work on abstract & intro

paper/main.tex

@@ -53,11 +53,35 @@
 
 
 \begin{abstract}
-This paper presents a minimal core calculus extending the \(\lambda\)-calculus by a polymorphic type-system similar to SystemF, but in addition it introduces a new type-constructor called the \emph{ladder-type}.
+ This work introduces \emph{representational polymorphism} as a form of
-Using ladder-types, multi-layered embeddings of higher-level data-types into lower-level data-types can be described by a type-level structure.
+ coercive subtyping, which differentiates between various concrete
-By facilitating automatic transformations between semantically compatible datatypes, ladder-typing opens up a new paradigm of abstraction.
+ representations w.r.t. an abstract concept using an explicit type
-We formally define the syntax \& semantics of this calculus and prove its \emph{type soundness}.
+ structure. This structure captures the 'represented-as' relation of
-Further we show how the Boehm-Berarducci encoding can be used to implement algebraic datatypes on the basis of the introduced core calculus.
+ multi-level data embeddings.  Motivated by the need to manage data
+ transformations —whether for hardware interfacing, IPC/RPC
+ communication, or performance optimizations— our type system aims to
+ reduce bugs and enhance code clarity by enabling implicit coercions
+ between semantically equivalent representations, while retaining
+ coherence and soundness.
+
+ We extend the polymorphic λ-calculus (System F) with a new type
+ constructor, termed \emph{ladder-type} to encode a subtype relation based on
+ syntactical embedding, which inversely also helps to disambiguate
+ multiple interpretations of the same presentation type. To facilitate
+ implicit coercions between semantically equivalent yet presentationally
+ different types, we introduce morphisms —functions that transform one
+ representation to another of the same abstract type. Morphisms can be
+ inductively combined to form complex morphism-paths allowing
+ transitivity, list-mappings and lifting of presentation subtypes
+ without loss of coherence.  This enables programmers to treat various
+ representational forms interchangeably as abstract objects, with
+ required transformations managed by the compiler during a separate
+ translation step based on expression typing, while still being able to
+ locally control specific representations.
+
+ We formalize our extended calculus in Coq and demonstrate that our
+ translation function preserves typing, with progress and preservation
+ theorems remaining valid.
 \end{abstract}
 
 \maketitle
@@ -65,6 +89,62 @@ Further we show how the Boehm-Berarducci encoding can be used to implement algeb
 
 
 %\newpage
+\section{Introduction}
+The issue of transformation between varying data encodings is all-pervasive in software development.
+Altough programming languages in principle try provide a 'realm of consistent abstraction',
+many parts of the code that interface with the outside world are still riddled with data transformation routines.
+
+While certain representational forms might be fixed already at the boundaries of an application,
+internally, some other representations might be desired for reasons of simplicity, efficiency or
+for the sake of interfacing with hardware, other libraries / processes, the user.
+Further, differing complexity-profiles of certain representations might even have the potential to complement
+each other and coexist in a single application.
+Often however, such specialized implementations become heavily dependent on concrete data formats
+and require technical knowledge of the low-level data structures.
+Making use of multiple such representations, additionally requires careful transformation of data.
+
+\paragraph{Interfacing}
+\todo{serilization / marshalling}
+
+\paragraph{How to get fast code ?}
+ -> algorithmic optimization
+   -> see which methods are used most frequently
+   -> switch structures to reduce complexity there
+   -> identify special cases
+   -> remove indirection
+
+ -> optimize implementation detail:
+ -- bottleneck? memory!
+ ---- plenty of Main memory,
+	  but FAST memory is scarce
+	--> improve cache efficiency: make compact representations
+	   * Balance De-/Encode Overhead
+	         vs. Load-Overhead
+
+       * Synchronize locality in access order and memory layout.
+       -> elements accessed in succession shall be close in memory.
+	        (e.g. AoS vs SoA)
+
+     ..while..
+     - accounting for machine specific cache-sizes
+     - accounting for SIMD instructions
+     - interfacing with kernels running on accelerator devices
+
+\paragraph{Elegant Abstractions}
+\todo{difference to traditional coercions (static cast)}
+\todo{relation with inheritance based subtyping:  bottom-up vs top-down inheritance vs ladder-types}
+\todo{relation to traits/type-classes}
+\todo{relation to coercive subtyping}
+
+\paragraph{Related Work}
+\todo{type specific languages}
+
+In order to facilitate programming at "high-level", we introduce a type-system that is able to disambiguate
+this multiplicity of representations and facilitate implicit coercions between them.
+We claim this to aid in (1) forgetting details about representational details during program composition
+and (2) keeping the system flexible enough to introduce representational optimizations at a later stage without
+compromising semantic correctness.
+
 \section{Core Calculus}
 \subsection{Syntax}