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Programming in Equational Logic: Beyond Strong Sequentiality

R.C. Sekar, I.V. Ramakrishnan
1993 Information and Computation  
Orthogonal term rewriting systems (also known as regular systems) provide an elegant framework for programming in equational logic.  ...  However, this algorithm required the input programs to be restricted to the subclass of strongly sequential systems.  ...  Introduction Equational logic programming is a style of declarative programming in which systems of oriented equations (called rewrite rules) of the form l !  ... 
doi:10.1006/inco.1993.1026 fatcat:fgjmffkbpngjvbvpfxy2yfuj44

Term-rewriting implementation of equational logic programming [chapter]

Michael J. O'Donnell
1987 Lecture Notes in Computer Science  
Such a view leads to the following schema for Logic Programming. A program is a set of assertions in some logical language.  ...  In 1975 I started a small project to explore the consequences of implementing equational programs with no semantic compromises.  ...  Sufficient relaxation of the nonoverlapping restriction will allow programming techniques that go well beyond those available in the regular systems of equations.  ... 
doi:10.1007/3-540-17220-3_1 fatcat:xq7v3m2nmzdb3cjh7bdygcv4ze

Specialization of inductively sequential functional logic programs

María Alpuente, Michael Hanus, Salvador Lucas, Germán Vidal
1999 SIGPLAN notices  
In this paper, we define a partial evaluator for inductively sequential functional logic programs.  ...  We prove strong correctness of this partial evaluator and show that the nice properties of inductively sequential programs carry over to the specialization process and the specialized programs.  ...  Theorem 4.16 (strong correctness) Let R be an inductively sequential program.  ... 
doi:10.1145/317765.317910 fatcat:4wudshh6off27d2wugucpnj37m

Specialization of inductively sequential functional logic programs

María Alpuente, Michael Hanus, Salvador Lucas, Germán Vidal
1999 Proceedings of the fourth ACM SIGPLAN international conference on Functional programming - ICFP '99  
In this paper, we define a partial evaluator for inductively sequential functional logic programs.  ...  We prove strong correctness of this partial evaluator and show that the nice properties of inductively sequential programs carry over to the specialization process and the specialized programs.  ...  Theorem 4.16 (strong correctness) Let R be an inductively sequential program.  ... 
doi:10.1145/317636.317910 dblp:conf/icfp/AlpuenteHLV99 fatcat:ms64h4f6cjhp7me4a2vzrwd4hu

Logics of Dynamical Systems

Andre Platzer
2012 2012 27th Annual IEEE Symposium on Logic in Computer Science  
In discrete dynamical systems, the state evolves in discrete steps, one step at a time, as described by a difference equation or discrete state transition relation.  ...  In continuous dynamical systems, the state evolves continuously along a function, typically described by a differential equation.  ...  The logic dL is a strong logical foundation for hybrid systems.  ... 
doi:10.1109/lics.2012.13 dblp:conf/lics/Platzer12 fatcat:uyo3s7frizgt7d2haga3yylifa

Functional logic programming

Sergio Antoy, Michael Hanus
2010 Communications of the ACM  
Last but not least, programming in a functional logic language is fun.  ...  Earlier, the equation was verified, whereas in the case the equation is solved for xs and ys.  ... 
doi:10.1145/1721654.1721675 fatcat:3jer6iphojcmxmkjh7sv4kdaeu

Logic Functions and Equations [chapter]

Christian Posthoff, Bernd Steinbach
2004 Logic Functions and Equations  
Calculate all test patterns for the selected sensible path x 2 − g 4 − h 3 − g 2 − g 1 − y in the circuit of Fig. 7 .16 on page 190 designed in Section 3. using the bi-decomposition. Practical tasks:  ...  The disadvantage of the method of the sensible path is that in many cases no test pattern can be found, although for each gate connection on the path both stuck-at-0 and stuck-at-1 test patterns exist.  ...  Exercise 8.5 (Behavior of a Sequential Circuit Based on a System of Logic Equations). Calculate the behavior of the sequential circuit given in Fig. 8. 2.  ... 
doi:10.1007/978-1-4020-2938-7_2 fatcat:6revlpw5izhjlgomr27hqdlama

Evaluation strategies for functional logic programming

Sergio Antoy
2005 Journal of symbolic computation  
Recent advances in the foundations and the implementations of functional logic programming languages originate from far-reaching results on narrowing evaluation strategies.  ...  This paper discusses the elements that play a relevant role in evaluation strategies for functional logic computations, describes some important classes of rewrite systems that model functional logic programs  ...  and Programming held in Utrecht, The Netherlands, in May 2001.  ... 
doi:10.1016/j.jsc.2004.12.007 fatcat:swjeqk5wgfaf3nai5v5ufuws7q

