Reconstructing a logic for inductive proofs of properties of functional programs

A logical framework consisting of a polymorphic call-by-value functional language and a first-order logic on the values is presented, which is a reconstruction of the logic of the verification system VeriFun. The reconstruction uses contextual semantics to define the logical value of equations. It equates undefinedness and non-termination, which is a standard semantical approach. The main results of this paper are: Meta-theorems about the globality of several classes of theorems in the logic, and proofs of global correctness of transformations and deduction rules. The deduction rules of VeriFun are globally correct if rules depending on termination are appropriately formulated. The reconstruction also gives hints on generalizations of the VeriFun framework: reasoning on nonterminating expressions and functions, mutual recursive functions and abstractions in the data values, and formulas with arbitrary quantifier prefix could be allowed

Strongly-Normalizing Higher-Order Relational Queries

Language-integrated query is a powerful programming construct allowing database queries and ordinary program code to interoperate seamlessly and safely. Language-integrated query techniques rely on classical results about the nested relational calculus, stating that its queries can be algorithmically translated to SQL, as long as their result type is a flat relation. Cooper and others advocated higher-order nested relational calculi as a basis for language-integrated queries in functional languages such as Links and F#. However, the translation of higher-order relational queries to SQL relies on a rewrite system for which no strong normalization proof has been published: a previous proof attempt does not deal correctly with rewrite rules that duplicate subterms. This paper fills the gap in the literature, explaining the difficulty with a previous proof attempt, and showing how to extend the $\top\top$-lifting approach of Lindley and Stark to accommodate duplicating rewrites. We also show how to extend the proof to a recently-introduced calculus for heterogeneous queries mixing set and multiset semantics

From LCF to Isabelle/HOL

Interactive theorem provers have developed dramatically over the past four decades, from primitive beginnings to today's powerful systems. Here, we focus on Isabelle/HOL and its distinctive strengths. They include automatic proof search, borrowing techniques from the world of first order theorem proving, but also the automatic search for counterexamples. They include a highly readable structured language of proofs and a unique interactive development environment for editing live proof documents. Everything rests on the foundation conceived by Robin Milner for Edinburgh LCF: a proof kernel, using abstract types to ensure soundness and eliminate the need to store proofs. Compared with the research prototypes of the 1970s, Isabelle is a practical and versatile tool. It is used by system designers, mathematicians and many others

A Semantics-Based Approach to Design of Query Languages for Partial Information

Most of work on partial information in databases asks which operations of standard languages, like relational algebra, can still be performed correctly in the presence of nulls. In this paper a different point of view is advocated. We believe that the semantics of partiality must be clearly understood and it should give us new design principles for languages for databases with partial information. There are different sources of partial information, such as missing information and conflicts that occur when different databases are merged. In this paper, we develop a common semantic framework for them which can be applied in a context more general than the flat relational model. This ordered semantics, which is based on ideas used in the semantics of programming languages, cleanly intergrates all kinds of partial information and serves as a tool to establish connections between them. Analyzing properties of semantic domains of types suitable for representing partial information, we come up with operations that are naturally associated with those types, and we organize programming syntax around these operations. We show how the languages that we obtain can be used to ask typical queries about incomplete information in relational databases, and how they can express some previously proposed languages. Finally, we discuss a few related topics such as mixing traditional constraints with partial information and extending semantics and languages to accommodate bags and recursive types

Architectural Refinement in HETS

The main objective of this work is to bring a number of improvements to the Heterogeneous Tool Set HETS, both from a theoretical and an implementation point of view. In the first part of the thesis we present a number of recent extensions of the tool, among which declarative specifications of logics, generalized theoroidal comorphisms, heterogeneous colimits and integration of the logic of the term rewriting system Maude. In the second part we concentrate on the CASL architectural refinement language, that we equip with a notion of refinement tree and with calculi for checking correctness and consistency of refinements. Soundness and completeness of these calculi is also investigated. Finally, we present the integration of the VSE refinement method in HETS as an institution comorphism. Thus, the proof manangement component of HETS remains unmodified

Bounded Linear Logic

A typed, modular paradigm for polynomial time computation is proposed