1,822 research outputs found

    Transformative learning relationships and the adult educator’s countertransference: a Jungian arts-based duoethnography

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    Transformative learning theory developed from Jack Mezirow’s seminal work on perspective transformation, is a predominant paradigm within adult education scholarship. Recent developments include Jungian perspectives in transformative learning that challenge the dominance of Mezirow’s rational conceptualisation and the exclusion of non-rational and unconscious aspects of learning. Whilst Jungian contributors elevate the role of the unconscious in transformative learning theory, scant attention is paid to the unconscious dynamics between educator and adult learner set within an intersubjective matrix. What is absent is any mention that feelings stirred up in the process of transformative learning might belong within a reciprocal relationship. Jung, who is arguably the pioneer of countertransference, offers a definite point of view about the importance of the subjective responses of the analyst and his/her ability to be influenced and impacted by the client. If the analyst is to transform others, then the analyst needs to be transformed. This relationship of mutual transformation is reconceptualised as a transformative learning relationship. A transformative learning relationship provides an intersubjective frame for exploring countertransferences and the emotional experience of the adult educator. The devised research method of collaborative imaginative engagement is an innovative post-Jungian extension of Jung’s method of active imagination, that involves two adult educators making and working with images of countertransference. The findings are presented as an arts-based duoethnographic portrayal of a co- individuation process between two adult educators. This duoethnographic process of co-individuation prototypes transformative reciprocity within the educator/learner relationship. This research addresses the imbalance or ‘one sidedness’ within transformative learning theory, that overlooks the educator’s subjective and intersubjective experience in favour of the learner’s experience. In doing so, the research contributes a more holistic and collaborative understanding of transformative learning that shows how both learner and educator can be inextricably bound together through a process of mutual transformation

    A foundation for synthesising programming language semantics

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    Programming or scripting languages used in real-world systems are seldom designed with a formal semantics in mind from the outset. Therefore, the first step for developing well-founded analysis tools for these systems is to reverse-engineer a formal semantics. This can take months or years of effort. Could we automate this process, at least partially? Though desirable, automatically reverse-engineering semantics rules from an implementation is very challenging, as found by Krishnamurthi, Lerner and Elberty. They propose automatically learning desugaring translation rules, mapping the language whose semantics we seek to a simplified, core version, whose semantics are much easier to write. The present thesis contains an analysis of their challenge, as well as the first steps towards a solution. Scaling methods with the size of the language is very difficult due to state space explosion, so this thesis proposes an incremental approach to learning the translation rules. I present a formalisation that both clarifies the informal description of the challenge by Krishnamurthi et al, and re-formulates the problem, shifting the focus to the conditions for incremental learning. The central definition of the new formalisation is the desugaring extension problem, i.e. extending a set of established translation rules by synthesising new ones. In a synthesis algorithm, the choice of search space is important and non-trivial, as it needs to strike a good balance between expressiveness and efficiency. The rest of the thesis focuses on defining search spaces for translation rules via typing rules. Two prerequisites are required for comparing search spaces. The first is a series of benchmarks, a set of source and target languages equipped with intended translation rules between them. The second is an enumerative synthesis algorithm for efficiently enumerating typed programs. I show how algebraic enumeration techniques can be applied to enumerating well-typed translation rules, and discuss the properties expected from a type system for ensuring that typed programs be efficiently enumerable. The thesis presents and empirically evaluates two search spaces. A baseline search space yields the first practical solution to the challenge. The second search space is based on a natural heuristic for translation rules, limiting the usage of variables so that they are used exactly once. I present a linear type system designed to efficiently enumerate translation rules, where this heuristic is enforced. Through informal analysis and empirical comparison to the baseline, I then show that using linear types can speed up the synthesis of translation rules by an order of magnitude