Evaluation Strategies for Functional Logic Programming

Sergio Antoy
2001 Electronical Notes in Theoretical Computer Science  
Recent advances in the foundations and the implementations of functional logic programming languages originate from far-reaching results on narrowing evaluation strategies.  ...  This paper discusses the elements that play a relevant role in evaluation strategies for functional logic computations, describes some important classes of rewrite systems that model functional logic programs  ...  and Programming held in Utrecht, The Netherlands, in May 2001.  ... 
doi:10.1016/s1571-0661(04)00265-8 fatcat:zpcju56vxba7dlr5uq4cyr7gma

Equational Logic and Rewriting [chapter]

Claude Kirchner, Hélène Kirchner
2014 Handbook of the History of Logic  
Handbook-History-Logic-Computation-EquationalLogic Handbook-History-Logic-Computation-Rewriting  ...  We focus on equational logic and its relation to rewriting logic and we consider their impact on automated deduction and programming languages.  ...  OBJ is algebraic programming language whose latest versions (OBJ-2 [56] and OBJ-3 [61] ) are based on order-sorted equational logic.  ... 
doi:10.1016/b978-0-444-51624-4.50006-x fatcat:eqtvr66m65eula7otl7fr6ppaa

Differential Dynamic Logic dℒ [chapter]

André Platzer
2010 Logical Analysis of Hybrid Systems  
., the logic where dL formulas are allowed in tests ?χ of hybrid programs and evolution domain restrictions χ of differential equations, when using χ # in place of χ in Fig. 2 .24.  ...  χ inside hybrid programs (and even in evolution domains χ of differential equations).  ...  We prefix each formula in the proof of φ with A and show that this gives a proof of A φ . i∃ is not needed in the proof due to the absence of free logical variables.  ... 
doi:10.1007/978-3-642-14509-4_2 fatcat:awfwcd5vqvc4lhmcfgpysr65bm

A logic of proofs for differential dynamic logic: toward independently checkable proof certificates for dynamic logics

Nathan Fulton, André Platzer
2016 Proceedings of the 5th ACM SIGPLAN Conference on Certified Programs and Proofs - CPP 2016  
from liveness proofs for nondeterministic programs.  ...  Examples include: an unambiguous separation between proof checking and proof search, the ability to extract program traces corresponding to counterexamples, and synthesis of surely-live deterministic programs  ...  We thank the members of the Logical Systems Lab at Carnegie Mellon University for helpful discussions related to this work. We also thank the anonymous reviewers for their suggestions and comments.  ... 
doi:10.1145/2854065.2854078 dblp:conf/cpp/FultonP16 fatcat:srmlvx5csjd5xbdozezl3zwlgm

Functional Logic Programming: From Theory to Curry [chapter]

Michael Hanus
2013 Lecture Notes in Computer Science  
The declarative multi-paradigm language Curry is influenced by recent advances in the foundations and implementation of functional logic languages.  ...  This paper surveys the foundations of functional logic programming that are relevant for Curry, the main features of Curry, and extensions and applications of Curry and functional logic programming.  ...  Acknowledgments I am grateful to Harald Ganzinger who put me on this research track and created a productive research environment in his group that lead to my most important contributions in this area.  ... 
doi:10.1007/978-3-642-37651-1_6 fatcat:bi7s3wzbvbh5xf57gsox7uhhjq

Constructive Game Logic [chapter]

Brandon Bohrer, André Platzer
2020 Lecture Notes in Computer Science  
Of these, we are the first for GL and the first with a proofs-asprograms interpretation for a full first-order program logic. Games in Logic.  ...  We thus develop Constructive Game Logic, which extends Parikh's Game Logic (GL) with constructivity and with first-order programs à la Pratt's first-order dynamic logic (DL).  ...  Like any program logic, reasoning in CGL consists of first applying program-logic rules to decompose a program until the program has been entirely eliminated, then applying first-order logic principles  ... 
doi:10.1007/978-3-030-44914-8_4 fatcat:by5xt6i2g5gi7ds2kebai5otgu

A cost-aware logical framework [article]

Yue Niu
2021 arXiv   pre-print
We present calf, a cost-aware logical framework for studying quantitative aspects of functional programs.  ...  Taking inspiration from recent work that reconstructs traditional aspects of programming languages in terms of a modal account of phase distinctions, we argue that the cost structure of programs motivates  ...  This work was supported in part by AFOSR under grants MURI FA9550-15-1-0053 and FA9550-19-1-0216, in part by the National Science Foundation under award number CCF-1901381, and by AFRL through the NDSEG  ... 
arXiv:2107.04663v2 fatcat:3bit6tz77ff65drvkyiid5zgne
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