@INPROCEEDINGS{Hanus24APLAS,
author    = "Hanus, M.",
title     = "Hybrid Verification of Declarative Programs with Arithmetic Non-fail Conditions",
year      = "2024",
pages     = "109-129",
booktitle = "Proc. of the 22nd Asian Symposium on Programming Languages
             and Systems (APLAS 2024)}",
publisher = {Springer LNCS 15194},
doi       = {10.1007/978-981-97-8943-6\_6},
abstract = {
Functions containing arithmetic operations have often restrictions
not expressible by standard type systems of programming languages.
The division operation requires that the divisor is non-zero
and the factorial function should not be applied to negative numbers.
Such partial operations might lead to program crashes
if they are applied to unintended arguments.
Checking the arguments before each call is tedious and decreases
the run-time efficiency.
To avoid these disadvantages and support the safe use of partially
defined operations, we present an approach to verify
the correct use of operations at compile time.
To simplify its use, our approach automatically infers
non-fail conditions of operations from their definitions
and checks whether these conditions are satisfied for all uses
of the operations.
Arithmetic conditions can be verified by SMT solvers,
whereas conditions in operations defined on algebraic data types
can be inferred and verified by appropriate type abstractions.
Therefore, we present a hybrid method which is applicable
to larger programs since only a few arithmetic non-fail conditions
need to be checked by an external SMT solver.
This approach is implemented for functional logic Curry programs
so that it is also usable for purely functional or logic programs.
}
}