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**1 - 4**of**4**### A Reference Version of HOL

"... Abstract. The second author has implemented a reference version of the HOL logic (henceforth called gtt). This version, written in Standard ML, is as simple as possible, making as few assumptions as necessary to present the essence of HOL. This simplicity makes the implementation easy to understand, ..."

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Abstract. The second author has implemented a reference version of the HOL logic (henceforth called gtt). This version, written in Standard ML, is as simple as possible, making as few assumptions as necessary to present the essence of HOL. This simplicity makes the implementation easy to understand, to port, to develop, to change, and to informally reason about. The first author has ported gtt to another dialect of ML, and developed the parsing, prettyprinting, and typechecking support needed to take gtt beyond its initial rudimentary conception. The implementation of gtt has already been of use in developing a variant of the HOL logic. As of this writing, there are at least four or five extant implementations of the HOL logic. These have been intensively developed, in some cases over decades, which leads us to an overwhelming question: why another? In particular, why gtt? There are several answers to this, stemming from different desires and needs in the HOL community.

### Desiderata for Interactive Verification Systems

, 1994

"... What facilities should an interactive verification system provide? We take the pragmatic view that the particular logic underlying a proof system is not as important as the support that is provided. Although a plethora of logics have been implemented, we think that there is a common kernel of suppor ..."

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What facilities should an interactive verification system provide? We take the pragmatic view that the particular logic underlying a proof system is not as important as the support that is provided. Although a plethora of logics have been implemented, we think that there is a common kernel of support that a proof system ought to provide. Towards this end, we give detailed suggestions for verification support in three major areas: formalization, proof, and interface. Although our perspective comes from experience with highly expressive logics such as set theory, higher order logic, and type theory, we think our analyses apply more generally. Introduction Currently, theorem provers are used in the verification of both hardware and software [GM93, ORS92, BM90, HRS90, FFMH92], the formalization of informal mathematical proofs [FGT90, CH85, Pau90b], the teaching of logic[AMC84], and as tools of mathematical and metamathematical research [WWM + 90, CAB + 86]. 1 In this paper we describ...

### HOL-Ml

"... . We describe here HOL-ML, an encoding of a subset of SML and its dynamic semantics (as described by The Definition of Standard ML) in HOL. This encoding, which is the first stage in a project that will include typechecking and SML Modules, allows the formal study of the evaluation of a real pro ..."

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. We describe here HOL-ML, an encoding of a subset of SML and its dynamic semantics (as described by The Definition of Standard ML) in HOL. This encoding, which is the first stage in a project that will include typechecking and SML Modules, allows the formal study of the evaluation of a real programming language including state and control constructs (exceptions). In this paper we describe the subset of SML that we encoded and the semantic objects needed for its evaluation. We explain how we defined the evaluation rules and how we proved that evaluation is deterministic. We describe briefly the next step, which is to define a larger language that includes type declarations and to define the typechecking rules on it. Finally, we give a short description of the mutually recursive type definition package that we wrote to enable us to define the types we needed to create the HOL-ML grammar. 1 Introduction This paper describes HOL-ML, our encoding of the dynamic Core of SML in...

### Induction

, 2002

"... The authors wish to thank two anonymous referees for their helpful comments. Please address your correspondence to Srini ..."

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The authors wish to thank two anonymous referees for their helpful comments. Please address your correspondence to Srini