    Shoggoth: A Formal Foundation for Strategic Rewriting

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    Rewriting is a versatile and powerful technique used in many domains. Strategic rewriting allows programmers to control the application of rewrite rules by composing individual rewrite rules into complex rewrite strategies. These strategies are semantically complex, as they may be nondeterministic, they may raise errors that trigger backtracking, and they may not terminate.Given such semantic complexity, it is necessary to establish a formal understanding of rewrite strategies and to enable reasoning about them in order to answer questions like: How do we know that a rewrite strategy terminates? How do we know that a rewrite strategy does not fail because we compose two incompatible rewrites? How do we know that a desired property holds after applying a rewrite strategy?In this paper, we introduce Shoggoth: a formal foundation for understanding, analysing and reasoning about strategic rewriting that is capable of answering these questions. We provide a denotational semantics of System S, a core language for strategic rewriting, and prove its equivalence to our big-step operational semantics, which extends existing work by explicitly accounting for divergence. We further define a location-based weakest precondition calculus to enable formal reasoning about rewriting strategies, and we prove this calculus sound with respect to the denotational semantics. We show how this calculus can be used in practice to reason about properties of rewriting strategies, including termination, that they are well-composed, and that desired postconditions hold. The semantics and calculus are formalised in Isabelle/HOL and all proofs are mechanised

    Fragments and frame classes:Towards a uniform proof theory for modal fixed point logics

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    This thesis studies the proof theory of modal fixed point logics. In particular, we construct proof systems for various fragments of the modal mu-calculus, interpreted over various classes of frames. With an emphasis on uniform constructions and general results, we aim to bring the relatively underdeveloped proof theory of modal fixed point logics closer to the well-established proof theory of basic modal logic. We employ two main approaches. First, we seek to generalise existing methods for basic modal logic to accommodate fragments of the modal mu-calculus. We use this approach for obtaining Hilbert-style proof systems. Secondly, we adapt existing proof systems for the modal mu-calculus to various classes of frames. This approach yields proof systems which are non-well-founded, or cyclic.The thesis starts with an introduction and some mathematical preliminaries. In Chapter 3 we give hypersequent calculi for modal logic with the master modality, building on work by Ori Lahav. This is followed by an Intermezzo, where we present an abstract framework for cyclic proofs, in which we give sufficient conditions for establishing the bounded proof property. In Chapter 4 we generalise existing work on Hilbert-style proof systems for PDL to the level of the continuous modal mu-calculus. Chapter 5 contains a novel cyclic proof system for the alternation-free two-way modal mu-calculus. Finally, in Chapter 6, we present a cyclic proof system for Guarded Kleene Algebra with Tests and take a first step towards using it to establish the completeness of an algebraic counterpart

    Formally verified animation for RoboChart using interaction trees

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    RoboChart is a core notation in the RoboStar framework. It is a timed and probabilistic domain-specific and state machine-based language for robotics. RoboChart supports shared variables and communication across entities in its component model. It has formal denotational semantics given in CSP. The semantic technique of Interaction Trees (ITrees) represents behaviours of reactive and concurrent programs interacting with their environments. Recent mechanisation of ITrees, ITree-based CSP semantics and a Z mathematical toolkit in Isabelle/HOL bring new applications of verification and animation for state-rich process languages, such as RoboChart. In this paper, we use ITrees to give RoboChart novel operational semantics, implement it in Isabelle, and use Isabelle’s code generator to generate verified and executable animations. We illustrate our approach using an autonomous chemical detector and patrol robot models, exhibiting nondeterminism and using shared variables. With animation, we show two concrete scenarios for the chemical detector when the robot encounters different environmental inputs and three for the patrol robot when its calibrated position is in other corridor sections. We also verify that the animated scenarios are trace refinements of the CSP denotational semantics of the RoboChart models using FDR, a refinement model checker for CSP. This ensures that our approach to resolve nondeterminism using CSP operators with priority is sound and correct

