A model of register transfer systems with applications to microcode and VLSI correctness

In this paper we describe and illustrate a simple semantic model of register transfer systems — i.e. systems built by connecting together storage devices like registers and.memories via combinational circuits like gates and arithmetic units. The goal is to develop an elegant and efficient framework in which to conduct correctness proofs. After explaining the model we illustrate our methods by presenting two case studies. In the first of these we completely specify a small general purpose computer, and then prove correct a microcoded implementation. This involves showing that the signals generated by the microprogrammed controller cause register transfers in the host which correctly fetch, decode and execute machine instructions; and also that the control unit correctly interprets and sequences microinstructions according to the microcode semantics. In the second case study we go down a level and verify nMOS implementations of devices like those used to build the computer. Starting from four primitives — gates, joins, pullups and ground — we first implement and verify not and nor elements. Using these we then specify, implement and verify a stackcell and controller taken from.Mead and Conway's book "Introduction to VLSI Systems". In both case studies the proofs are highly structured. For example, in the nMOS study the stack controller is expressed as the composition of two subsystems and a clock, and its correctness follows from the correctness of the subsystems; the correctness of these, in turn, follows from the correctness of their immediate constituents (not and nor elements). It is not necessary to flatten down to the gate level and hence proofs do not explode in size

Theory Morphisms in Church's Type Theory with Quotation and Evaluation

${\rm CTT}_{\rm qe}$ is a version of Church's type theory with global quotation and evaluation operators that is engineered to reason about the interplay of syntax and semantics and to formalize syntax-based mathematical algorithms. ${\rm CTT}_{\rm uqe}$ is a variant of ${\rm CTT}_{\rm qe}$ that admits undefined expressions, partial functions, and multiple base types of individuals. It is better suited than ${\rm CTT}_{\rm qe}$ as a logic for building networks of theories connected by theory morphisms. This paper presents the syntax and semantics of ${\rm CTT}_{\rm uqe}$, defines a notion of a theory morphism from one ${\rm CTT}_{\rm uqe}$ theory to another, and gives two simple examples that illustrate the use of theory morphisms in ${\rm CTT}_{\rm uqe}$.Comment: 17 page

Friends with benefits: implementing corecursion in foundational proof assistants

We introduce AmiCo, a tool that extends a proof assistant, Isabelle/HOL, with flexible function definitions well beyond primitive corecursion. All definitions are certified by the assistant’s inference kernel to guard against inconsistencies. A central notion is that of friends: functions that preserve the productivity of their arguments and that are allowed in corecursive call contexts. As new friends are registered, corecursion benefits by becoming more expressive. We describe this process and its implementation, from the user’s specification to the synthesis of a higher-order definition to the registration of a friend. We show some substantial case studies where our approach makes a difference

Collecting Psycholinguistic Response Time Data Using Amazon Mechanical Turk

Researchers in linguistics and related fields have recently begun exploiting online crowd-sourcing tools, like Amazon Mechanical Turk (AMT), to gather behavioral data. While this method has been successfully validated for various offline measures--grammaticality judgment or other forced-choice tasks--its use for mainstream psycholinguistic research remains limited. This is because psycholinguistic effects are often dependent on relatively small differences in response times, and there remains some doubt as to whether precise timing measurements can be gathered over the web. Here we show that three classic psycholinguistic effects can in fact be replicated using AMT in combination with open-source software for gathering response times client-side. Specifically, we find reliable effects of subject definiteness, filler-gap dependency processing, and agreement attraction in self-paced reading tasks using approximately the same numbers of participants and/or trials as similar laboratory studies. Our results suggest that psycholinguists can and should be taking advantage of AMT and similar online crowd-sourcing marketplaces as a fast, low-resource alternative to traditional laboratory research

Search for long-lived, massive particles in events with a displaced vertex and a muon with large impact parameter in pp collisions at root s=13 TeV with the ATLAS detector

A search for long-lived particles decaying into hadrons and at least one muon is presented. The analysis selects events that pass a muon or missing-transverse-momentum trigger and contain a displaced muon track and a displaced vertex. The analyzed dataset of proton-proton collisions at √ s = 13 TeV was collected with the ATLAS detector and corresponds to 136 fb − 1. The search employs dedicated reconstruction techniques that significantly increase the sensitivity to long-lived particle decays that occur in the ATLAS inner detector. Background estimates for Standard Model processes and instrumental effects are extracted from data. The observed event yields are compatible with those expected from background processes. The results are presented as limits at 95% confidence level on model-independent cross sections for processes beyond the Standard Model, and interpreted as exclusion limits in scenarios with pair production of long-lived top squarks that decay via a small R -parity-violating coupling into a quark and a muon. Top squarks with masses up to 1.7 TeV are excluded for a lifetime of 0.1 ns, and masses below 1.3 TeV are excluded for lifetimes between 0.01 ns and 30 ns

Abstraction Mechanisms for Hardware Verification

ion Mechanisms for Hardware Verification Thomas F. Melham University of Cambridge Computer Laboratory New Museums Site, Pembroke Street Cambridge, CB2 3QG, England Abstract: It is argued that techniques for proving the correctness of hardware designs must use abstraction mechanisms for relating formal descriptions at different levels of detail. Four such abstraction mechanisms and their formalization in higher order logic are discussed. Introduction Recent advances in microelectronics have given designers of digital hardware the potential to build electronic devices of unprecedented size and complexity. With increasing size and complexity, however, it becomes increasingly difficult to ensure that such systems will not malfunction because of design errors. This problem has prompted some researchers to look for a firm theoretical basis for correct design of hardware systems. Mathematical methods have been developed to model the functional behaviour of electronic devices and to verify,..