Certified Context-Free Parsing: A formalisation of Valiant's Algorithm in Agda

Valiant (1975) has developed an algorithm for recognition of context free languages. As of today, it remains the algorithm with the best asymptotic complexity for this purpose. In this paper, we present an algebraic specification, implementation, and proof of correctness of a generalisation of Valiant's algorithm. The generalisation can be used for recognition, parsing or generic calculation of the transitive closure of upper triangular matrices. The proof is certified by the Agda proof assistant. The certification is representative of state-of-the-art methods for specification and proofs in proof assistants based on type-theory. As such, this paper can be read as a tutorial for the Agda system

Dynamic IFC Theorems for Free!

We show that noninterference and transparency, the key soundness theorems for dynamic IFC libraries, can be obtained "for free", as direct consequences of the more general parametricity theorem of type abstraction. This allows us to give very short soundness proofs for dynamic IFC libraries such as faceted values and LIO. Our proofs stay short even when fully mechanized for Agda implementations of the libraries in terms of type abstraction.Comment: CSF 2021 final versio

Ästhetisches Erkenntnisinteresse und literarische Artikulationsform

In diesem Beitrag wird versucht, das Verhältnis des ästhetischen Erkenntnisinteresses zur literarischen Artikulationsform als dessen möglicher Gegenstand zu bestimmen. Ausgehend von Habermas‘ Unterscheidung von drei verschiedenen Forschungsprozessen und erkenntnisleitenden Interessen soll das ästhetische Erkenntnisinteresse als vierte grundlegende Unterscheidung und Kategorie hinzufügt und dessen Bedeutung an einigen Beurteilungen und Artikulationsformen von Jürgen Habermas verdeutlicht werden

Proofs for free - parametricity for dependent types

Reynolds' abstraction theorem shows how a typing judgement in System F can be translated into a relational statement (in second order predicate logic) about inhabitants of the type. We obtain a similar result for pure type systems: for any PTS used as a programming language, there is a PTS that can be used as a logic for parametricity. Types in the source PTS are translated to relations (expressed as types) in the target. Similarly, values of a given type are translated to proofs that the values satisfy the relational interpretation. We extend the result to inductive families. We also show that the assumption that every term satisfies the parametricity condition generated by its type is consistent with the generated logic

Quad Strengthening and Hamstring Stretching as a Treatment of Pes Anserine Bursitis

Background/Purpose: This case study describes a 28-year-old woman’s six physical therapy visits over a period of four weeks for treatment of right pes anserine bursitis. The purpose of this case study is to describe the treatment of an individual with pes anserine bursitis using hamstring stretching, quadriceps strengthening, and iontophoresis and to describe the outcomes. Case Description: Following a fall down eight steps in her home with her right knee underneath her. The patient presented with increased pain, swelling, loss of range of motion, and tenderness at the pes anserine. Treatment consisted of iontophoresis, hamstring stretches, and quadriceps strengthening. Outcomes: The patient improved by 85% to 90% since initial visit as indicated by patient visual analog scale ranking and was able to return to all work activities and exercise on the elliptical at home. She had increased range of motion and no swelling at the bursa. The patient responded well to treatment and was able to return to all activities. Discussion: Current literature provides protocols, case studies, and individual doctor’s papers about pes anserine bursitis but no evidence based practice for interventions. This case study is an initiative that randomized controlled trials need to be performed to determine what the best treatment of pes anserine bursitis

The Effective Use of Technology in Faith Formation Programs

Technology has been underutilized in nontraditional academic settings like faith formation programs, but there is a place for it if implemented appropriately. While traditions of the Catholic Church uphold certain aesthetic standards and ways of participating in Mass, nothing says the ways in which children are taught about the Mass have to remain stagnant. This research revolves around the evolution of formal faith formation in church settings and how technology can play a role in its growth to engage youth in churches. The findings indicate a need for further change in faith formation in order to fully connect with the youth it tries to impact. The project is a mobile app developed specifically for youth groups and youth group leaders to adhere to policies in a safe environment while connecting with one another online. The goal of the app is to bridge the gap between the tradition of churches and their elders and the modernity of the youth that inhabit the spaces through the provision of a platform in which students can interact with religious content and ask the questions they may not have the resources to ask otherwise

Linear Haskell: practical linearity in a higher-order polymorphic language

Linear type systems have a long and storied history, but not a clear path forward to integrate with existing languages such as OCaml or Haskell. In this paper, we study a linear type system designed with two crucial properties in mind: backwards-compatibility and code reuse across linear and non-linear users of a library. Only then can the benefits of linear types permeate conventional functional programming. Rather than bifurcate types into linear and non-linear counterparts, we instead attach linearity to function arrows. Linear functions can receive inputs from linearly-bound values, but can also operate over unrestricted, regular values. To demonstrate the efficacy of our linear type system - both how easy it can be integrated in an existing language implementation and how streamlined it makes it to write programs with linear types - we implemented our type system in GHC, the leading Haskell compiler, and demonstrate two kinds of applications of linear types: mutable data with pure interfaces; and enforcing protocols in I/O-performing functions

A Computational Interpretation of Parametricity

Reynolds' abstraction theorem has recently been extended to lambda-calculi with dependent types. In this paper, we show how this theorem can be internalized. More precisely, we describe an extension of Pure Type Systems with a special parametricity rule (with computational content), and prove fundamental properties such as Church-Rosser's and strong normalization. All instances of the abstraction theorem can be both expressed and proved in the calculus itself. Moreover, one can apply parametricity to the parametricity rule: parametricity is itself parametric