Using Modes to Ensure Subject Reduction for Typed Logic Programs with Subtyping

Typing constraint logic programs

We present a prescriptive type system with parametric polymorphism and subtyping for constraint logic programs. The aim of this type system is to detect programming errors statically. It introduces a type discipline for constraint logic programs and modules, while maintaining the capabilities of performing the usual coercions between constraint domains, and of typing meta-programming predicates...

Subtyping, Modular Specification, and Modular Verification for Applicative Object-Oriented Programs

We present a formal specification language and a formal verification logic for a simple object-oriented programming language. The language is applicative and statically typed, and supports subtyping and messagepassing. The verification logic relies on a behavioral notion of subtyping that captures the intuition that a subtype behaves like its supertypes. We give a formal definition for legal su...

Typed operational semantics for higher-order subtyping

Bounded operator abstraction is a language construct relevant to object oriented programming languages and to ML2000, the successor to Standard ML. In this paper, we introduce Fω ≤, a variant of Fω <: with this feature and with Cardelli and Wegner’s kernel Fun rule for quantifiers. We define a typed operational semantics with subtyping and prove that it is equivalent with Fω ≤, using a Kripke m...

Typed Constraint Logic Programs: checking domain coercions and metaprograms through subtyping

Subject Reduction of Logic Programs as Proof-Theoretic Property

We consider prescriptive type systems for logic programs (as in Gödel or Mercury). In such systems, the typing is static, but it guarantees an operational property: if a program is “well-typed”, then all derivations starting in a “well-typed” query are again “well-typed”. This property has been called subject reduction. We show that this property can also be phrased as a property of the proof-t...