D. Basin, "Extracting circuits from Constructive Proofs", ACM/SIGDA Workshop on Formal Methods in VLSI Design, Miami, Florida, Jan. 1991. (Unfortunately, the proceedings of the workshop have not been officially published)  Home/Search   Document Not in Database   Summary   Related Articles   Check

....goal splitting activities. Constructive type theory (CTT) has also been used for system design. Suk has described a method to synthesise hardware from logical specifications using a CTT implemented in the ISABELLE logical framework [90] Basin has done similar work using the Nuprl proof assistant [4]. 2.4.1.1 Discussion Of the different approaches to formal digital system design presented above we have found the approaches of Fourman et al. and Hanna et al. to be the most relevant to our work. The approach of Hanna et al. is different from ours because of the stronger type system of the ....

D. A. Basin. Extracting Circuits From Constructive Proofs. In [1].

....ffl Constructiveness. In contrast to classical logic proofs in intuitionistic logic are constructive. Following the propositions as types or proofs as programs principle they encode computations. By interpreting proofs as terms of the lambda calculus one can extract programs [46, 25] or circuits [3]. In this paper we use a more specialised version which might be called the proofs as delays principle. Every proof p of an atomic proposition a = 1 represents a computation of a natural number [ p] 2 [ a = 1] N Theta fg = N that gives an upper bound on the time when signal a stabilises to ....

D. Basin. Extracting circuits from constructive proofs. In Int'l Workshop on: Formal Methods for VLSI Design, Miami, USA, January 1991. IFIP-IEEE.

....names, to their values. As we briefly indicated in Section 3 because the data type expressions are ordinary proof system terms we may quantify over structural descriptions. This feature was used to relate the switch level and threshold models of hardware formally, i.e. as a theorem in hol. In [7] Basin uses the Nuprl proof assistant [22] which implements a constructive type theory. He uses the proofs as circuits paradigm, which is an adaptation of the propositions as types idea [44] A constructive proof contains computable evidence, e.g. a circuit, of the truth of the proposition it ....

David A Basin. Extracting circuits from constructive proofs. In 1991 International Workshop on Formal Verification in VLSI Design. ACM IFIP WG 10.2, January 1991.

....wire names, to their values. As we briefly indicated on page 20, because the data type expressions are ordinary proof system terms we may quantify over structural descriptions. This feature was used to relate the switch level and threshold models of hardware formally, i.e. as a theorem in hol. In [8] Basin uses the Nuprl proof assistant [46] which implements a constructive type theory. He uses the proofs as circuits paradigm, which is an adaptation of the propositions as types idea [97] A constructive proof contains computable evidence, e.g. a program, of the truth of the proposition it ....

....S(i; o) Where env is the environment linking the bound variables i and o with their syntactic representations in c (cf. e in Equation 2.6, str in Equation 2.5. Note that the circuit description c does not appear in S because Interp trans c env provides the relation between c, i, and o. In fact, [8] gives a more general correctness statement; parametrised circuits and an arbitrary number of input and output ports are also allowed. To emphasise the use of the behaviour function Interp trans , we have also ignored the distinction between the type bool and the type of truth values in Nuprl. The ....

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David A Basin. Extracting circuits from constructive proofs. In 1991 International Workshop on Formal Verification in VLSI Design. ACM IFIP WG 10.2, January 1991.

....as specifications of programs. The programs themselves are implicit in the proofs of the theorems and can be extracted out of the proofs. Basin has been using Nuprl to see whether one could adapt this idea so that one could extract circuit designs from proofs of theorems which specify the circuits [5]. He has succeeded in extracting such combinational circuits as barrel shifters and look ahead carry adders, and is looking into extracting more complex combinational circuits and timed circuits. 7.3 Verification of Hardware Synthesis Systems This work started with Basin, Brown and Leeser ....

David A. Basin. Extracting circuits from constructive proofs. In International Workshop on Formal Methods in VLSI Design. ACM, 1991.

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David A. Basin. Extracting circuits from constructive proofs. In IFIP-IEEE International Workshop on Formal Methods in VLSI Design, Miami, USA, January 1991.

....of Gamma add , we can now apply the theorem as before and conclude that the term is equivalent to a circuit. Providing a formal proof of the above specification would take us outside the scope of this paper; the reader may find details of proofs conducted in Nuprl for similar specifications in [3]. Such specifications are proved by induction and different proofs will construct terms representing different kinds of parameterized adders (e.g. ripple carry, carry look ahead, etc. As with software development, the simultaneous synthesis and verification of hardware can simplify the design ....

....process. This methodology can put to particularly good advantage when circuit terms can be constructed and reasoned about in parts. 9] and [7] give examples of this kind of development methodology applied to the top down synthesis of proven correct combinational logic and sequential circuits. [3] provides examples of using type theory to synthesize recursive circuit schemas from their schematic specification (such as the n bit adder just specified) Our results here give a method of rigorously demonstrating that this kind of development is correct within TT. ....

D. A. Basin. Extracting circuits from constructive proofs. In IFIP-IEEE International Workshop on Formal Methods in VLSI Design, Miami, USA, January 1991.

No context found.

D. Basin, "Extracting circuits from Constructive Proofs", ACM/SIGDA Workshop on Formal Methods in VLSI Design, Miami, Florida, Jan. 1991. (Unfortunately, the proceedings of the workshop have not been officially published)

No context found.

David A. Basin. Extracting circuits from constructive proofs. Research Paper 533, Dept. of Artificial Intelligence, Edinburgh, 1991. Also appeared in Proceedings of the IFIP-IEEE International Workshop on Formal Methods in VLSI Design, Miami USA, 1991.

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