scholarly journals Removing Algebraic Data Types from Constrained Horn Clauses Using Difference Predicates

2020 ◽  
pp. 83-102
Author(s):  
Emanuele De Angelis ◽  
Fabio Fioravanti ◽  
Alberto Pettorossi ◽  
Maurizio Proietti
Keyword(s):  
Data Types ◽  
Horn Clauses ◽  
Algebraic Data Types

scholarly journals Solving constrained Horn clauses modulo algebraic data types and recursive functions

2022 ◽  
Vol 6 (POPL) ◽  
pp. 1-29
Author(s):  
Hari Govind V K ◽  
Sharon Shoham ◽  
Arie Gurfinkel
Keyword(s):  
Data Structures ◽  
General Class ◽  
Data Types ◽  
Deductive Verification ◽  
Recursive Definition ◽  
Underlying Theory ◽  
Horn Clauses ◽  
Verification Conditions ◽  
Algebraic Data Types ◽  
Inductive Invariants

This work addresses the problem of verifying imperative programs that manipulate data structures, e.g., Rust programs. Data structures are usually modeled by Algebraic Data Types (ADTs) in verification conditions. Inductive invariants of such programs often require recursively defined functions (RDFs) to represent abstractions of data structures. From the logic perspective, this reduces to solving Constrained Horn Clauses (CHCs) modulo both ADT and RDF. The underlying logic with RDFs is undecidable. Thus, even verifying a candidate inductive invariant is undecidable. Similarly, IC3-based algorithms for solving CHCs lose their progress guarantee: they may not find counterexamples when the program is unsafe. We propose a novel IC3-inspired algorithm Racer for solving CHCs modulo ADT and RDF (i.e., automatically synthesizing inductive invariants, as opposed to only verifying them as is done in deductive verification). Racer ensures progress despite the undecidability of the underlying theory, and is guaranteed to terminate with a counterexample for unsafe programs. It works with a general class of RDFs over ADTs called catamorphisms. The key idea is to represent catamorphisms as both CHCs, via relationification , and RDFs, using novel abstractions . Encoding catamorphisms as CHCs allows learning inductive properties of catamorphisms, as well as preserving unsatisfiabilty of the original CHCs despite the use of RDF abstractions, whereas encoding catamorphisms as RDFs allows unfolding the recursive definition, and relying on it in solutions. Abstractions ensure that the underlying theory remains decidable. We implement our approach in Z3 and show that it works well in practice.

DERIVING AND SCHEDULING COMMUNICATION OPERATIONS FOR GENERIC SKELETON IMPLEMENTATIONS

2005 ◽  
Vol 15 (03) ◽  
pp. 337-352 ◽  
Author(s):  
THOMAS NITSCHE
Keyword(s):  
Iterative Solution ◽  
Synchronous Communication ◽  
Data Types ◽  
Communication Scheduling ◽  
Overlapping Data ◽  
Abstract Notion ◽  
Algebraic Data Types ◽  
Data Elements ◽  
Communication Operations

Data distributions are an abstract notion for describing parallel programs by means of overlapping data structures. A generic data distribution layer serves as a basis for implementing specific data distributions over arbitrary algebraic data types and arrays as well as generic skeletons. The necessary communication operations for exchanging overlapping data elements are derived automatically from the specification of the overlappings. This paper describes how the communication operations used internally by the generic skeletons are derived, especially for the asynchronous and synchronous communication scheduling. As a case study, we discuss the iterative solution of PDEs and compare a hand-coded MPI version with a skeletal one based on overlapping data distributions.

scholarly journals Stratified type inference for generalized algebraic data types

2006 ◽  
Vol 41 (1) ◽  
pp. 232-244 ◽  
Author(s):  
François Pottier ◽  
Yann Régis-Gianas
Keyword(s):  
Type Inference ◽  
Data Types ◽  
Algebraic Data Types

A fresh look at binary search trees

2002 ◽  
Vol 12 (6) ◽  
pp. 601-607 ◽  
Author(s):  
RALF HINZE
Keyword(s):  
Binary Search ◽  
Binary Search Trees ◽  
Search Trees ◽  
Data Types ◽  
Code Size ◽  
Introductory Computer Science ◽  
Functional Formulation ◽  
Algebraic Data Types ◽  
Science Classes ◽  
Programming Courses

Binary search trees are old hat, aren't they? Search trees are routinely covered in introductory computer science classes and they are widely used in functional programming courses to illustrate the benefits of algebraic data types and pattern matching. And indeed, the operation of insertion enjoys a succinct and elegant functional formulation. Figure 1 contains the six-liner given in the language Haskell 98.Alas, both succinctness and elegance are lost when it comes to implementing the dual operation of deletion, also shown in figure 1. Two additional helper functions are required causing the code size to double in comparison with insertion.

scholarly journals The ins and outs of Clean I/O

1995 ◽  
Vol 5 (1) ◽  
pp. 81-110 ◽  
Author(s):  
Peter Achten ◽  
Rinus Plasmeijer
Keyword(s):  
Programming Languages ◽  
Programming Language ◽  
Functional Programming ◽  
Data Types ◽  
Spreadsheet Program ◽  
Functional Programming Languages ◽  
Hard Time ◽  
Functional Programming Language ◽  
Algebraic Data Types ◽  
High Level

AbstractFunctional programming languages have banned assignment because of its undesirable properties. The reward of this rigorous decision is that functional programming languages are side-effect free. There is another side to the coin: because assignment plays a crucial role in Input/Output (I/O), functional languages have a hard time dealing with I/O. Functional programming languages have therefore often been stigmatised as inferior to imperative programming languages because they cannot deal with I/O very well. In this paper, we show that I/O can be incorporated in a functional programming language without loss of any of the generally accepted advantages of functional programming languages. This discussion is supported by an extensive account of the I/O system offered by the lazy, purely functional programming language Clean. Two aspects that are paramount in its I/O system make the approach novel with respect to other approaches. These aspects are the technique of explicit multiple environment passing, and the Event I/O framework to program Graphical User I/O in a highly structured and high-level way. Clean file I/O is as powerful and flexible as it is in common imperative languages (one can read, write, and seek directly in a file). Clean Event I/O provides programmers with a high-level framework to specify complex Graphical User I/O. It has been used to write applications such as a window-based text editor, an object based drawing program, a relational database, and a spreadsheet program. These graphical interactive programs are completely machine independent, but still obey the look-and-feel of the concrete window environment being used. The specifications are completely functional and make extensive use of uniqueness typing, higher-order functions, and algebraic data types. Efficient implementations are present on the Macintosh, Sun (X Windows under Open Look) and PC (OS/2).

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