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In this paper we extend the model of program variables from the Refinement Calculus  in order to be able to reason more algebraically about recursive procedures with parameters and local variables. ... We give a predicate transformer semantics to recursive procedures with parameters and prove a refinement rule for introduction of recursive procedure calls. ... Our main goal is to be able to reason about recursive procedures so that at any recursive call the procedure parameters are saved (in a stack) and the procedures work with these parameters as if they were ...doi:10.1145/976571.976573 dblp:conf/icfp/BackP03 fatcat:eo2nme3txvdgzazsp3qbmmdhc4
In particular, we demonstrate that recursive procedure declarations and recursive procedure activations are logically disjoint concepts. ... We investigate the origin of recursive procedures in imperative programming languages. ... The first one is that Dijkstra's comments are about 'recursion', whereas Naur speaks of 'recursive procedure activations'. ...doi:10.1093/comjnl/bxu145 fatcat:exsiargadjfktl5ixs4laytrsm
By allowing formulas p and q to place conditions on global procedures, we provide a method for reasoning about programs with calls to global procedures based on hypotheses about procedure inputoutput behavior ... Termination assertions are studied for a programming language which includes local variable declarations, calls to undeclared global procedures, and nondeterministic recursive procedures with call. by-address ... To demonstrate the axiomatizability of termination assertions about programs with recursive procedures with parameters, we have chosen to consider recursive procedures with call-by-value and cal ...doi:10.1145/582153.582188 dblp:conf/popl/MeyerM82 fatcat:e3ur3uqa4vbotbkvyprtfiwokq
However, there are as yet no general methods for reasoning about (mutual) recursive procedures and ancilla quantum data structure in quantum computing (with measurement). ... In particular, two counterexamples for illustrating incompleteness of non-parameterized assertions in verifying recursive procedures, and, one counterexample for showing the failure of reasoning with exact ... Tab. 6) can't be used universally for reasoning about recursive procedures with exact probabilities (even if involving nontermination). Ying's rules revisited. ...arXiv:2107.11679v1 fatcat:eocby6agm5a6bdfhdeufsiv4fu
More specifically, it presents teaching methods to be applied while establishing the notion of recursion in grades 3-8 of primary education, and at the same time it also focuses on various realization ... Info-technology (problem solving with the tools and methods of informatics), a subject matter within informatics, provides outstanding opportunities to reach the aims outlined above. ... The recursive procedure without a parameter: to square_3 forward 100 right 90 square_3 end b. ...doi:10.5485/tmcs.2008.0209 fatcat:2sb3g25k2vfurmiazjkgulr5qy
For example, no account of reasoning about recursive procedures or pointers was given. ... Hoare noted that the above two rules are not sufficient to reason about recursive procedures. ...arXiv:1904.03917v2 fatcat:kfpjuntx35g4vhnkvsnetmkdnm
The program S may declare and use local variables and nondeterministic procedures with call-by-value and call-by-address parameters. In addition, the program may call undeclared global procedures. ... Formulas p and q are first-order formulas extended to express hypotheses about the termination of calls to undeclared procedures. ... We have chosen to consider recursive procedures with call-by-value and callby-address parameters. ...doi:10.1016/s0019-9958(83)80053-9 fatcat:2c3a4pt6b5fwtnomfauaxz5oya
We argue that verification of recursive programs by means of the assertional method of C.A.R. Hoare can be conceptually simplified using a modular reasoning. ... We arrive at recursive programs by adding recursive procedures with call-by-value parameters. ... Procedure calls with parameters are introduced by the grammar rule S ::= P (t 1 , . . . , t n ), where P is a procedure identifier and t 1 , . . . , t n , with n ≥ 0, are expressions called actual parameters ...arXiv:0907.4316v1 fatcat:dzok4sunhjgzfbeoltry73xmsq
It can function as a back-end for reasoning about recursive programs that manipulate algebraic types. ... We have used RADA for reasoning about functional implementations of complex data structures and to reason about guard applications that determine whether XML messages should be allowed to cross network ... Algorithm RADA works based on a semi-decision procedure proposed by Suter et al.  to reason about recursive functions with abstractions. ...doi:10.1145/2491411.2494597 dblp:conf/sigsoft/PhamW13 fatcat:djeajzodsjhezhxdppdipogbkm
Lecture Notes in Computer Science
We argue that verification of recursive programs by means of the assertional method of C.A.R. Hoare can be conceptually simplified using a modular reasoning. ... We arrive at recursive programs by adding recursive procedures with call-by-value parameters. ... Procedure calls with parameters are introduced by the grammar rule S ::= P (t 1 , . . . , t n ), where P is a procedure identifier and t 1 , . . . , t n , with n ≥ 0, are expressions called actual parameters ...doi:10.1007/978-3-642-01748-3_1 fatcat:awzqdmf44na55lm2qay7kaz33q
These constructs include procedures with procedure parameters under standard Algol 60 scope rules and coroutines in a language with parameterless recursive procedures. ... These constructs include procedures with procedure parameters under standard Algol 60 scope rules and coroutines in a language with parameterless recursive procedures. ... formal procedure parameters or names of procedures with no formal procedure parameters. ...doi:10.1098/rsta.1984.0068 fatcat:6t4lqc2uzbeyrjyfsjtgaou6vq
We present a fully implemented interprocedural analysis algorithm that handles recursive procedures. ... A key strength of separation logic is that it facilitates, via explicit expression of structural separation, local reasoning about heap where the effects of altering one part of a data structure are analyzed ... Chapter 4 Truncation Points and Location Reasoning To facilitate reasoning about local updates to recursive data structures, the idea of truncation points (Chapter 2) is introduced to model pointers ...doi:10.1145/1250734.1250764 dblp:conf/pldi/GuoVA07 fatcat:ovl3pyb4p5dzhmudly3rqj4rku
procedure of the parameter estimation. ... The accuracy of the recursive forecasting appeared better than that of forecasting without updating the parameters when the latter were estimated by the data available prior to starting the on- line procedure ...
The coefficients of variation associated with random disturbance errors are generally about 0.5—1.5% for frequency and 5—15% for damping. ... Nonetheless, the T < 7* condition makes impossible the implementation of fixed-base parameter estimation procedures in Stewart and Fenves (1998). ...
The rule combines earlier proof rules for (mutually) recursive procedures with the frame rule for pointer programs. The theory, including the proofs, is implemented in the theorem prover PVS. ... We prove a powerful Hoare total correctness rule for mutually recursive procedures manipulating pointers. ... Acknowledgments We thank Carsten Varming and Lars Birkedal for the discussion about their work on higher-order separation logic and the anonymous referees for their useful comments and suggestions which ...doi:10.1016/j.tcs.2009.05.016 fatcat:34wxxjeuyffwfjzm6u7u5yx3oa
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