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Verifying Higher-Order Functions with Tree Automata [chapter]

Thomas Genet, Timothée Haudebourg, Thomas Jensen
2018 Lecture Notes in Computer Science  
This paper describes a fully automatic technique for verifying safety properties of higher-order functional programs.  ...  We identify a subclass of higher-order functional programs for which the completion is guaranteed to terminate.  ...  The use of abstract interpretation for verifying higher-order functional programs has comparatively received less attention.  ... 
doi:10.1007/978-3-319-89366-2_31 fatcat:twn4gzf7vfextngvzojzdkkdbi

TravMC2: higher-order model checking for alternating parity tree automata

Robin P. Neatherway, C.-H. Luke Ong
2014 Proceedings of the 2014 International SPIN Symposium on Model Checking of Software - SPIN 2014  
Higher-order model checking is the problem of model checking (possibly) infinite trees generated by higher-order recursion schemes (HORS).  ...  Building on our previous work, we present a higher-order model checker, TRAVMC2, which supports properties specified using alternating parity tree automata (or equivalently monadic second order logic).  ...  INTRODUCTION Model checking has been applied with great success to first-order imperative programs, but only recently has started to gain traction in the verification of higher-order functional programs  ... 
doi:10.1145/2632362.2632381 dblp:conf/spin/NeatherwayO14 fatcat:23hdd6axrrbg5ox6qpqqvrqvgi

Automata-Based Abstraction for Automated Verification of Higher-Order Tree-Processing Programs [chapter]

Yuma Matsumoto, Naoki Kobayashi, Hiroshi Unno
2015 Lecture Notes in Computer Science  
By combining them with higher-order model checking, we can construct a fully-automated verification tool for higher-order, treeprocessing functional programs.  ...  Higher-order model checking has been recently applied to automated verification of higher-order functional programs, but there have been difficulties in dealing with algebraic data types such as lists  ...  Thus, with a suitable abstraction of data, we can verify functional programs fully automatically by using higher-order model checking. For example, Kobayashi et al.  ... 
doi:10.1007/978-3-319-26529-2_16 fatcat:trwl6pik6rflbay6iotkx2ui7a

Higher-Order Model Checking: From Theory to Practice

Naoki Kobayashi
2011 2011 IEEE 26th Annual Symposium on Logic in Computer Science  
From a practical perspective, higher-order model checking provides a foundation for software model checkers for functional programming languages such as ML and Haskell.  ...  The model checking of higher-order recursion schemes (higher-order model checking for short) has been actively studied in the last decade, and has seen significant progress in both theory and practice.  ...  The class of trees generated by safe higher-order recursion schemes coincides with those generated by higher-order pushdown automata [20] and also with the class of trees in Caucal hierarchy [7] .  ... 
doi:10.1109/lics.2011.15 dblp:conf/lics/Kobayashi11 fatcat:uc23ml5ekbc23ojg3herppprdq

Recognizability in the Simply Typed Lambda-Calculus [chapter]

Sylvain Salvati
2009 Lecture Notes in Computer Science  
Using intersection types, we generalize the notions of automata for strings and trees so as to grasp recognizability for λ-terms.  ...  We define a notion of recognizable sets of simply typed λterms that extends the notion of recognizable sets of strings or trees. This definition is based on finite models.  ...  Higher order matching The γ-higher-order matching problem (γ-HOM), with γ ∈ {β; βη}, consists in solving an equation of the form M ? = γ N where N is a closed term.  ... 
doi:10.1007/978-3-642-02261-6_5 fatcat:z2n4kdoccrbuvdojryja5ag7ma

Learning Formulas in Finite Variable Logics [article]

Paul Krogmeier, P. Madhusudan
2021 arXiv   pre-print
of queries and terms with recursively-defined functions.  ...  We also establish positive results using our technique for other logics and variants of the learning problem, including first-order logic with least fixed point definitions, higher-order logics, and synthesis  ...  The same idea sketched above easily extends to logics with variables over higher-order functions. RELATED WORK Program Synthesis from Examples.  ... 
arXiv:2111.03534v2 fatcat:x6varjwstnhcjmc6mml4cgdxri

Automated techniques for higher-order program verification

Naoki KOBAYASHI, Luke ONG, David Van HORN
2013 Progress in Informatics  
automata have yielded model checkers for higher-order functional programs.  ...  The workshop also aimed for cross-fertilization of different techniques for higher-order program verification, such as game semantics, type theories, higher-order grammars and pushdown systems, control  ...  A prototype verifier for higher-order functional programs is also demonstrated.  ... 
doi:10.2201/niipi.2013.10.9 fatcat:xqfyvx6m25d4jcodwl373vlxlq

