An Abstract Interpretation for ML Equality Kinds

The definition of Standard ML provides a form of generic equality which is inferred for certain types, called equality types, on which it is possible to define an equality relation in ML. However, the standard definition is incomplete in the sense that there are interesting and useful types which are not inferred to be equality types but for which an equality relation can be defined in ML in a uniform manner. In this paper, a refinement of the Standard ML system of equality types is introduced and is proven sound and complete with respect to the existence of a definable equality. The technique used here is based on an abstract interpretation of ML operators as monotone functions over a three point lattice. It is shown how the equality relation can be defined (as an ML program) from the definition of a type with our equality property. Finally, a sound, efficient algorithm for inferring the equality property which corrects the limitations of the standard definition in all cases of practical interest is demonstrated

Relational parametricity for higher kinds

Reynolds’ notion of relational parametricity has been extremely influential and well studied for polymorphic programming languages and type theories based on System F. The extension of relational parametricity to higher kinded polymorphism, which allows quantification over type operators as well as types, has not received as much attention. We present a model of relational parametricity for System Fω, within the impredicative Calculus of Inductive Constructions, and show how it forms an instance of a general class of models defined by Hasegawa. We investigate some of the consequences of our model and show that it supports the definition of inductive types, indexed by an arbitrary kind, and with reasoning principles provided by initiality

Adding HL7 version 3 data types to PostgreSQL

The HL7 standard is widely used to exchange medical information electronically. As a part of the standard, HL7 defines scalar communication data types like physical quantity, point in time and concept descriptor but also complex types such as interval types, collection types and probabilistic types. Typical HL7 applications will store their communications in a database, resulting in a translation from HL7 concepts and types into database types. Since the data types were not designed to be implemented in a relational database server, this transition is cumbersome and fraught with programmer error. The purpose of this paper is two fold. First we analyze the HL7 version 3 data type definitions and define a number of conditions that must be met, for the data type to be suitable for implementation in a relational database. As a result of this analysis we describe a number of possible improvements in the HL7 specification. Second we describe an implementation in the PostgreSQL database server and show that the database server can effectively execute scientific calculations with units of measure, supports a large number of operations on time points and intervals, and can perform operations that are akin to a medical terminology server. Experiments on synthetic data show that the user defined types perform better than an implementation that uses only standard data types from the database server.Comment: 12 pages, 9 figures, 6 table

On choice rules in dependent type theory

In a dependent type theory satisfying the propositions as types correspondence together with the proofs-as-programs paradigm, the validity of the unique choice rule or even more of the choice rule says that the extraction of a computable witness from an existential statement under hypothesis can be performed within the same theory. Here we show that the unique choice rule, and hence the choice rule, are not valid both in Coquand\u2019s Calculus of Constructions with indexed sum types, list types and binary disjoint sums and in its predicative version implemented in the intensional level of the Minimalist Founda- tion. This means that in these theories the extraction of computational witnesses from existential statements must be performed in a more ex- pressive proofs-as-programs theory

Decorated proofs for computational effects: Exceptions

We define a proof system for exceptions which is close to the syntax for exceptions, in the sense that the exceptions do not appear explicitly in the type of any expression. This proof system is sound with respect to the intended denotational semantics of exceptions. With this inference system we prove several properties of exceptions.Comment: 11 page

Matching Logic

This paper presents matching logic, a first-order logic (FOL) variant for specifying and reasoning about structure by means of patterns and pattern matching. Its sentences, the patterns, are constructed using variables, symbols, connectives and quantifiers, but no difference is made between function and predicate symbols. In models, a pattern evaluates into a power-set domain (the set of values that match it), in contrast to FOL where functions and predicates map into a regular domain. Matching logic uniformly generalizes several logical frameworks important for program analysis, such as: propositional logic, algebraic specification, FOL with equality, modal logic, and separation logic. Patterns can specify separation requirements at any level in any program configuration, not only in the heaps or stores, without any special logical constructs for that: the very nature of pattern matching is that if two structures are matched as part of a pattern, then they can only be spatially separated. Like FOL, matching logic can also be translated into pure predicate logic with equality, at the same time admitting its own sound and complete proof system. A practical aspect of matching logic is that FOL reasoning with equality remains sound, so off-the-shelf provers and SMT solvers can be used for matching logic reasoning. Matching logic is particularly well-suited for reasoning about programs in programming languages that have an operational semantics, but it is not limited to this

Compensation methods to support cooperative applications: A case study in automated verification of schema requirements for an advanced transaction model

Compensation plays an important role in advanced transaction models, cooperative work and workflow systems. A schema designer is typically required to supply for each transaction another transaction to semantically undo the effects of . Little attention has been paid to the verification of the desirable properties of such operations, however. This paper demonstrates the use of a higher-order logic theorem prover for verifying that compensating transactions return a database to its original state. It is shown how an OODB schema is translated to the language of the theorem prover so that proofs can be performed on the compensating transactions