A. David-basin, W. Fokkink, S. Merz, A. Middeldorp, T. Nipkow et al., We are grateful to the FroCoS 2017 program chairs, Clare Dixon and Marcelo Finger, and to the program committee for giving us this opportunity to present our research. We are also indebted to Andreas Abel, Daniel Wand, and Makarius Wenzel, and to dozens of anonymous reviewers (including those who rejected our manuscript " Witnessing (co)datatypes " [18] six times

P. Kun?ar and . Were, Security Type Systems and Deduction " (NI 491/13-2 and NI 491/13-3) as part of the program Reliably Secure Software Systems (RS 3 , priority program 1496) Kun?ar was also supported by the DFG project Integration der Logik HOL mit den Programmiersprachen ML und Haskell " (NI 491/10-2). Lochbihler was supported by the Swiss National Science Foundation (SNSF) grant " Formalising Computational Soundness for Protocol Implementations VOWS: Verification of Web-based Systems, Popescu was supported by the UK Engineering and Physical Sciences Research Council (EPSRC) starting grant Sternagel and Thiemann were supported by the Austrian Science Fund (FWF)

F. Bartels, Generalised coinduction, Mathematical Structures in Computer Science, vol.13, issue.2, pp.321-348, 2003.
DOI : 10.1017/S0960129502003900
URL : http://doi.org/10.1016/s1571-0661(04)80903-4

H. Becker, J. C. Blanchette, U. Waldmann, and D. Wand, Formalization of Knuth?Bendix orders for lambda-free higher-order terms Formal proof development, Archive of Formal Proofs, 2016.

H. Becker, J. C. Blanchette, U. Waldmann, and D. Wand, A Transfinite Knuth???Bendix Order for Lambda-Free Higher-Order Terms, CADE-26, 2017.
DOI : 10.1016/j.jsc.2014.09.033

S. Berghofer and M. Wenzel, Inductive Datatypes in HOL ??? Lessons Learned in Formal-Logic Engineering, TPHOLs '99, pp.19-36, 1999.
DOI : 10.1007/3-540-48256-3_3
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.22.7659

Y. Bertot and P. Casteran, Interactive Theorem Proving and Program Development?Coq'Art: The Calculus of Inductive Constructions, Texts in Theoretical Computer Science, 2004.
URL : https://hal.archives-ouvertes.fr/hal-00344237

J. C. Blanchette, Relational analysis of (co)inductive predicates, (co)algebraic datatypes, and (co)recursive functions, Software Quality Journal, vol.20, issue.1, pp.101-126, 2013.
DOI : 10.1007/978-3-662-22646-9
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.190.1514

J. C. Blanchette, M. Fleury, and D. Traytel, Nested multisets, hereditary multisets, and syntactic ordinals in Isabelle/HOL, FSCD 2017. LIPIcs Schloss Dagstuhl?Leibniz-Zentrum für Informatik, pp.1-1117, 2017.

J. C. Blanchette and T. Nipkow, Nitpick: A Counterexample Generator for Higher-Order Logic Based on a Relational Model Finder, ITP 2010, pp.131-146, 2010.
DOI : 10.1007/978-3-642-14052-5_11

J. C. Blanchette, A. Popescu, and D. Traytel, Soundness and Completeness Proofs by Coinductive Methods, Journal of Automated Reasoning, vol.20, issue.3, pp.149-179, 2017.
DOI : 10.1017/CBO9781139168717

J. C. Blanchette, A. Bouzy, A. Lochbihler, A. Popescu, and D. Traytel, Friends with Benefits, ESOP 2017, pp.111-140, 2017.
DOI : 10.1016/0304-3975(91)90043-2
URL : https://hal.archives-ouvertes.fr/hal-01401812

J. C. Blanchette, M. Fleury, and D. Traytel, Formalization of nested multisets, hereditary multisets, and syntactic ordinals. Archive of Formal Proofs Formal proof development, 2016.

J. C. Blanchette, J. Hölzl, A. Lochbihler, L. Panny, A. Popescu et al., Truly Modular (Co)datatypes for Isabelle/HOL, ITP 2014, pp.93-110, 2014.
DOI : 10.1007/978-3-319-08970-6_7

J. C. Blanchette, F. Meier, A. Popescu, and D. Traytel, Foundational nonuniform (Co)datatypes for higher-order logic, 2017 32nd Annual ACM/IEEE Symposium on Logic in Computer Science (LICS), 2017.
DOI : 10.1109/LICS.2017.8005071

J. C. Blanchette, A. Popescu, and D. Traytel, Abstract completeness Formal proof development, Archive of Formal Proofs, 2014.

J. C. Blanchette, A. Popescu, and D. Traytel, Cardinals in Isabelle/HOL, ITP 2014, pp.111-127, 2014.
DOI : 10.1007/978-3-319-08970-6_8
URL : http://eprints.mdx.ac.uk/15164/2/card.pdf

J. C. Blanchette, A. Popescu, and D. Traytel, Unified Classical Logic Completeness, IJCAR 2014, pp.46-60, 2014.
DOI : 10.1007/978-3-319-08587-6_4

J. C. Blanchette, A. Popescu, and D. Traytel, Foundational extensible corecursion?A proof assistant perspective, ICFP '15, pp.192-204, 2015.
DOI : 10.1145/2858949.2784732
URL : https://hal.archives-ouvertes.fr/hal-01212589

J. C. Blanchette, A. Popescu, and D. Traytel, Witnessing (Co)datatypes, ESOP 2015, pp.359-382, 2015.
DOI : 10.1007/978-3-662-46669-8_15
URL : https://hal.archives-ouvertes.fr/hal-01212587

