Dependent types and formal synthesis

The relative advantages offered by the use of dependent types (rather than polymorphic ones) in a higher-order logic used for reasoning about digital systems are explored. Dependent types and subtypes are shown to provide an effective means of expressing the bounded, parametrized types typically encountered in this field. Heuristic methods can be used to minimize problems arising from the loss of decidable type-checking. A second topic discussed is formal synthesis, an approach to design in which the activities of behavioural synthesis and of formal verification are combined. The starting point is a behavioural specification, the end result is a specification of an implementation together with a proof of its correctness.

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Automatic Formal Synthesis of Hardware from Higher Order Logic

Electronic Notes in Theoretical Computer Science ◽

10.1016/j.entcs.2005.10.003 ◽

2006 ◽

Vol 145 ◽

pp. 27-43 ◽

Cited By ~ 8

Author(s):

Mike Gordon ◽

Juliano Iyoda ◽

Scott Owens ◽

Konrad Slind

Keyword(s):

Higher Order ◽

Order Logic ◽

Higher Order Logic ◽

Formal Synthesis

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Formal verification of state-machines using higher-order logic

Proceedings 1989 IEEE International Conference on Computer Design: VLSI in Computers and Processors ◽

10.1109/iccd.1989.63356 ◽

2003 ◽

Cited By ~ 5

Author(s):

P.N. Loewenstein

Keyword(s):

Formal Verification ◽

Higher Order ◽

Order Logic ◽

State Machines ◽

Higher Order Logic

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Formal verification of Matrix based MATLAB models using interactive theorem proving

PeerJ Computer Science ◽

10.7717/peerj-cs.440 ◽

2021 ◽

Vol 7 ◽

pp. e440

Author(s):

Ayesha Gauhar ◽

Adnan Rashid ◽

Osman Hasan ◽

João Bispo ◽

João M.P. Cardoso

Keyword(s):

Formal Verification ◽

Finite Impulse Response ◽

Formal Analysis ◽

Digital Signal ◽

Interactive Theorem Proving ◽

Higher Order ◽

Order Logic ◽

Theorem Prover ◽

Formal Models ◽

Higher Order Logic

MATLAB is a software based analysis environment that supports a high-level programing language and is widely used to model and analyze systems in various domains of engineering and sciences. Traditionally, the analysis of MATLAB models is done using simulation and debugging/testing frameworks. These methods provide limited coverage due to their inherent incompleteness. Formal verification can overcome these limitations, but developing the formal models of the underlying MATLAB models is a very challenging and time-consuming task, especially in the case of higher-order-logic models. To facilitate this process, we present a library of higher-order-logic functions corresponding to the commonly used matrix functions of MATLAB as well as a translator that allows automatic conversion of MATLAB models to higher-order logic. The formal models can then be formally verified in an interactive theorem prover. For illustrating the usefulness of the proposed library and approach, we present the formal analysis of a Finite Impulse Response (FIR) filter, which is quite commonly used in digital signal processing applications, within the sound core of the HOL Light theorem prover.

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Higher Order Logic and Hardware Verification

10.1017/cbo9780511569845 ◽

1993 ◽

Cited By ~ 42

Author(s):

T. F. Melham

Keyword(s):

Higher Order ◽

Order Logic ◽

Hardware Verification ◽

Higher Order Logic

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Closed Structure

Journal of Philosophical Logic ◽

10.1007/s10992-021-09598-5 ◽

2021 ◽

Author(s):

Peter Fritz ◽

Harvey Lederman ◽

Gabriel Uzquiano

Keyword(s):

Formal Language ◽

Syntactic Structure ◽

Natural Extension ◽

Propositional Attitudes ◽

Higher Order ◽

Order Logic ◽

Bertrand Russell ◽

Structured Propositions ◽

Higher Order Logic ◽

Closed Structure

AbstractAccording to the structured theory of propositions, if two sentences express the same proposition, then they have the same syntactic structure, with corresponding syntactic constituents expressing the same entities. A number of philosophers have recently focused attention on a powerful argument against this theory, based on a result by Bertrand Russell, which shows that the theory of structured propositions is inconsistent in higher order-logic. This paper explores a response to this argument, which involves restricting the scope of the claim that propositions are structured, so that it does not hold for all propositions whatsoever, but only for those which are expressible using closed sentences of a given formal language. We call this restricted principle Closed Structure, and show that it is consistent in classical higher-order logic. As a schematic principle, the strength of Closed Structure is dependent on the chosen language. For its consistency to be philosophically significant, it also needs to be consistent in every extension of the language which the theorist of structured propositions is apt to accept. But, we go on to show, Closed Structure is in fact inconsistent in a very natural extension of the standard language of higher-order logic, which adds resources for plural talk of propositions. We conclude that this particular strategy of restricting the scope of the claim that propositions are structured is not a compelling response to the argument based on Russell’s result, though we note that for some applications, for instance to propositional attitudes, a restricted thesis in the vicinity may hold some promise.

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