A fully adequate shallow embedding of the 
π-calculus in Isabelle/HOL with mechanized syntax analysis

Röckl, Christine; Hirschkoff, Daniel

doi:10.1017/s0956796802004653

Cited by 19 publications

(20 citation statements)

References 39 publications

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“…al., and in Isabelle by Röckl and Hirschkoff [39]. In [25] the late operational semantics is encoded together with late strong bisimulation.…”

Section: Results and Conclusionmentioning

confidence: 99%

“…However, if these functions range over the entire function space they may produce exotic terms, so the formalisations need to ensure that those are avoided. In [39], a special well-formedness predicate is used to filter out the exotic terms. Another problem is that since abstraction is handled by the meta-logic of the theorem prover, reasoning about binders at the object level can become problematic.…”

Section: Results and Conclusionmentioning

confidence: 99%

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Formalising the pi-calculus using nominal logic

Bengtson¹,

Parrow²

2009

Logical Methods in Computer Science

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Abstract. We formalise the pi-calculus using the nominal datatype package, based on ideas from the nominal logic by Pitts et al., and demonstrate an implementation in Isabelle/HOL. The purpose is to derive powerful induction rules for the semantics in order to conduct machine checkable proofs, closely following the intuitive arguments found in manual proofs. In this way we have covered many of the standard theorems of bisimulation equivalence and congruence, both late and early, and both strong and weak in a uniform manner. We thus provide one of the most extensive formalisations of a process calculus ever done inside a theorem prover.A significant gain in our formulation is that agents are identified up to alpha-equivalence, thereby greatly reducing the arguments about bound names. This is a normal strategy for manual proofs about the pi-calculus, but that kind of hand waving has previously been difficult to incorporate smoothly in an interactive theorem prover. We show how the nominal logic formalism and its support in Isabelle accomplishes this and thus significantly reduces the tedium of conducting completely formal proofs. This improves on previous work using weak higher order abstract syntax since we do not need extra assumptions to filter out exotic terms and can keep all arguments within a familiar first-order logic.

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“…al., and in Isabelle by Röckl and Hirschkoff [39]. In [25] the late operational semantics is encoded together with late strong bisimulation.…”

Section: Results and Conclusionmentioning

confidence: 99%

Section: Results and Conclusionmentioning

confidence: 99%

Formalising the pi-calculus using nominal logic

Bengtson¹,

Parrow²

2009

Logical Methods in Computer Science

View full text Add to dashboard Cite

show abstract

“…An extension of our incremental coinductive technique to more general formats such as GSOS [6] or tyft/tyxt [15] is of course desirable. Another direction for generalization is the allowance of bindings in the syntax of terms, including π-calculus-like bindings featuring scope extrusion (thus generalizing HOL-based settings for π-calculus such as [22,30]). …”

Section: Discussionmentioning

confidence: 99%

Incremental Pattern-Based Coinduction for Process Algebra and Its Isabelle Formalization

Popescu

Gunter

2010

Foundations of Software Science and Computational Structures

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Abstract. We present a coinductive proof system for bisimilarity in transition systems specifiable in the de Simone SOS format. Our coinduction is incremental, in that it allows building incrementally an a priori unknown bisimulation, and pattern-based, in that it works on equalities of process patterns (i.e., universally quantified equations of process terms containing process variables), thus taking advantage of equational reasoning in a "circular" manner, inside coinductive proof loops. The proof system has been formalized and proved sound in Isabelle/HOL.

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“…Both capture object-level bindings by meta-level functional bindings; "weak" refers to the considered functions mapping variables to terms, while "strong" refers to these functions mapping terms to terms. Weak HOAS approaches are taken in [18], [34], [57], [30], including in category-theoretic form (with a denotational-semantics flavor) in [23], [33], [8], [24]. Our work in this paper, the above HOAS-tailored approaches, as well as [19], the work on Hybrid [7], [44], [46], [22], as well as parametric HOAS [17], parametricity-based HOAS [35], 6 and de-Bruijn-mixed-HOAS [32], fall within strong HOAS.…”

Section: More Related Workmentioning

confidence: 99%

Strong Normalization for System F by HOAS on Top of FOAS

Popescu

Gunter

Osborn

2010

2010 25th Annual IEEE Symposium on Logic in Computer Science

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Abstract-We present a point of view concerning HOAS (Higher-Order Abstract Syntax) and an extensive exercise in HOAS along this point of view. The point of view is that HOAS can be soundly and fruitfully regarded as a definitional extension on top of FOAS (First-Order Abstract Syntax). As such, HOAS is not only an encoding technique, but also a higher-order view of a first-order reality. A rich collection of concepts and proof principles is developed inside the standard mathematical universe to give technical life to this point of view. The exercise consists of a new proof of Strong Normalization for System F. HOAS makes our proof considerably more direct than previous proofs. The concepts and results presented here have been formalized in the theorem prover Isabelle/HOL. [49] and has ever since been extensively developed in frameworks with a wide variety of features and flavors. We distinguish two main (overlapping) directions in these developments. Keywords--(I) First, the employment of a chosen meta logic as a pure logical framework, used for defining object systems for the purpose of reasoning inside those systems. A standard example is higher-order logic (HOL) as the meta logic and firstorder logic (FOL) as the object system. Thanks to affinities between the mechanisms of these two logics, one obtains an adequate encoding of FOL in HOL by merely declaring in HOL types and constants and stating the FOL axioms and rules as HOL axioms -then the mechanisms for building FOL deductions (including substitution, instantiation, etc.) are already present in the meta logic, HOL.-(II) Second, the employment of the meta-logic to reason about the represented object systems, i.e., to represent not only the object systems, but also (some of) their metatheory. (E.g., cut elimination is a property about Gentzenstyle FOL, not expressible in a standard HOAS-encoding of FOL into HOL.) While direction (I) has been quasi-saturated by the achievement of quasi-maximally convenient logical frameworks (such Edinburgh LF [31] and generic Isabelle [49]), this second direction undergoes these days a period of active research. We distinguish two main approaches here:

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A fully adequate shallow embedding of the π-calculus in Isabelle/HOL with mechanized syntax analysis

Cited by 19 publications

References 39 publications

Formalising the pi-calculus using nominal logic

Formalising the pi-calculus using nominal logic

Incremental Pattern-Based Coinduction for Process Algebra and Its Isabelle Formalization

Strong Normalization for System F by HOAS on Top of FOAS

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