Efficient First Order Functional Program Interpreter with Time Bound Certifications

This paper describes the Automated Complexity Analysis Prototype (ACAp) system for automated complexity analysis of functional programs synthesized with the Nuprl proof development system. We define a simple abstract cost model for NUPRL's term language based on the current call-by-name evaluator. The framework uses abstract functions and abstract lists to facilitate reasoning about primitive recursive programs with first-order functions, lazy lists and a subclass of higher-order functions. The ACAp system automatically derives upper bounds on the time complexity of NUPRL extracts relative to a given profiling semantics. Analysis proceeds by abstract interpretation of the extract, where symbolic evaluation rules extend standard evaluation to terms with free variables. Symbolic evaluation of recursive programs generates systems of multi-variable difference equations, which are solved using the MATHEMATICA computer algebra system. The use of the system is exemplified by analyzing a proof extract that computes the maximum segment sum of a list and a functional program that determines the minimum of a list via sorting. For both results, we compare call-by-name to call-by-value evaluation.

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The expressive power of higher-order types or, life without CONS

Journal of Functional Programming ◽

10.1017/s0956796800003889 ◽

2001 ◽

Vol 11 (1) ◽

pp. 55-94 ◽

Cited By ~ 42

Author(s):

NEIL D. JONES

Keyword(s):

Programming Languages ◽

Expressive Power ◽

Higher Order ◽

Second Order ◽

Complexity Classes ◽

Functional Program ◽

Control Structures ◽

First Order ◽

Partial Recursive Functions ◽

Turing Complete

Compare first-order functional programs with higher-order programs allowing functions as function parameters. Can the the first program class solve fewer problems than the second? The answer is no: both classes are Turing complete, meaning that they can compute all partial recursive functions. In particular, higher-order values may be first-order simulated by use of the list constructor ‘cons’ to build function closures. This paper uses complexity theory to prove some expressivity results about small programming languages that are less than Turing complete. Complexity classes of decision problems are used to characterize the expressive power of functional programming language features. An example: second-order programs are more powerful than first-order, since a function f of type [Bool]-〉Bool is computable by a cons-free first-order functional program if and only if f is in PTIME, whereas f is computable by a cons-free second-order program if and only if f is in EXPTIME. Exact characterizations are given for those problems of type [Bool]-〉Bool solvable by programs with several combinations of operations on data: presence or absence of constructors; the order of data values: 0, 1, or higher; and program control structures: general recursion, tail recursion, primitive recursion.

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Dual systems for all: Higher-order, role-based relational reasoning as a uniquely derived feature of human cognition

Behavioral and Brain Sciences ◽

10.1017/s0140525x19000451 ◽

2019 ◽

Vol 42 ◽

Author(s):

Daniel J. Povinelli ◽

Gabrielle C. Glorioso ◽

Shannon L. Kuznar ◽

Mateja Pavlic

Keyword(s):

Temporal Reasoning ◽

Higher Order ◽

Important Case ◽

Human Cognition ◽

Relational Reasoning ◽

Dual Systems ◽

First Order ◽

Reasoning System ◽

Role Based

Abstract Hoerl and McCormack demonstrate that although animals possess a sophisticated temporal updating system, there is no evidence that they also possess a temporal reasoning system. This important case study is directly related to the broader claim that although animals are manifestly capable of first-order (perceptually-based) relational reasoning, they lack the capacity for higher-order, role-based relational reasoning. We argue this distinction applies to all domains of cognition.

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Stochasting modeling of planetary ring systems

International Astronomical Union Colloquium ◽

10.1017/s025292110010154x ◽

1984 ◽

Vol 75 ◽

pp. 461-469 ◽

Cited By ~ 1

Author(s):

Robert W. Hart

Keyword(s):

Maximum Entropy ◽

Ring System ◽

The Sun ◽

Ultimate State ◽

Interparticle Interactions ◽

Ring Systems ◽

First Order ◽

Planetary Ring ◽

Insight Into

ABSTRACTThis paper models maximum entropy configurations of idealized gravitational ring systems. Such configurations are of interest because systems generally evolve toward an ultimate state of maximum randomness. For simplicity, attention is confined to ultimate states for which interparticle interactions are no longer of first order importance. The planets, in their orbits about the sun, are one example of such a ring system. The extent to which the present approximation yields insight into ring systems such as Saturn's is explored briefly.

