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Type TheoryJust What is it that Makes MartinLof's Type Theory so Different, so Appealing?MartinLÃ¶f's Type Theory (MLTT) was developed by Per MartinLÃ¶f in the early 1970s, as a constructive foundation for mathematics. The theory is clear and simple. Because of this it has been used for everything from program derivation to handling donkey sentences. Yet another propositionsastypes tutorial. It seems pretty easy to follow, and it is quite short (16 pages). P.S Why all the theory on LtU these days? Because the editors who keep posting are into theory. The other editors should be nudged to start posting cool handson stuff... Linear types for aliased resources
Linear types for aliased resources. Chris Hawblitzel.
Type systems that track aliasing can verify statedependent program properties. For example, such systems can verify that a program does not access a resource after deallocating the resource. The simplest way to track aliasing is to use linear types, which on the surface appear to ban the aliasing of linear resources entirely. Since banning aliasing is considered too draconian for many practical programs, researchers have proposed type systems that allow limited forms of aliasing, without losing total control over statedependent properties. This paper describes how to encode one such system, the capability calculus, using a type system based on plain linear types with no special support for aliasing. Given welltyped capability calculus source programs, the encodings produce welltyped target programs based on linear types. These encodings demonstrate that, contrary to common expectations, linear type systems can express aliasing of linear resources. The prose is slightly confusing, but the code examples help. Sections 1 & 2 should be enough for those who only want to understand the problem with aliasing, and get a glimpse of what linear types are. By Ehud Lamm at 20051021 16:12  Software Engineering  Type Theory  30 comments  other blogs  10985 reads
NumberParameterized Types by Oleg KiselyovNumberParameterized Types by Oleg Kiselyov
Oleg shows several approaches towards encoding numbers into types and using those numbers to check list length, matching sizes for matrices or vectors. Oleg also points out connections to dependent types, phantom types, and shapeinvariant programming. A Type Discipline for Authorization Policies
Cedric Fournet; Andrew D. Gordon; Sergio Maffeis. A Type Discipline for Authorization Policies. ESOP 2005.
Distributed systems and applications are often expected to enforce highlevel authorization policies. To this end, the code for these systems relies on lowerlevel security mechanisms such as, for instance, digital signatures, local ACLs, and encrypted communications. In principle, authorization specifications can be separated from code and carefully audited. Logic programs, in particular, can express policies in a simple, abstract manner. We consider the problem of checking whether a distributed implementation based on communication channels and cryptography complies with a logical authorization policy. We formalize authorization policies and their connection to code by embedding logical predicates and claims within a process calculus. We formulate policy compliance operationally by composing a process model of the distributed system with an arbitrary opponent process. Moreover, we propose a new dependent type system for verifying policy compliance of implementation code. Using Datalog as an authorization logic, we show how to type several examples using policies and present a general schema for compiling policies. Another "extreme" use of static typing... By Ehud Lamm at 20050923 18:57  Logic/Declarative  Parallel/Distributed  Type Theory  1 comment  other blogs  8458 reads
Guarded Induction and Weakly Final Coalgebras in Dependent Type Theory
Quite a mouthful, I wonder if it would attract more people if it were titled "Interactive programming in Epigram" :)
Guarded Induction and Weakly Final Coalgebras in Dependent Type Theory In this article we are going to explore one approach to the representation of interactive programs in dependent type theory. The approach we take centres on the concept of "monadic IO" used in functional programming. We will see that in dependent type theory, besides nondependent interactive programs in which the interface between the user and the real world is fixed, as in ordinary functional programming, there is a natural notion of statedependent interactive programs, in which the interface changes over time. Automatic type inference via partial evaluation
Automatic type inference via partial evaluation. Aaron Tomb, Cormac Flanagan. PPDPâ€™05.
Type checking and type inference are fundamentally similar problems. However, the algorithms for performing the two operations, on the same type system, often differ significantly. The type checker is typically a straightforward encoding of the original type rules. For many systems, type inference is performed using a twophase, constraintbased algorithm.We present an approach that, given the original type rules written as clauses in a logic programming language, automatically generates an efficient, twophase, constraintbased type inference algorithm. Our approach works by partially evaluating the type checking rules with respect to the target program to yield a set of constraints suitable for input to an external constraint solver. This approach avoids the need to manually develop and verify a separate type inference algorithm, and is ideal for experimentation with and rapid prototyping of novel type systems. Also somewhat relevant to the discussions here about type checking as abstract interpretation. By Ehud Lamm at 20050717 10:55  Logic/Declarative  MetaProgramming  Type Theory  4 comments  other blogs  6563 reads
A Typed, Compositional Logic for a StackBased Abstract Machine
A Typed, Compositional Logic for a StackBased Abstract Machine. Nick Benton. MSRTR200584. June 2005.
We define a compositional program logic in the style of Floyd and Hoare for a simple, typed, stackbased abstract machine with unstructured control flow, global variables and mutually recursive procedure calls. Notable features of the logic include a careful treatment of auxiliary variables and quantification and the use of substructural typing to permit local, modular reasoning about program fragments. Semantic soundness is established using an interpretation of types and assertions defined by orthogonality with respect to sets of contexts. By Ehud Lamm at 20050702 09:14  Implementation  Semantics  Type Theory  2 comments  other blogs  7597 reads
A FormulaeasTypes Interpretation of Subtractive LogicA FormulaeasTypes Interpretation of Subtractive Logic
Yet another connection between subtractive logic and control. I remember the author mentioned on LtU, but I cannot find any citations. By Andris Birkmanis at 20050629 11:46  Functional  Lambda Calculus  Type Theory  1 comment  other blogs  4120 reads
Generics are a mistake?Generics Considered HarmfulKen Arnold, "programmer and author who helped create Jini, JavaSpaces, Curses, and Rogue", writes that the usefulness of generics is outweighed by their complexity. Ken is talking about Java 5, but such critiques are wellknown for C++, and C# is not immune either. Ken describes the Java case as follows:
The article contains a few simple supporting examples, including the interesting definition of Java 5's Enum<T extends Enum<T>> ...which "we're assured by the type theorists ... we should simply not think about too much, for which we are grateful." If we accept the article's premise, here's a question with an LtU spin: do the more elegant, tractable polymorphic inferencing type systems, as found in functional languages, improve on this situation enough to be a viable alternative that could address these complexity problems? In other words, are these problems a selling point for better type systems, or another barrier to adoption? [Thanks to Perry Metzger for the pointer.] By Anton van Straaten at 20050628 03:37  OOP  Type Theory  51 comments  other blogs  25834 reads
TypeCase: A Design Pattern for TypeIndexed Functions
Bruno C. d. S. Oliveira and Jeremy Gibbons. TypeCase: A Design Pattern for TypeIndexed Functions. Submitted for publication, June 2005.
A typeindexed function is a function that is defined for each member of some family of types. Haskell's type class mechanism provides open typeindexed functions, in which the indexing family can be extended at any time by defining a new type class instance. The purpose of this paper is to present TypeCase: a design pattern that allows the definition of closed typeindexed functions. It is inspired by Cheney and Hinze's work on lightweight approaches to generic programming. We generalise their techniques as a design pattern. Furthermore, we show that typeindexed functions with typeindexed types, and consequently generic functions with generic types, can also be encoded in a lightweight manner, thereby overcoming one of the main limitations of the lightweight approaches. A new paper in a field we follow quite closely (i.e., generic programming). The paper starts with a useful summary of important previous results, which is worth reading even if you don't plan on studying the whole paper. By Ehud Lamm at 20050620 19:37  Functional  Software Engineering  Type Theory  1 comment  other blogs  8344 reads

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