Higher-Order Model Checking: An Overview

Luke Ong
2015 2015 30th Annual ACM/IEEE Symposium on Logic in Computer Science  
Because the trees generated by recursion schemes are computation trees of higher-order functional programs, higherorder model checking provides a foundation for model checkers of such programming languages  ...  Advances have been made in determining the expressive power of recursion schemes and other higher-order families of generators, automata-theoretic characterisations of these generator families, and the  ...  It is important to extend these algorithms to model check the computation trees of higher-type functional programs, which are trees with λ-binders i.e. higher-type Böhm trees.  ... 
doi:10.1109/lics.2015.9 dblp:conf/lics/Ong15 fatcat:55bfxqlkuzhbtgmzc32m46ooku

VERIFICATION OF CONGESTION CONTROL PROTOCOL IN VANETs USING FORMAL METHOD

Ayana S, Shimmi Asokan.
2016 International Journal of Advanced Research  
The model was verified against reachability, safety and liveness properties to analyze the reliability and functional aspects of the protocol.  ...  In this work we focused on formally verifying congestion control protocol in VANETs using model checking technique. The protocol was formally modeled using a network of timed automata.  ...  In order to verify the protocol, UPPAAL framework was used. The protocol was modeled using a network of timed automata.  ... 
doi:10.21474/ijar01/1682 fatcat:kf4z6g7gb5gfjgizhocd5q56he

Extending Timbuk to Verify Functional Programs [chapter]

Thomas Genet, Tristan Gillard, Timothée Haudebourg, Sébastien Lê Cong
2018 Lecture Notes in Computer Science  
In this paper we present two extensions of Timbuk which permit us to automatically verify safety properties on functional programs.  ...  Timbuk implements the Tree Automata Completion algorithm whose purpose is to over-approximate sets of terms reachable by a term rewriting system.  ...  From a theoretical perspective, Tree Automata Completion can be seen as an alternative to well-established higher-order model-checking techniques like PMRS [21] or HORS [19] to verify higher-order  ... 
doi:10.1007/978-3-319-99840-4_9 fatcat:4suu76ksvfaxzoyzk5quung6ka

Compile-Time Debugging of C Programs Working on Trees [chapter]

Jacob Elgaard, Anders Møller, Michael I. Schwartzbach
2000 Lecture Notes in Computer Science  
We exhibit a technique for automatically verifying the safety of simple C programs working on tree-shaped data structures.  ...  This extension of MONA defines the new WSRT logic together with its decision procedure.  ...  First-order terms are built from first-order variables and the special WSRT functions: tree root(x) which evaluates to the root of the tree denoted by x; and succ(t, T, v, c) which, provided that the first-order  ... 
doi:10.1007/3-540-46425-5_8 fatcat:amito2ij7fholctghqw4q3mzgi

Syntax-Tree Regular Expression Based DFA FormalConstruction

Nazir Ahmad Zafar, Fawaz Alsaade
2012 Intelligent Information Management  
In next, the transition diagram is described from the follow positions and converted into deterministic finite automata by defining a relationship among syntax tree, transition diagram and DFA.  ...  Compiler is a program whose functionality is to translate a computer program written in source language into an equivalent machine code.  ...  Formal specification is a description of a system using mathematical notations and abstract models in terms of set theory and first order or higher order logic.  ... 
doi:10.4236/iim.2012.44021 fatcat:pnn76dixeffypocegygf5zfwum

Page 6562 of Mathematical Reviews Vol. , Issue 2000i [page]

2000 Mathematical Reviews  
With this approach and by introducing counters called step functions, efficiency measures for probabilistic pro- grams can be formally specified and verified.  ...  Rabin showed that a set 7 of trees can be expressed in WS2S if and only if both 7 and its comple- ment can be recognized by nondeterministic Biichi tree automata. For the ‘only if?  ... 

Recursion Schemes, Collapsible Pushdown Automata and Higher-Order Model Checking [chapter]

Luke Ong
2013 Lecture Notes in Computer Science  
We conclude with a brief overview of recent applications to the model checking of higher-order functional programs.  ...  Collapsible pushdown automata are a generalisation of pushdown automata to higher-order stacks -which are iterations of stack of stacks -that contain symbols equipped with links.  ...  The Hierarchy of Higher-Order Pushdown Trees Fix a ranked alphabet Σ with m : = max { ar(f ) | f ∈ Σ }.  ... 
doi:10.1007/978-3-642-37064-9_3 fatcat:vmzogjyskfahbeklhyssyajvuy

Verification of Tree-Processing Programs via Higher-Order Model Checking [chapter]

Hiroshi Unno, Naoshi Tabuchi, Naoki Kobayashi
2010 Lecture Notes in Computer Science  
We propose a new method to verify that a higher-order, treeprocessing functional program conforms to an input/output specification.  ...  Unlike previous methods, our new method can deal with arbitrary higher-order functional programs manipulating algebraic data structures, as long as certain invariants on intermediate data structures are  ...  In essence, EHMTTs are higher-order, simply-typed functional programs with recursion and tree primitives.  ... 
doi:10.1007/978-3-642-17164-2_22 fatcat:s3nawjsdsreqnehsyxzspq7cfa
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