Wellfounded Schematic Definitions

Slind, Konrad

doi:10.1007/10721959_4

Cited by 6 publications

(3 citation statements)

References 17 publications

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“…From this we can again use standard techniques of HOL to obtain a function from lam α to α (see for example Slind [28]). We first show that in rec f1 f2 f3 the "result" r has finite support provided the functions f 1 , f 2 and f 3 have finite support.…”

Section: Definition 6 (Freshness Condition For Binders)mentioning

confidence: 99%

Nominal Techniques in Isabelle/HOL

Urban¹

2008

J Autom Reasoning

140

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This paper describes a formalisation of the lambda-calculus in a HOLbased theorem prover using nominal techniques. Central to the formalisation is an inductive set that is bijective with the alpha-equated lambda-terms. Unlike de-Bruijn indices, however, this inductive set includes names and reasoning about it is very similar to informal reasoning with "pencil and paper". To show this we provide a structural induction principle that requires to prove the lambda-case for fresh binders only. Furthermore, we adapt work by Pitts providing a recursion combinator for the inductive set. The main technical novelty of this work is that it is compatible with the axiom of choice (unlike earlier nominal logic work by Pitts et al); thus we were able to implement all results in Isabelle/HOL and use them to formalise the standard proofs for Church-Rosser, strong-normalisation of beta-reduction, the correctness of the type-inference algorithm W, typical proofs from SOS and much more.

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Section: Definition 6 (Freshness Condition For Binders)mentioning

confidence: 99%

Nominal Techniques in Isabelle/HOL

Urban¹

2008

J Autom Reasoning

140

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“…Thus, we obtain a similar degree of generality as in [Slind, 2000] (for example, we can use arbitrary ACL2 well-founded relations). Thus, we obtain a similar degree of generality as in [Slind, 2000] (for example, we can use arbitrary ACL2 well-founded relations).…”

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confidence: 99%

Thirty Five Years of Automating Mathematics

Kamareddine¹

2003

Applied Logic Series

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“…The proof of the main lemma can just follow the structure of the recursive calls in the definition, expressed in the generated theorem redecL.induct that is a version of the respective "functional induction" scheme in Coq, without dependent types and hence without the need to reference redecL in it. This functionality has been developed by Konrad Slind [14].…”

Section: Details On Formal Verification With Isabellementioning

confidence: 99%

Verification of the Redecoration Algorithm for Triangular Matrices

Matthes

Strecker

Lecture Notes in Computer Science

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Abstract. Triangular matrices with a dedicated type for the diagonal elements can be profitably represented by a nested datatype, i. e., a heterogeneous family of inductive datatypes. These families are fully supported since the version 8.1 of the Coq theorem proving environment, released in 2007. Redecoration of triangular matrices has a succinct implementation in this representation, thus giving the challenge of proving it correct. This has been achieved within Coq, using also induction with measures. An axiomatic approach allowed a verification in the Isabelle theorem prover, giving insights about the differences of both systems.

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Wellfounded Schematic Definitions

Cited by 6 publications

References 17 publications

Nominal Techniques in Isabelle/HOL

Nominal Techniques in Isabelle/HOL

Thirty Five Years of Automating Mathematics

Verification of the Redecoration Algorithm for Triangular Matrices

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