# Types, Subtypes, and ASL+

@inproceedings{Aspinall1994TypesSA, title={Types, Subtypes, and ASL+}, author={David Aspinall}, booktitle={COMPASS/ADT}, year={1994} }

ASL+ is a formalism for specification and programming in-the-large, based on an arbitrary institution. It has rules for proving the satisfaction and refinement of specifications, which can be seen as a type theory with subtyping, including contravariant refinement for II-abstracted specifications and a notion of stratified equality for higher-order objects. We describe the syntax of the language and a partial equivalence relation semantics. This style of semantics is familiar from subtyping…

## 7 Citations

### Subtyping with Power Types

- Computer ScienceCSL
- 2000

This paper introduces a typed λ-calculus called λPOWER, a predicative reformulation of part of Cardelli's power type system, which is given a model definition using a form of applicative structures and "rough" types are used to prove strong normalization of the calculus and to structure models.

### What is an Abstract Data Type, after all?

- PhysicsCOMPASS/ADT
- 1994

We look back on ten Workshops on Abstract Data Types. Organizers and publications, a list of authors referencing their talks and papers on the workshops, and a workshop bibliography are presented.

### Type Checking Parametrised Programs and Specifications in ASL+FPC

- Computer ScienceWADT
- 2002

This paper introduces \(\mathcal{FPC}\) and ASL+FPC and their type checking systems and is notable for including sharing equations inside signatures, reminiscent of so-called manifest types or translucent sums in type systems for programming language modules.

### Amalgamation in CASL via Enriched Signatures

- Computer ScienceICALP
- 2001

Enriched CASL satisfies the amalgamation property, which fails in the CASL institution, as well as its converse, so the previously suggested institution-independent semantics of architectural specifications is actually applicable to CASL.

## References

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- Computer ScienceCSL
- 1994

We give syntax and a PER-model semantics for a typed λ-calculus with subtypes and singleton types. The calculus may be seen as a minimal calculus of subtyping with a simple form of dependent types.…

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- Computer ScienceJournal of Functional Programming
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The type inference rules for Quest are described in detail, and the meaning of these rules are given using a partial equivalence relation model of types.

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This thesis presents a collection of sublanguages, infeience systems and side conditions which add a new dimension to the fascinating job started by ASL in [SW 831], and encounters four main problems for the verification of implementations: hiding of auxiliary functions, behavioural abstraction, reachability constraints and parameterization.

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The mixing of value and type levels becomes a considerable obstacle when considering compiled languages, or languages extended with imperative features, which must make a clear distinction between compile-time and run-time phases.

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- Computer ScienceMathematical Structures in Computer Science
- 1992

A normalizing rewriting system on proofs is defined, which transforms different proofs of the same typing judgement into a unique normal proof, with the further property that all the normal proofs assigning different types to a given term in a given environment differ only by a final application of the subsumption rule.

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- MathematicsPOPL '92
- 1992

The question of the decidability of subtyping, and hence of typechecking, is settled here in the negative, using a reduction from the halting problem for two-counter Turing machines to show that the subtype relation of F≤ is undecidable.

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- Computer ScienceJACM
- 1992

This paper says that any institution such that signatures can be glued together, also allows gluing together theories (which are just collections of sentences over a fixed signature), and shows how to define institutions that allow sentences and constraints from two or more institutions.

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- Computer ScienceTAPSOFT, Vol.2
- 1991

The language includes constructs for defining general higher-order functions yielding specifications or program modules, and concepts of subtyping and (object-oriented) inheritance are included to support the specification development process and to enhance re-usability.