1,797 research outputs found
Mixin Composition Synthesis based on Intersection Types
We present a method for synthesizing compositions of mixins using type
inhabitation in intersection types. First, recursively defined classes and
mixins, which are functions over classes, are expressed as terms in a lambda
calculus with records. Intersection types with records and record-merge are
used to assign meaningful types to these terms without resorting to recursive
types. Second, typed terms are translated to a repository of typed combinators.
We show a relation between record types with record-merge and intersection
types with constructors. This relation is used to prove soundness and partial
completeness of the translation with respect to mixin composition synthesis.
Furthermore, we demonstrate how a translated repository and goal type can be
used as input to an existing framework for composition synthesis in bounded
combinatory logic via type inhabitation. The computed result is a class typed
by the goal type and generated by a mixin composition applied to an existing
class
Syntax for free: representing syntax with binding using parametricity
We show that, in a parametric model of polymorphism, the type ∀ α. ((α → α) → α) → (α → α → α) → α is isomorphic to closed de Bruijn terms. That is, the type of closed higher-order abstract syntax terms is isomorphic to a concrete representation. To demonstrate the proof we have constructed a model of parametric polymorphism inside the Coq proof assistant. The proof of the theorem requires parametricity over Kripke relations. We also investigate some variants of this representation
On Role Logic
We present role logic, a notation for describing properties of relational
structures in shape analysis, databases, and knowledge bases. We construct role
logic using the ideas of de Bruijn's notation for lambda calculus, an encoding
of first-order logic in lambda calculus, and a simple rule for implicit
arguments of unary and binary predicates. The unrestricted version of role
logic has the expressive power of first-order logic with transitive closure.
Using a syntactic restriction on role logic formulas, we identify a natural
fragment RL^2 of role logic. We show that the RL^2 fragment has the same
expressive power as two-variable logic with counting C^2 and is therefore
decidable. We present a translation of an imperative language into the
decidable fragment RL^2, which allows compositional verification of programs
that manipulate relational structures. In addition, we show how RL^2 encodes
boolean shape analysis constraints and an expressive description logic.Comment: 20 pages. Our later SAS 2004 result builds on this wor
Eta-Expansion Does The Trick (Revised Version)
Partial-evaluation folklore has it that massaging one's source programs can make them specialize better. In Jones, Gomard, and Sestoft's recent textbook, a whole chapter is dedicated to listing such "binding-time improvements": nonstandard use of continuation passing style, eta-expansion, and a popular transformation called "The Trick". We provide a unified view of these binding-time improvements, from a typing perspective.Just as a proper treatment of product values in partial evaluationrequires partially static values, a proper treatment of disjoint sums requires moving static contexts across dynamic case expressions. This requirement precisely accounts for the nonstandard use of continuation-passing style encountered in partial evaluation. Eta-expansion thusacts as a uniform binding-time coercion between values and contexts, be they of function type, product type, or disjoint-sum type. For the latter case, it enables "The Trick".In this article, we extend Gomard and Jones's partial evaluatorfor the lambda-calculus, lambda-Mix, with products and disjoint sums; we pointout how eta-expansion for (finite) disjoint sums enables The Trick; we generalize our earlier work by identifying that eta-expansion can be obtained in the binding-time analysis simply by adding two coercion rules; and we specify and prove the correctness of our extension to lambda-Mix.Keywords: Partial evaluation, binding-time analysis, program specialization,binding-time improvement, eta-expansion, static reduction
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