L. Bulwahn, A. Krauss, and T. Nipkow, Finding Lexicographic Orders for Termination Proofs in Isabelle/HOL, TPHOLs 2007, pp.38-53, 2007.
DOI : 10.1007/978-3-540-74591-4_5

N. Dershowitz and Z. Manna, Proving termination with multiset orderings, Communications of the ACM, vol.22, issue.8, pp.465-476, 1979.
DOI : 10.1145/359138.359142
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.145.8728

K. Gödel, Über die Vollständigkeit des Logikkalküls, 1929.

E. L. Gunter, Why We Can't have SML Style datatype Declarations in HOL, IFIP Transactions, vol.20, pp.561-568, 1993.
DOI : 10.1016/B978-0-444-89880-7.50042-5

R. Hinze and R. Paterson, Finger trees: a simple general-purpose data structure, Journal of Functional Programming, vol.16, issue.02, pp.197-217, 2006.
DOI : 10.1017/S0956796805005769

J. Hölzl, Markov chains and Markov decision processes in Isabelle/HOL

J. Hölzl, Markov processes in Isabelle/HOL, pp.100-111, 2017.

B. Huffman and O. Kun?ar, Lifting and Transfer: A Modular Design for Quotients in Isabelle/HOL, CPP 2013, pp.131-146, 2013.
DOI : 10.1007/978-3-319-03545-1_9

S. C. Kleene, Mathematical Logic, 1967.

L. Kovács, S. Robillard, and A. Voronkov, Coming to terms with quantified reasoning, POPL 2017, pp.260-270, 2017.

A. Krauss, Partial Recursive Functions in Higher-Order Logic, IJCAR 2006, pp.589-603, 2006.
DOI : 10.1007/11814771_48
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.93.5387

A. Lochbihler, Jinja with threads Archive of Formal Proofs, 2007.

A. Lochbihler, Verifying a Compiler for Java Threads, ESOP 2010, pp.427-447, 2010.
DOI : 10.1007/978-3-642-11957-6_23
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.496.8823

A. Lochbihler, Making the java memory model safe, ACM Transactions on Programming Languages and Systems, vol.35, issue.4, pp.1-65, 2014.
DOI : 10.1145/2518191

A. Lochbihler, Probabilistic Functions and Cryptographic Oracles in Higher Order Logic, ESOP 2016, pp.503-531, 2016.
DOI : 10.1145/99370.99404

A. Lochbihler and J. Hölzl, Recursive Functions on Lazy Lists via Domains and Topologies, ITP 2014, pp.341-357, 2014.
DOI : 10.1007/978-3-319-08970-6_22

F. Meier, Non-Uniform Datatypes in Isabelle, 2016.

S. Milius, L. S. Moss, and D. Schwencke, Abstract GSOS Rules and a Modular Treatment of Recursive Definitions, Logical Methods in Computer Science, vol.9, issue.3, 2013.
DOI : 10.2168/LMCS-9(3:28)2013

L. De-moura and N. Bjørner, Z3: An Efficient SMT Solver, TACAS 2008, pp.337-340, 2008.
DOI : 10.1007/978-3-540-78800-3_24

C. Okasaki, Purely functional data structures, 1999.
DOI : 10.1017/CBO9780511530104

L. Panny, Primitively (Co)recursive Function Definitions for Isabelle, 2014.

A. Reynolds and J. C. Blanchette, A Decision Procedure for (Co)datatypes in SMT Solvers, Journal of Automated Reasoning, vol.34, issue.3, pp.341-362, 2017.
DOI : 10.1007/s10817-005-5204-9
URL : https://hal.archives-ouvertes.fr/hal-01212585

J. C. Reynolds, Types, abstraction and parametric polymorphism. In: IFIP '83, pp.513-523, 1983.

J. J. Rutten, Automata and coinduction (an exercise in coalgebra), CONCUR '98, pp.194-218, 1998.
DOI : 10.1007/BFb0055624
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.221.6957

A. Schropp and A. Popescu, Nonfree Datatypes in Isabelle/HOL, CPP 2013, pp.114-130, 2013.
DOI : 10.1007/978-3-319-03545-1_8

C. Sternagel and R. Thiemann, Deriving Comparators and Show Functions in Isabelle/HOL, ITP 2015, pp.421-437, 2015.
DOI : 10.1007/978-3-319-22102-1_28

C. Sternagel and R. Thiemann, Deriving class instances for datatypes, Archive of Formal Proofs, 2015.

R. Thiemann and C. Sternagel, Certification of Termination Proofs Using CeTA, TPHOLs 2009, pp.452-468, 2009.
DOI : 10.1007/978-3-540-25979-4_6
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.212.9460

E. Torlak and D. Jackson, Kodkod: A Relational Model Finder, TACAS 2007, pp.632-647, 2007.
DOI : 10.1007/978-3-540-71209-1_49
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.697.8573

D. Traytel, Formal languages, formally and coinductively, FSCD 2016. LIPIcs, pp.1-31, 2016.

D. Traytel, A. Popescu, and J. C. Blanchette, Foundational, Compositional (Co)datatypes for Higher-Order Logic: Category Theory Applied to Theorem Proving, 2012 27th Annual IEEE Symposium on Logic in Computer Science, pp.596-605, 2012.
DOI : 10.1109/LICS.2012.75
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.221.844

D. Traytel, A Category Theory Based (Co)datatype Package for Isabelle, 2012.

M. Wenzel, Isabelle/Isar?A generic framework for human-readable proof documents From Insight to Proof: Festschrift in Honour of Andrzej Trybulec, Studies in Logic, Grammar, and Rhetoric, 2007.

M. Wenzel, Re: [isabelle] " Unfolding " the sum-of-products encoding of datatypes (2015), https