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Higher-order Cons-free Interpreters [article]

Cynthia Kop, Jakob Grue Simonsen
2017 arXiv   pre-print
This paper concerns the construction of interpreters for cons-free term rewriting.  ...  In earlier work by several authors, (typed) cons-free systems have been used to characterise complexity classes such as polynomial or exponential time or space by varying the type orders, and the recursion  ...  Our work concerns the construction of cons-free interpreters for higher-order term rewriting.  ... 
arXiv:1711.03407v1 fatcat:mzrmjjs4xvfgfc2z3wjervdlsa

Bootstrapping higher-order program transformers from interpreters

Michael Sperber, Robert Glück, Peter Thiemann
1996 Proceedings of the 1996 ACM symposium on Applied Computing - SAC '96  
In the context of functional languages, we investigate the design space of higher-order interpreters to achieve certain transformation effects.  ...  We have generated higher-order online partial evaluators, optimizing closure converters, and converters to first-order tail form. The latter can serve as the middle end of a compiler.  ...  treat a higher-order, side-effect free subset of Scheme [20] .  ... 
doi:10.1145/331119.331417 dblp:conf/sac/SperberGT96 fatcat:4y3w7di4jbc2lkx27ifr4swoly

The Strength of Non-size-increasing Computation (Introduction and Summary) [chapter]

Martin Hofmann
2001 Lecture Notes in Computer Science  
The key tool for establishing upper bounds on the complexity of derivable functions is an interpretation in a finite relational model whose correctness with respect to the standard interpretation is shown  ...  This notion of computation is such that the size of all intermediate results will automatically be bounded by the size of the input so that the interpretation in a finite model is sound with respect to  ...  Another piece of related work is Jones' [9] where the expressive power of cons-free higher-order programs is studied.  ... 
doi:10.1007/3-540-44683-4_6 fatcat:onuiifzytvasrm6ngumxdmtgwe

Polynomial Interpretations for Higher-Order Rewriting

Carsten Fuhs, Cynthia Kop, Marc Herbstritt
2012 International Conference on Rewriting Techniques and Applications  
Using this theory, we define higher-order polynomial interpretations, and show how the implementation challenges of this technique can be tackled.  ...  The termination method of weakly monotonic algebras, which has been defined for higher-order rewriting in the HRS formalism, offers a lot of power, but has seen little use in recent years.  ...  From these parametric higher-order polynomials, we calculate the interpretations of terms, and simplify the resulting higher-order polynomials into a sum of monomials.  ... 
doi:10.4230/lipics.rta.2012.176 dblp:conf/rta/FuhsK12 fatcat:nf4r7h2icbfkxng6qovfa5fg7q

Realistic compilation by partial evaluation

Michael Sperber, Peter Thiemann
1996 SIGPLAN notices  
We show that the interpretive approach can achieve optimizing compilation of a strict, higher-order functional language.  ...  Our compilation system consists of two parts: an optimizing transformer, which translates higher-order recursion equations into first-order tail-recursive Scheme programs, generated automatically from  ...  (freevars( ) computes the list of the free variables of the expression at in an arbitrary but fixed order.) Consequently, we now have a first-order interpreter for a higher-order language.  ... 
doi:10.1145/249069.231419 fatcat:kml5jbmzhnflnfe3tyfjm4x5ei

Realistic compilation by partial evaluation

Michael Sperber, Peter Thiemann
1996 Proceedings of the ACM SIGPLAN 1996 conference on Programming language design and implementation - PLDI '96  
We show that the interpretive approach can achieve optimizing compilation of a strict, higher-order functional language.  ...  Our compilation system consists of two parts: an optimizing transformer, which translates higher-order recursion equations into first-order tail-recursive Scheme programs, generated automatically from  ...  (freevars( ) computes the list of the free variables of the expression at in an arbitrary but fixed order.) Consequently, we now have a first-order interpreter for a higher-order language.  ... 
doi:10.1145/231379.231419 dblp:conf/pldi/SperberT96 fatcat:h6dcxdjxn5e45hi3wn44ofi2he

Polynomial Interpretations for Higher-Order Rewriting [article]

Carsten Fuhs, Cynthia Kop
2012 arXiv   pre-print
Using this theory, we define higher-order polynomial interpretations, and show how the implementation challenges of this technique can be tackled.  ...  The termination method of weakly monotonic algebras, which has been defined for higher-order rewriting in the HRS formalism, offers a lot of power, but has seen little use in recent years.  ...  From these parametric higher-order polynomials, we calculate the interpretations of terms, and simplify the resulting higher-order polynomials into a sum of monomials.  ... 
arXiv:1203.5754v1 fatcat:mwaqnt5cxfbdfazm4ihxky456q

The variable containment problem [chapter]

