# Types, Subtypes, and ASL+

@inproceedings{Aspinall1994TypesSA,
title={Types, Subtypes, and ASL+},
author={David Aspinall},
year={1994}
}
• D. Aspinall
• Published in COMPASS/ADT 30 May 1994
• Computer Science
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
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.
• Computer Science
Inf. Comput.
• 2013
• Physics
• 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.
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.
• Computer Science
ICALP
• 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

SHOWING 1-10 OF 25 REFERENCES

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.
• Computer Science
Journal of Functional Programming
• 1991
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.
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.
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.
• Computer Science
Mathematical 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.
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.
• Computer Science
JACM
• 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.
• Computer Science
TAPSOFT, 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.