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Programming in Equational Logic: Beyond Strong Sequentiality

1993
*
Information and Computation
*

Orthogonal term rewriting systems (also known as regular systems) provide an elegant framework for

doi:10.1006/inco.1993.1026
fatcat:fgjmffkbpngjvbvpfxy2yfuj44
*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 ! ...##
###
Term-rewriting implementation of equational logic programming
[chapter]

1987
*
Lecture Notes in Computer Science
*

Such a view leads to the following schema for

doi:10.1007/3-540-17220-3_1
fatcat:xq7v3m2nmzdb3cjh7bdygcv4ze
*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*. ...##
###
Specialization of inductively sequential functional logic programs

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*. ...

##
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Specialization of inductively sequential functional logic programs

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*. ...

##
###
Logics of Dynamical Systems

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. ...

##
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Functional logic programming

2010
*
Communications of the ACM
*

Last but not least,

doi:10.1145/1721654.1721675
fatcat:3jer6iphojcmxmkjh7sv4kdaeu
*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. ...##
###
Logic Functions and Equations
[chapter]

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

doi:10.1007/978-1-4020-2938-7_2
fatcat:6revlpw5izhjlgomr27hqdlama
*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. ...##
###
Evaluation strategies for functional logic programming

2005
*
Journal of symbolic computation
*

Recent advances

doi:10.1016/j.jsc.2004.12.007
fatcat:swjeqk5wgfaf3nai5v5ufuws7q
*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. ...##
###
Evaluation Strategies for Functional Logic Programming

2001
*
Electronical Notes in Theoretical Computer Science
*

Recent advances

doi:10.1016/s1571-0661(04)00265-8
fatcat:zpcju56vxba7dlr5uq4cyr7gma
*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. ...##
###
Equational Logic and Rewriting
[chapter]

2014
*
Handbook of the History of Logic
*

Handbook-History-

doi:10.1016/b978-0-444-51624-4.50006-x
fatcat:eqtvr66m65eula7otl7fr6ppaa
*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*. ...##
###
Differential Dynamic Logic dℒ
[chapter]

2010
*
Logical Analysis of Hybrid Systems
*

., the

doi:10.1007/978-3-642-14509-4_2
fatcat:awfwcd5vqvc4lhmcfgpysr65bm
*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. ...##
###
A logic of proofs for differential dynamic logic: toward independently checkable proof certificates for dynamic logics

2016
*
Proceedings of the 5th ACM SIGPLAN Conference on Certified Programs and Proofs - CPP 2016
*

from liveness proofs for nondeterministic

doi:10.1145/2854065.2854078
dblp:conf/cpp/FultonP16
fatcat:srmlvx5csjd5xbdozezl3zwlgm
*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. ...##
###
Functional Logic Programming: From Theory to Curry
[chapter]

2013
*
Lecture Notes in Computer Science
*

The declarative multi-paradigm language Curry is influenced by recent advances

doi:10.1007/978-3-642-37651-1_6
fatcat:bi7s3wzbvbh5xf57gsox7uhhjq
*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. ...##
###
Constructive Game Logic
[chapter]

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

doi:10.1007/978-3-030-44914-8_4
fatcat:by5xt6i2g5gi7ds2kebai5otgu
*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 ...##
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A cost-aware logical framework
[article]

2021
*
arXiv
*
pre-print

We present calf, a cost-aware

arXiv:2107.04663v2
fatcat:3bit6tz77ff65drvkyiid5zgne
*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 ...
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