Stefan Kahrs
1996 Lecture Notes in Computer Science  
This set is signicant o n c e w e consider equivalence classes of -terms rather than -terms themselves, as for instance in higher-order rewriting.  ...  The essentially free variables of a term t in some -calculus, FV (t), form the set fx j 8 u: t = u ) x 2 FV(u)g.  ...  F or higher types, we a l s o h a ve t o m o d e l h o w the freeness of x can be a ected by -reduction. Thus we can interpret 0 : 2 by t h e partially ordered set f? >g (with ?  ... 
doi:10.1007/3-540-61254-8_22 fatcat:lvmuy2yxdvexbcjupng45qzlvu

First-class nonstandard interpretations by opening closures

Jeffrey Mark Siskind, Barak A. Pearlmutter
2007 Proceedings of the 34th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages - POPL '07  
reifies the continuations that are only implicit in programs written in direct style, map-closure is a nonreferentially-transparent mechanism that reifies the closure environments that are only implicit in higher-order  ...  We motivate and discuss a novel functional programming construct that allows convenient modular run-time nonstandard interpretation via reflection on closure environments.  ...  Acknowledgments This work was supported, in part, by NSF grant CCF-0438806, Science Foundation Ireland grant 00/PI.1/C067, and a grant from the Higher Education Authority of Ireland.  ... 
doi:10.1145/1190216.1190230 dblp:conf/popl/SiskindP07 fatcat:6xyuf23vufdwxniunf56rjlnwa

First-class nonstandard interpretations by opening closures

Jeffrey Mark Siskind, Barak A. Pearlmutter
2007 SIGPLAN notices  
reifies the continuations that are only implicit in programs written in direct style, map-closure is a nonreferentially-transparent mechanism that reifies the closure environments that are only implicit in higher-order  ...  We motivate and discuss a novel functional programming construct that allows convenient modular run-time nonstandard interpretation via reflection on closure environments.  ...  Acknowledgments This work was supported, in part, by NSF grant CCF-0438806, Science Foundation Ireland grant 00/PI.1/C067, and a grant from the Higher Education Authority of Ireland.  ... 
doi:10.1145/1190215.1190230 fatcat:acdlb5ce6vbh3bjsdeozzkiutq

Top-down mathematical semantics and symbolic execution

G. Lévi, A. M. Pegna
1983 RAIRO Informatique théorique  
If we want to be able to cope with higher order types, i. e. functional arguments, we have to define higher order domains and to provide symbolic constants and axioms for higher order types.  ...  If such constraints are satisfied, we need no formalization of storage. iii) Higher order types.  ... 
doi:10.1051/ita/1983170100551 fatcat:6bd4elhvxfelpfy7o3aa2ompy4

Safety of abstract interpretations for free, via logical relations and Galois connections

Kevin Backhouse, Roland Backhouse
2004 Science of Computer Programming  
"Theorems-for-free" is used to show that the construction ensures safe abstract interpretation of parametrically polymorphic functions.  ...  It is shown how to construct a logical relation that extends a collection of base Galois connections to a Galois connection of arbitrary higher-order type.  ...  Lemma 37 (Higher-order Galois connections).  ... 
doi:10.1016/j.scico.2003.06.002 fatcat:igwwlhdcybaznkbs3maww2m544

Reducing Higher-order Recursion Scheme Equivalence to Coinductive Higher-order Constrained Horn Clauses

Jerome Jochems
2021 Electronic Proceedings in Theoretical Computer Science  
Higher-order constrained Horn clauses (HoCHC) are a semantically-invariant system of higher-order logic modulo theories.  ...  Less is known about its relation to larger classes of higher-order verification problems.  ...  Preliminaries Higher-order constrained Horn clauses Following [6] , we work in higher-order logic presented as a typed (sorted) lambda calculus.  ... 
doi:10.4204/eptcs.344.4 fatcat:pufqgwo65vax5c7tzrz32mlzue

Semantics of Separation-Logic Typing and Higher-order Frame Rules for Algol-like Languages

Lars Birkedal, Noah Torp-Smith, Hongseok Yang, Prakash Panangaden
2006 Logical Methods in Computer Science  
In particular, we provide simple sound rules for deriving higher-order frame rules, allowing for local reasoning.  ...  We show how to give a coherent semantics to programs that are well-specified in a version of separation logic for a language with higher types: idealized algol extended with heaps (but with immutable stack  ...  local reasoning in the presence of higher-order procedures.  ... 
doi:10.2168/lmcs-2(5:1)2006 fatcat:lbe27m2pkfhs3ofumqd7kkqjju

Higher-order interpretations and program complexity

Patrick Baillot, Ugo Dal Lago
2016 Information and Computation  
In order to obtain a criterion flexible enough to validate interesting programs using higher-order primitives, we introduce a notion of polynomial quasi-interpretations, coupled with a simple termination  ...  In this paper, we extend this approach to the higher-order setting.  ...  Higher-Order Polynomial Interpretations We want to demonstrate how first-order rewriting-based techniques for ICC can be adapted to the higher-order setting.  ... 
doi:10.1016/j.ic.2015.12.008 fatcat:dhl3e24oofe2fpd5b23auqmvga
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