Staged Composition Synthesis

Düdder, Boris; Martens, Moritz; Rehof, Jakob

doi:10.1007/978-3-642-54833-8_5

Cited by 16 publications

(5 citation statements)

References 19 publications

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“…Future work includes further studies on the possibilities to encode predicates exploiting patterns similar to the negative information encoding. Another direction of future work is to extend types of mixins and classes by semantic as well as modal types [DMR14], a development initiated in [BDDM14]. In particular, the expressiveness of semantic types can be used to assign meaning to multiple applications of a single mixin and allow to reason about object-oriented code on a higher abstraction level as well as with higher semantic accuracy.…”

Section: Discussionmentioning

confidence: 99%

“…We refer to types enriched with semantic specifications through intersection types as semantic types. In addition to semantic types, Rehof et al have introduced the idea of staging into synthesis via modal types [DMR14]. Simple types were used by Steffen et al [SMvdB97] in the context of temporal logic synthesis to semantically enrich temporal specifications with taxonomic information.…”

Section: Introductionmentioning

confidence: 99%

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Mixin Composition Synthesis based on Intersection Types

Bessai¹,

Chen²,

Dudenhefner³

et al. 2018

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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.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Mixin Composition Synthesis based on Intersection Types

Bessai¹,

Chen²,

Dudenhefner³

et al. 2018

Self Cite

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“…(x x), which is not typable in simple types. The full expressive power of * is subject to ongoing research as a candidate combinatory logic suitable for software synthesis [Reh13,DMR14].…”

Section: The Unification Problem Problem 4 (Satisfiability) Given a S...mentioning

confidence: 99%

“…For one, the theory of subtyping and equivalence of [BCDC83] is particularly rich, and several variants can be seen as subsystems thereof. Second, we adopted this theory for applications within type-based program synthesis based on combinatory logic with intersection types [Reh13,DMR14], where it is useful for supporting type refinement with semantic types (compare also [FP91]). Similar theories of intersection type subtyping and equivalence have been adopted, or adapted, in many contexts, an example being the programming language Forsythe by Reynolds [Rey96].…”

Section: Introductionmentioning

confidence: 99%

The Algebraic Intersection Type Unification Problem

Dudenhefner¹,

Martens²,

Rehof³

2017

Logical Methods in Computer Science ; Volume 13

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The algebraic intersection type unification problem is an important component in proof search related to several natural decision problems in intersection type systems. It is unknown and remains open whether the algebraic intersection type unification problem is decidable. We give the first nontrivial lower bound for the problem by showing (our main result) that it is exponential time hard. Furthermore, we show that this holds even under rank 1 solutions (substitutions whose codomains are restricted to contain rank 1 types). In addition, we provide a fixed-parameter intractability result for intersection type matching (one-sided unification), which is known to be NP-complete.We place the algebraic intersection type unification problem in the context of unification theory. The equational theory of intersection types can be presented as an algebraic theory with an ACI (associative, commutative, and idempotent) operator (intersection type) combined with distributivity properties with respect to a second operator (function type). Although the problem is algebraically natural and interesting, it appears to occupy a hitherto unstudied place in the theory of unification, and our investigation of the problem suggests that new methods are required to understand the problem. Thus, for the lower bound proof, we were not able to reduce from known results in ACI-unification theory and use game-theoretic methods for two-player tiling games.

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“…One possibility here consist in restricting the programming language so that there is no need to introduce binders. This method was used in the work of Düdder et al [3], which was enough to synthesise λ-terms that were programs in a simple but expressive functional language.…”

Section: Introductionmentioning

confidence: 99%

Automata Theory Approach to Predicate Intuitionistic Logic

Zielenkiewicz

Schubert

2017

Logic-Based Program Synthesis and Transformation

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Abstract. Predicate intuitionistic logic is a well established fragment of dependent types. According to the Curry-Howard isomorphism proof construction in the logic corresponds well to synthesis of a program the type of which is a given formula. We present a model of automata that can handle proof construction in full intuitionistic first-order logic. The automata are constructed in such a way that any successful run corresponds directly to a normal proof in the logic. This makes it possible to discuss formal languages of proofs or programs, the closure properties of the automata and their connections with the traditional logical connectives.

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Staged Composition Synthesis

Cited by 16 publications

References 19 publications

Mixin Composition Synthesis based on Intersection Types

Mixin Composition Synthesis based on Intersection Types

The Algebraic Intersection Type Unification Problem

Automata Theory Approach to Predicate Intuitionistic Logic

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