    Complete and easy type Inference for first-class polymorphism

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    The Hindley-Milner (HM) typing discipline is remarkable in that it allows statically typing programs without requiring the programmer to annotate programs with types themselves. This is due to the HM system offering complete type inference, meaning that if a program is well typed, the inference algorithm is able to determine all the necessary typing information. Let bindings implicitly perform generalisation, allowing a let-bound variable to receive the most general possible type, which in turn may be instantiated appropriately at each of the variable’s use sites. As a result, the HM type system has since become the foundation for type inference in programming languages such as Haskell as well as the ML family of languages and has been extended in a multitude of ways. The original HM system only supports prenex polymorphism, where type variables are universally quantified only at the outermost level. This precludes many useful programs, such as passing a data structure to a function in the form of a fold function, which would need to be polymorphic in the type of the accumulator. However, this would require a nested quantifier in the type of the overall function. As a result, one direction of extending the HM system is to add support for first-class polymorphism, allowing arbitrarily nested quantifiers and instantiating type variables with polymorphic types. In such systems, restrictions are necessary to retain decidability of type inference. This work presents FreezeML, a novel approach for integrating first-class polymorphism into the HM system, focused on simplicity. It eschews sophisticated yet hard to grasp heuristics in the type systems or extending the language of types, while still requiring only modest amounts of annotations. In particular, FreezeML leverages the mechanisms for generalisation and instantiation that are already at the heart of ML. Generalisation and instantiation are performed by let bindings and variables, respectively, but extended to types beyond prenex polymorphism. The defining feature of FreezeML is the ability to freeze variables, which prevents the usual instantiation of their types, allowing them instead to keep their original, fully polymorphic types. We demonstrate that FreezeML is as expressive as System F by providing a translation from the latter to the former; the reverse direction is also shown. Further, we prove that FreezeML is indeed a conservative extension of ML: When considering only ML programs, FreezeML accepts exactly the same programs as ML itself. # We show that type inference for FreezeML can easily be integrated into HM-like type systems by presenting a sound and complete inference algorithm for FreezeML that extends Algorithm W, the original inference algorithm for the HM system. Since the inception of Algorithm W in the 1970s, type inference for the HM system and its descendants has been modernised by approaches that involve constraint solving, which proved to be more modular and extensible. In such systems, a term is translated to a logical constraint, whose solutions correspond to the types of the original term. A solver for such constraints may then be defined independently. To this end, we demonstrate such a constraint-based inference approach for FreezeML. We also discuss the effects of integrating the value restriction into FreezeML and provide detailed comparisons with other approaches towards first-class polymorphism in ML alongside a collection of examples found in the literature

    LIPIcs, Volume 251, ITCS 2023, Complete Volume

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    LIPIcs, Volume 251, ITCS 2023, Complete Volum

    Twin-Width V: Linear Minors, Modular Counting, and Matrix Multiplication

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    Staged Specifications for Automated Verification of Higher-Order Imperative Programs

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    Higher-order functions and imperative references are language features supported by many mainstream languages. Their combination enables the ability to package references to code blocks with the captured state from their environment. Higher-order imperative programs are expressive and useful, but complicate formal specification and reasoning due to the use of yet-to-be-instantiated function parameters, especially when their invocations may mutate memory captured by or reachable from their arguments. Existing state-of-the-art works for verifying higher-order imperative behaviors are restricted in two ways: achieving strong theoretical results without automated implementations, or achieving automation with the help of strong assumptions from dedicated type systems (e.g. Rust). To enable an automated verification solution for imperative languages without the above restrictions, we introduce Higher-order Staged Separation Logic (HSSL), an extension of Hoare logic for call-by-value higher-order functions with ML-like local references. In this paper, we design a novel staged specification logic, prove its soundness, develop a new automated higher-order verifier, Heifer, for a core OCaml-like language, report on experimental results, and present various case studies investigating its capabilities

    Morpheus: Automated Safety Verification of Data-Dependent Parser Combinator Programs

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    Parser combinators are a well-known mechanism used for the compositional construction of parsers, and have shown to be particularly useful in writing parsers for rich grammars with data-dependencies and global state. Verifying applications written using them, however, has proven to be challenging in large part because of the inherently effectful nature of the parsers being composed and the difficulty in reasoning about the arbitrarily rich data-dependent semantic actions that can be associated with parsing actions. In this paper, we address these challenges by defining a parser combinator framework called Morpheus equipped with abstractions for defining composable effects tailored for parsing and semantic actions, and a rich specification language used to define safety properties over the constituent parsers comprising a program. Even though its abstractions yield many of the same expressivity benefits as other parser combinator systems, Morpheus is carefully engineered to yield a substantially more tractable automated verification pathway. We demonstrate its utility in verifying a number of realistic, challenging parsing applications, including several cases that involve non-trivial data-dependent relations
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