A categorical interpretation of partial function logic and Hoare logic

2005 ◽  
pp. 229-240
Author(s):  
P. M. W. Knijnenburg ◽  
F. Nordemann
Keyword(s):  
Partial Function ◽  
Hoare Logic

Partial hyperdoctrines: categorical models for partial function logic and Hoare logic

1994 ◽  
Vol 4 (2) ◽  
pp. 117-146
Author(s):  
Peter Knijnenburg ◽  
Frank Nordemann
Keyword(s):  
Programming Language ◽  
Partial Function ◽  
Hoare Logic ◽  
Weakest Precondition ◽  
First Order ◽  
Categorical Models ◽  
Intended Use

In this paper we provide a categorical interpretation of the first-order Hoare logic of a small programming language by giving a weakest precondition semantics for the language. To this end, we extend the well-known notion of a (first-order) hyperdoctrine to include partial maps. The most important new aspect of the resulting partial (first-order) hyperdoctrine is a different notion of morphism between the fibres. We also use this partial hyperdoctrine to give a model for Beeson's Partial Function Logic such that (a version of) his axiomatization is complete with respect to this model. This shows the usefulness of the notion, independent of its intended use as a model for Hoare logic.

scholarly journals An Inference System of an Extension of Floyd-Hoare Logic for Partial Predicates

2018 ◽  
Vol 26 (2) ◽  
pp. 159-164
Author(s):  
Ievgen Ivanov ◽  
Artur Korniłowicz ◽  
Mykola Nikitchenko
Keyword(s):  
Input Data ◽  
Partial Function ◽  
Hoare Logic ◽  
Sequential Programs ◽  
Inference System ◽  
Semantic Level ◽  
System 2 ◽  
Partial Predicate ◽  
Partial Predicates ◽  
Post Condition

Summary In the paper we give a formalization in the Mizar system [2, 1] of the rules of an inference system for an extended Floyd-Hoare logic with partial pre- and post-conditions which was proposed in [7, 9]. The rules are formalized on the semantic level. The details of the approach used to implement this formalization are described in [5]. We formalize the notion of a semantic Floyd-Hoare triple (for an extended Floyd-Hoare logic with partial pre- and post-conditions) [5] which is a triple of a pre-condition represented by a partial predicate, a program, represented by a partial function which maps data to data, and a post-condition, represented by a partial predicate, which informally means that if the pre-condition on a program’s input data is defined and true, and the program’s output after a run on this data is defined (a program terminates successfully), and the post-condition is defined on the program’s output, then the post-condition is true. We formalize and prove the soundness of the rules of the inference system [9, 7] for such semantic Floyd-Hoare triples. For reasoning about sequential composition of programs and while loops we use the rules proposed in [3]. The formalized rules can be used for reasoning about sequential programs, and in particular, for sequential programs on nominative data [4]. Application of these rules often requires reasoning about partial predicates representing preand post-conditions which can be done using the formalized results on the Kleene algebra of partial predicates given in [8].

Synthesizing Conjunctive & Disjunctive Linear Invariants by K-means++ and SVM

2020 ◽  
Vol 17 (6) ◽  
pp. 847-856
Author(s):  
Shengbing Ren ◽  
Xiang Zhang
Keyword(s):  
Software Verification ◽  
State Of The Art ◽  
Positive Sample ◽  
Machine Learning Algorithms ◽  
Support Vector ◽  
Hoare Logic ◽  
Excellent Performance ◽  
Automated Software ◽  
Inductive Invariants ◽  
Linear Invariants

The problem of synthesizing adequate inductive invariants lies at the heart of automated software verification. The state-of-the-art machine learning algorithms for synthesizing invariants have gradually shown its excellent performance. However, synthesizing disjunctive invariants is a difficult task. In this paper, we propose a method k++ Support Vector Machine (SVM) integrating k-means++ and SVM to synthesize conjunctive and disjunctive invariants. At first, given a program, we start with executing the program to collect program states. Next, k++SVM adopts k-means++ to cluster the positive samples and then applies SVM to distinguish each positive sample cluster from all negative samples to synthesize the candidate invariants. Finally, a set of theories founded on Hoare logic are adopted to check whether the candidate invariants are true invariants. If the candidate invariants fail the check, we should sample more states and repeat our algorithm. The experimental results show that k++SVM is compatible with the algorithms for Intersection Of Half-space (IOH) and more efficient than the tool of Interproc. Furthermore, it is shown that our method can synthesize conjunctive and disjunctive invariants automatically

A Hoare Logic for GPU Kernels

2017 ◽  
Vol 18 (1) ◽  
pp. 1-43 ◽  
Author(s):  
Kensuke Kojima ◽  
Atsushi Igarashi
Keyword(s):  
Hoare Logic

scholarly journals Deriving a Floyd–Hoare logic for non-local jumps from a formulæ-as-types notion of control

2012 ◽  
Vol 81 (3) ◽  
pp. 181-208 ◽  
Author(s):  
T. Crolard ◽  
E. Polonowski
Keyword(s):  
Hoare Logic ◽  
Non Local

A note on the complexity of propositional Hoare logic

2000 ◽  
Vol 1 (1) ◽  
pp. 171-174 ◽  
Author(s):  
Ernie Cohen ◽  
Dexter Kozen
Keyword(s):  
Hoare Logic

Soundness of Hoare logic

2014 ◽  
pp. 25-32
Author(s):  
Andrew W. Appel ◽  
Robert Dockins ◽  
Aquinas Hobor ◽  
Lennart Beringer ◽  
Josiah Dodds ◽  
...  
Keyword(s):  
Hoare Logic

scholarly journals Hoare Logic for Realistically Modelled Machine Code

2007 ◽  
pp. 568-582 ◽  
Author(s):  
Magnus O. Myreen ◽  
Michael J. C. Gordon
Keyword(s):  
Hoare Logic ◽  
Machine Code
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