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Morphological studies of linear (AB)n multiblock copolymers and their blends

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100122320 ◽

1992 ◽

Vol 50 (1) ◽

pp. 384-385

Author(s):

Richard J. Spontak ◽

Steven D. Smith ◽

Arman Ashraf

Keyword(s):

Electron Microscopy ◽

Microphase Separation ◽

Multiblock Copolymers ◽

First Order ◽

Morphological Studies ◽

Transmission Electron ◽

First Order Phase Transition ◽

Covalently Bonded ◽

Total Molecular Weight ◽

First Order Phase

Block copolymers are composed of sequences of dissimilar chemical moieties covalently bonded together. If the block lengths of each component are sufficiently long and the blocks are thermodynamically incompatible, these materials are capable of undergoing microphase separation, a weak first-order phase transition which results in the formation of an ordered microstructural network. Most efforts designed to elucidate the phase and configurational behavior in these copolymers have focused on the simple AB and ABA designs. Few studies have thus far targeted the perfectly-alternating multiblock (AB)n architecture. In this work, two series of neat (AB)n copolymers have been synthesized from styrene and isoprene monomers at a composition of 50 wt% polystyrene (PS). In Set I, the total molecular weight is held constant while the number of AB block pairs (n) is increased from one to four (which results in shorter blocks). Set II consists of materials in which the block lengths are held constant and n is varied again from one to four (which results in longer chains). Transmission electron microscopy (TEM) has been employed here to investigate the morphologies and phase behavior of these materials and their blends.

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Exact First Order Finite Element Modeling for Eddy Current NDE

Research in Nondestructive Evaluation ◽

10.1080/09349849108968051 ◽

1991 ◽

Vol 3 (1) ◽

pp. 235-253 ◽

Cited By ~ 1

Author(s):

L. D. Philipp ◽

Q. H. Nguyen ◽

D. D. Derkacht ◽

D. J. Lynch ◽

A. Mahmood

Keyword(s):

Finite Element ◽

Finite Element Modeling ◽

Eddy Current ◽

Element Modeling ◽

First Order ◽

Eddy Current Nde

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Challenging the Multidimensional Conception of Perceived Person-Environment Fit

European Journal of Psychological Assessment ◽

10.1027/1015-5759/a000622 ◽

2020 ◽

pp. 1-9

Author(s):

Julian M. Etzel ◽

Gabriel Nagy

Keyword(s):

Higher Education ◽

University Students ◽

Educational Outcomes ◽

Factor Model ◽

Higher Order ◽

Substantial Proportion ◽

Unique Variance ◽

First Order ◽

Person Environment Fit ◽

Order Factor

Abstract. In the current study, we examined the viability of a multidimensional conception of perceived person-environment (P-E) fit in higher education. We introduce an optimized 12-item measure that distinguishes between four content dimensions of perceived P-E fit: interest-contents (I-C) fit, needs-supplies (N-S) fit, demands-abilities (D-A) fit, and values-culture (V-C) fit. The central aim of our study was to examine whether the relationships between different P-E fit dimensions and educational outcomes can be accounted for by a higher-order factor that captures the shared features of the four fit dimensions. Relying on a large sample of university students in Germany, we found that students distinguish between the proposed fit dimensions. The respective first-order factors shared a substantial proportion of variance and conformed to a higher-order factor model. Using a newly developed factor extension procedure, we found that the relationships between the first-order factors and most outcomes were not fully accounted for by the higher-order factor. Rather, with the exception of V-C fit, all specific P-E fit factors that represent the first-order factors’ unique variance showed reliable and theoretically plausible relationships with different outcomes. These findings support the viability of a multidimensional conceptualization of P-E fit and the validity of our adapted instrument.

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