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-\begin{document}
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-\title{Topics in Compilers and Concurrency \\ Seminar Report on\\ Background Materials and Related Work}
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-%\titlerunning{Abbreviated paper title}
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-\author{Julius Fischer}
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-\institute{Student at Univerity of Freiburg (ALU)\\
-    \email{julius.fischer@email.uni-freiburg.com}\\
-    Matriculation Number: 5317202
-    }
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-\newcommand{\lad}{$\lambda_d$}
-\newcommand{\dpsf}{DPS-$\tilde{F}$}
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-\section{Introduction}
-In their work Bagrel and Spiwack \cite{bagrel_dp_2025} build on many prior contributions,
-both directly in their calculus grammar and semantics, but also in their structural approach regarding typing and evaluation contexts.
-From now on the calculus introduced in this specific paper will be referred to as \lad.
-This report will highlight a number of select works, which are of significance to the $lambda_d$ calculus.
-
-\section{A Functional Representation of Data Structures with a Hole - Y. Minamide\cite{minamide_holes_1998}}
-This paper contributes fundamental work on holes in functional languages. 
-It introduces a hole abstraction $\hat\lambda x. T$ to formalize data structures with a single hole. 
-Which, while syntactically different, in principle remains similar to the \lad calculus.
-Both utilize holes as the core features, where \lad has a type $T_1 \ltimes T_2$ to represent a
-structure that is missing $T_1$ to complete a $T_2$, Minamide's calculus features $(T_1, T_2) hfun$.
-In generael Minamide focusses more on the similarity of his hole abstraction to the regular $\lambda$ abstraction
-and the similarity of a strucutre containing a hole, to a function that returns an type $T_2$, when applied argument to an argument $T_1$.
-Notably both calculi contain linearity constraints on holes, but Bagrel's work eliviates some of those constraints by allowing for weakening.
-Overall Minamide lays a lot of ground work, and influences that can be seen in the \lad formulation and in its discussion, as
-similar benefits regarding tail recursion are adressed.
-
-\section{Destination-Passing Style for Efficient Memory Management - Shaikhha et al. \cite{shaikhha_array_dps_2017}}
-While Bagrel mostly theorizes on the advantages of the \lad calculus,
-this paper give emprical evidence on runtime and memory improvements of Destination Passing Style (DPS) in a functional language.
-Shaikhha et al. demonstrate the benefits of implementing a DPS-transformation step into the compilation of an array-programming language.
-The authors chose to not give any direct memory control to the programmer, but their intermediate language '\dpsf' still feature
-some similarity to \lad.
-\dpsf is typed using a shape type, which contains the dimensions of the array, which will be written to a memory location/ destination.
-Because of to the array-programming nature of the langauge, the shape type is fit only to arrays, but displays some flexibility, 
-which, in a way, is more akin to the constructors used in \lad than to the holes used by Minamide \cite{minamide_holes_1998}.
-
-\section{Tail Modulo Cons - \cite{bour_et_al_tmc_2021}}
-This paper proposes a annotation controled, compile time transformation of OCaml into a DPS itermediate language.
-The intermediate language only features structures with single holes/ single destinations.
-The driving goal of Tail Modulo Cons (TMC) is, as the name suggests, to eliviate the issues of constructors wrapping a recursive call.
-Particularly TMC allows for tail recursion, even if the recursive call is hidden behind a data constructor.
-While TMC is an intermediate langauge it allows for some source level control, as only annotated functions are converted into DPS.
-
-
-\section{Linear Haskell: practical linearity in a higher-order polymorphic language - Bernardy et al. \cite{lh_bernardy_2017}}
-Linear logic/ typing stands at the core of the \lad type system, and its concrete form is massively influenced by Linear Haskell.
-Bernardy et al. give deeper insight into linear typing as it is the sole focus of this paper. 
-They focus on implementing linear typing in haskell but give good intuition on linear types as a whole.
-Though unrestricted types are not a core language feature but implemented in the language itself, the type system is
-very similar to \lad, in fact the calculi even share syntax for the linear function.
-Bernardy et al discuss many benefits of linear typing and \lad in it's whole bases on the idea of lienar types to make
-multiple writes on data impossible.
-
-\section{A Unified View of Modalities in Type Systems - Abel and Bernardy \cite{abel_bernardy_2020}}
-\lad includes a notion of modality using the exponential $!_mT$, of which the ground work is laid by Abel and Bernardy in this work.
-They discuss modalities not exlusively for linear types in rigorous formality, diving into the precise algebraic and logical background.
-In fact this paper shows a generilization of the modes used in \lad's type system, to ensure linearity.
-The main strategy, which is used in \lad, is including the modality in an algebraic structure of the calculus (by indexing the modality $!_m$).
-Bagrel claims this approach "greatly simplif[ies] [the] context management (especially in the computer-mechanized proofs)" \cite{bagrel_dp_2025} (Page 11).
-
-
-
-\section{Formalization and Implementation of Safe Destination Passing in Pure Functional Programming Settings - \cite{bagrel_thesis_2025}}
-Another honorable mention is Bagrel's dissertation, in which the author not only includes the findings of the original paper but 
-also goes into further detail regarding linear typing and the entire intuition behind \lad.
-It includes a more comprehensive explanation for most of which is convered in the article, as well as further on the usefulness of \lad
-and an application of it.
-
-
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+---
+theme: dracula
+paginate: true
+_paginate: false
+footer: Mini-Haskell · Julius Fischer · 19.11.2024
+_footer: ""
+---
+
+# Destination Calculus:
+## A Linear 𝜆-Calculus for Purely Functional Memory Writes
+### Technische Fakultät Freiburg
+#### Julius Fischer
+
+###### 10. Juni 2026
+
+---
+
+# Referenes