the Laplace equation using a finite element method algorithm. Magnesium acted as the anode of the system while oxygen and water were reduced on aluminum. Calculations predicted a large current peak at the Al/Mg interface related to a local increase in both Mg dissolution and oxygen and water reduction on aluminum, leading to a local pH increase. Optical and scanning electron microscope observations confirmed the strong dissolution of magnesium concomitantly with depassivation of aluminum at the Al/Mg interface. Local electrochemical impedance spectroscopy showed the detrimental effects of the galvanic coupling both on aluminum and magnesium

Simulating the galvanic coupling between S-Al2CuMg phase particles and the matrix of 2024 aerospace aluminium alloy

Study of the corrosion behaviour of a magnetron sputtered Al–Cu/Al–Cu–Mg model alloy couple in sulphate solutions has been undertaken to gain insight into the galvanic coupling between the matrix and SAl2CuMg particles in the 2024 aluminium alloy (AA2024). Polarisation curves and local electrochemical impedance spectroscopy measurements (LEIS) were performed on the individual alloys and on the model alloy couple. SEM enabled correlation of electrochemical phenomena to the observed damage. The corrosion behaviour of the sputtered alloys was shown to be representative of the AA2024, with the Al–Cu–Mg alloy part undergoing localised corrosion and the Al–Cu alloy part remaining passive