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

Towards a canonical classical natural deduction system

This paper studies a new classical natural deduction system, presented as a typed calculus named \lml. It is designed to be isomorphic to Curien-Herbelin's calculus, both at the level of proofs and reduction, and the isomorphism is based on the correct correspondence between cut (resp. left-introduction) in sequent calculus, and substitution (resp. elimination) in natural deduction. It is a combination of Parigot's $\lambda\mu$-calculus with the idea of ``coercion calculus'' due to Cervesato-Pfenning, accommodating let-expressions in a surprising way: they expand Parigot's syntactic class of named terms. This calculus aims to be the simultaneous answer to three problems. The first problem is the lack of a canonical natural deduction system for classical logic. \lml is not yet another classical calculus, but rather a canonical reflection in natural deduction of the impeccable treatment of classical logic by sequent calculus. The second problem is the lack of a formalization of the usual semantics of Curien-Herbelin's calculus, that explains co-terms and cuts as, respectively, contexts and hole-filling instructions. The mentioned isomorphism is the required formalization, based on the precise notions of context and hole-expression offered by \lml. The third problem is the lack of a robust process of ``read-back'' into natural deduction syntax of calculi in the sequent calculus format, that affects mainly the recent proof-theoretic efforts of derivation of $\lambda$-calculi for call-by-value. An isomorphic counterpart to the $Q$-subsystem of Curien-Herbelin's-calculus is derived, obtaining a new $\lambda$-calculus for call-by-value, combining control and let-expressions.Fundação para a Ciência e a Tecnologia (FCT

General homomorphic overloading

A general homomorphic overloading in a first-order type system is discussed and its attendant subtype inference problem is formulated. We propose a computationally efficient type inference algorithm by converting the attendant constraint-satisfaction problem into the algebraic path problem for a constraint graph weighted with elements of a specially constructed non-commutative star semiring. The elements of the semiring are monotonic functions from integers to integers (including ±∞) with pointwise maximum and function composition as semiring operations. The computational efficiency of our method is due to Kleene’s algebraic path method’s cubic complexit

Modal Intersection Types, Two-Level Languages, and Staged Synthesis

A typed λ-calculus, λ∩⎕, is introduced, combining intersection types and modal types. We develop the metatheory of λ∩⎕, with particular emphasis on the theory of subtyping and distributivity of the modal and intersection type operators. We describe how a stratification of λ∩⎕ leads to a multi-linguistic framework for staged program synthesis, where metaprograms are automatically synthesized which, when executed, generate code in a target language. We survey the basic theory of staged synthesis and illustrate by example how a two-level language theory specialized from λ∩⎕ can be used to understand the process of staged synthesis

Rank 3 Inhabitation of Intersection Types Revisited: (Extended Version)

We revisit the undecidability result of rank 3 intersection type inhabitation (Urzyczyn 2009) in pursuit of two goals. First, we strengthen the previous result by showing that intersection type inhabitation is undecidable for types of rank 3 and order 3, i.e. it is not necessary to introduce new functional dependencies (new instructions) during proof search. Second, we pinpoint the principles necessary to simulate Turing machine computation directly, whereas previous constructions used a highly parallel and non-deterministic computation model. Since our construction is more concise than existing approaches taking no detours, we believe that it is valuable for a better understanding of the expressiveness of intersection type inhabitation

Modular synthesis of product lines (ModSyn-PL)

Developing a Software Product Line is a significant investment since domain experts must work together with software developers to understand and model a specific domain and then transform those models into a working software system. A product line increases the essential complexity of software assets because of the widespread variability among the member applications and the requirement to configure an application by its desired features. We seek mechanisms and theories to reduce the manual effort in writing the software. This workshop focuses on a broad range of approaches that increase the amount of synthesized code in both the shared code assets of the product line as well as individual member applications. We are especially interested in modular approaches that provide a theory of composition for assembling together modular units (such as classes, mixins, combinators, aspects, and modules)

Typability in bounded dimension

Recently (authors, POPL 2017), a notion of dimensionality for intersection types was introduced, and it was shown that the bounded-dimensional inhabitation problem is decidable under a non-idempotent interpretation of intersection and undecidable in the standard set-theoretic model. In this paper we study the typability problem for bounded-dimensional intersection types and prove that the problem is decidable in both models. We establish a number of bounding principles depending on dimension. In particular, it is shown that dimensional bound on derivations gives rise to a bounded width property on types, which is related to a generalized subformula property for typings of arbitrary terms. Using the bounded width property we can construct a nondeterministic transformation of the typability problem to unification, and we prove that typability in the set-theoretic model is PSPACE-complete, whereas it is in NP in the multiset model

ModSyn-PP: Modular Synthesis of Programs and Processes Track Introduction

It is an old and beautiful dream of computer science to synthesize software applications from specifications. The beginning can be traced back to, at least, to 1957 (Summer Institute of Symbolic Logic, Cornell 1957) when Alonzo Church proposed to consider the problem of automatically constructing a finite-state procedure implementing a given input/output relation over infinite bitstreams specified as a logical formula. The problem, since then widely known as "Church’s Problem", gave rise to a major branch of theoretical computer science which has been concerned with many different forms of synthesis

Combinatory synthesis of classes using feature grammars

We describe a method for automatically transforming feature grammars into type-specifications which are subsequently used to synthesize a code-generator for a product of a given feature selection. Feature models are assumed to be given in the form of feature grammars with constraints, and we present a generic type-theoretic representation of such grammars. Our synthesis method is based on an extension of previous work in combinatory logic synthesis, where semantic types can be superimposed onto native APIs to specify a repository of components as well as synthesis goals. In our case, semantic types correspond to feature selections. We use an encoding of boolean logic in intersection types, which allows us to directly represent logical formulas expressing complex feature selection constraints. The novelty of our approach is the possibility to perform retrieval, selection and composition of products in a unified form, without sacrificing modularity. In contrast to constraint based methods, multiple selections of a single feature can coexist