## Modeling a Hardware Synthesis Methodology in Isabelle (1996)

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Venue: | In Theorem Proving in Higher Order Logics (TPHOLs'96), volume 1125 of LNCS |

Citations: | 6 - 4 self |

### BibTeX

@INPROCEEDINGS{Basin96modelinga,

author = {David Basin and Stefan Friedrich},

title = {Modeling a Hardware Synthesis Methodology in Isabelle},

booktitle = {In Theorem Proving in Higher Order Logics (TPHOLs'96), volume 1125 of LNCS},

year = {1996},

pages = {33--50},

publisher = {Springer-Verlag}

}

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### Abstract

. Formal Synthesis is a methodology developed at Kent for combining circuit design and verification, where a circuit is constructed from a proof that it meets a given formal specification. We have reinterpreted this methodology in Isabelle's theory of higher-order logic so that circuits are incrementally built during proofs using higher-order resolution. Our interpretation simplifies and extends Formal Synthesis both conceptually and in implementation. It also supports integration of this development style with other proof-based synthesis methodologies and leads to techniques for developing new classes of circuits, e.g., recursive descriptions of parametric designs. Keywords: Hardware verification and synthesis, theorem proving, higher-order logic, higherorder unification. 1. Introduction Verification by formal proof is time intensive and this is a burden in bringing formal methods into software and hardware design. One approach to reducing the verification burden is to combine develop...

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Citation Context ... early detection of design errors. Such approaches have been actively investigated for software development, e.g., the use of constructive logics [4, 9] and the many approaches to deductive synthesis =-=[5, 6, 20, 22]-=-. Of particular relevance to our work here are the approaches to synthesis where resolution is used to construct programs during proofs. This methodology goes back to Green's use of first-order resolu... |

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Citation Context ...e treated as metavariables, which can be instantiated when applying the rule using higher-order unification. In our work we use Isabelle's theory of higher-order logic, which is based on Gordon's HOL =-=[14]-=-, extended with theories of sets, well-founded recursion, natural numbers, and the like. Within Isabelle the proof state is represented by a theorem [[ /1 ; : : : ; /m ]] =) / of the meta-theory. Proo... |

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Citation Context ...and synthesize logic programs [2]. There is also a growing body of work on proof based hardware synthesis [21, 24, 25, 26] including synthesis based on higher-order resolution using the Lambda system =-=[10, 12, 13]-=-. We present work here on combining two different development methodologies: synthesis based on higher-order resolution and a particular methodology for the top-down deductive refinement of specificat... |

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Citation Context ...automatically synthesize programs during proofs [15]. More recently, within Isabelle, interactive and tactic guided proof by higher-order resolution has been used to construct programs in type theory =-=[23]-=-, develop functional programs using classical logics [1, 8], and synthesize logic programs [2]. There is also a growing body of work on proof based hardware synthesis [21, 24, 25, 26] including synthe... |

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Citation Context ...thodology for the top-down deductive refinement of specifications into circuits. The latter is a novel 2 approach to hardware synthesis, called Formal Synthesis, proposed by the Veritas group at Kent =-=[16]-=-. In Formal Synthesis, one starts with a design goal, which specifies the behavioral properties of a circuit to be constructed, and interactively refines the design using a small but powerful set of t... |

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Citation Context ...e recently, within Isabelle, interactive and tactic guided proof by higher-order resolution has been used to construct programs in type theory [23], develop functional programs using classical logics =-=[1, 8]-=-, and synthesize logic programs [2]. There is also a growing body of work on proof based hardware synthesis [21, 24, 25, 26] including synthesis based on higher-order resolution using the Lambda syste... |

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Citation Context ...where the OE i are the hypotheses. Isabelle's resolution tactics apply rules in a way that maintains this illusion of working with sequents and we will often refer to the OE i as assumptions. Veritas =-=[18, 17]-=- is a tactic based theorem prover similar to Isabelle and the HOL system, but its higher-order logic is augmented with constructions from type theory, e.g., standard type constructors such as (depende... |

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Citation Context ...ve and tactic guided proof by higher-order resolution has been used to construct programs in type theory [23], develop functional programs using classical logics [1, 8], and synthesize logic programs =-=[2]-=-. There is also a growing body of work on proof based hardware synthesis [21, 24, 25, 26] including synthesis based on higher-order resolution using the Lambda system [10, 12, 13]. We present work her... |

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Citation Context ...ruct programs in type theory [23], develop functional programs using classical logics [1, 8], and synthesize logic programs [2]. There is also a growing body of work on proof based hardware synthesis =-=[21, 24, 25, 26]-=- including synthesis based on higher-order resolution using the Lambda system [10, 12, 13]. We present work here on combining two different development methodologies: synthesis based on higher-order r... |

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Citation Context ...e recently, within Isabelle, interactive and tactic guided proof by higher-order resolution has been used to construct programs in type theory [23], develop functional programs using classical logics =-=[1, 8]-=-, and synthesize logic programs [2]. There is also a growing body of work on proof based hardware synthesis [21, 24, 25, 26] including synthesis based on higher-order resolution using the Lambda syste... |

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Citation Context ...ruct programs in type theory [23], develop functional programs using classical logics [1, 8], and synthesize logic programs [2]. There is also a growing body of work on proof based hardware synthesis =-=[21, 24, 25, 26]-=- including synthesis based on higher-order resolution using the Lambda system [10, 12, 13]. We present work here on combining two different development methodologies: synthesis based on higher-order r... |

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Citation Context ...8, 23]. The work most closely related to ours is that of Mike Fourman 's group based on the Lambda system, which is a proof development system that supports synthesis based on second-order resolution =-=[10, 11]-=-. Motivated by Isabelle, they too use rules in order to represent the design state. The difference lies in the particular approach they use in proof construction; 3 instead of using general purpose te... |

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Citation Context ...and synthesize logic programs [2]. There is also a growing body of work on proof based hardware synthesis [21, 24, 25, 26] including synthesis based on higher-order resolution using the Lambda system =-=[10, 12, 13]-=-. We present work here on combining two different development methodologies: synthesis based on higher-order resolution and a particular methodology for the top-down deductive refinement of specificat... |

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Citation Context ...where the OE i are the hypotheses. Isabelle's resolution tactics apply rules in a way that maintains this illusion of working with sequents and we will often refer to the OE i as assumptions. Veritas =-=[18, 17]-=- is a tactic based theorem prover similar to Isabelle and the HOL system, but its higher-order logic is augmented with constructions from type theory, e.g., standard type constructors such as (depende... |

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