Polynomial Size Analysis of First-Order Shapely Functions

We present a size-aware type system for first-order shapely function definitions. Here, a function definition is called shapely when the size of the result is determined exactly by a polynomial in the sizes of the arguments. Examples of shapely function definitions may be implementations of matrix multiplication and the Cartesian product of two lists. The type system is proved to be sound w.r.t. the operational semantics of the language. The type checking problem is shown to be undecidable in general. We define a natural syntactic restriction such that the type checking becomes decidable, even though size polynomials are not necessarily linear or monotonic. Furthermore, we have shown that the type-inference problem is at least semi-decidable (under this restriction). We have implemented a procedure that combines run-time testing and type-checking to automatically obtain size dependencies. It terminates on total typable function definitions.Comment: 35 pages, 1 figur

Type Checking and Weak Type Inference for Polynomial Size Analysis of First-Order Functions

Abstract. We present a size-aware type system for first-order shapely functions. Here, a function is called shapely when the size of the result is determined exactly by a polynomial in the sizes of the arguments. Examples of shapely functions are matrix multiplication and the Cartesian product of two lists. The type checking problem for the type system is shown to be undecidable in general. We define a natural syntactic restriction such that the type checking becomes decidable, even though size polynomials are not necessarily linear. Furthermore, an algorithm for weak type inference for this system is given

Estimating the Cost of Native Method Calls for Resource-bounded Functional Programming Languages

AbstractWe address the problem of applying resource-bounded functional programming languages in practice on object-oriented virtual machines which include calls to native methods coded in low-level languages without garbage collection support. We consider the application of a functional language with a high-level type system which incorporates measures of heap space consumption in types on such an execution platform. We supplement the syntactic type inference procedure of the functional language with a separate analysis which estimates the costs of memory leaks incurred by calls to garbage collection-ignorant functions

Observation of implicit complexity by non confluence

We propose to consider non confluence with respect to implicit complexity. We come back to some well known classes of first-order functional program, for which we have a characterization of their intentional properties, namely the class of cons-free programs, the class of programs with an interpretation, and the class of programs with a quasi-interpretation together with a termination proof by the product path ordering. They all correspond to PTIME. We prove that adding non confluence to the rules leads to respectively PTIME, NPTIME and PSPACE. Our thesis is that the separation of the classes is actually a witness of the intentional properties of the initial classes of programs

Cost Analysis of Nondeterministic Probabilistic Programs

We consider the problem of expected cost analysis over nondeterministic probabilistic programs, which aims at automated methods for analyzing the resource-usage of such programs. Previous approaches for this problem could only handle nonnegative bounded costs. However, in many scenarios, such as queuing networks or analysis of cryptocurrency protocols, both positive and negative costs are necessary and the costs are unbounded as well. In this work, we present a sound and efficient approach to obtain polynomial bounds on the expected accumulated cost of nondeterministic probabilistic programs. Our approach can handle (a) general positive and negative costs with bounded updates in variables; and (b) nonnegative costs with general updates to variables. We show that several natural examples which could not be handled by previous approaches are captured in our framework. Moreover, our approach leads to an efficient polynomial-time algorithm, while no previous approach for cost analysis of probabilistic programs could guarantee polynomial runtime. Finally, we show the effectiveness of our approach by presenting experimental results on a variety of programs, motivated by real-world applications, for which we efficiently synthesize tight resource-usage bounds.Comment: A conference version will appear in the 40th ACM Conference on Programming Language Design and Implementation (PLDI 2019

Cost analysis of nondeterministic probabilistic programs

We consider the problem of expected cost analysis over nondeterministic probabilistic programs, which aims at automated methods for analyzing the resource-usage of such programs. Previous approaches for this problem could only handle nonnegative bounded costs. However, in many scenarios, such as queuing networks or analysis of cryptocurrency protocols, both positive and negative costs are necessary and the costs are unbounded as well. In this work, we present a sound and efficient approach to obtain polynomial bounds on the expected accumulated cost of nondeterministic probabilistic programs. Our approach can handle (a) general positive and negative costs with bounded updates in variables; and (b) nonnegative costs with general updates to variables. We show that several natural examples which could not be handled by previous approaches are captured in our framework. Moreover, our approach leads to an efficient polynomial-time algorithm, while no previous approach for cost analysis of probabilistic programs could guarantee polynomial runtime. Finally, we show the effectiveness of our approach using experimental results on a variety of programs for which we efficiently synthesize tight resource-usage bounds

International Workshop on Foundational and Practical Aspects of Resource Analysis FOPARA '09 3rd of November Eindhoven, The Netherlands of the 16th International Symposium on Formal Methods

Contains fulltext : 76128.pdf (preprint version ) (Open Access)208 p

Collected Size Semantics for Functional Programs over Polymorphic Nested Lists

Contains fulltext : 75338.pdf (preprint version ) (Open Access)10th symposium on trends in functional programming TFP 2009 SELYE JANOS UNIVERSITY, KOMARNO, SLOVAKIA, JUNE 2-4, 2009, 02 juni 200