Modules over relative monads for syntax and semantics, MSCS, vol.26, pp.3-37, 2016. ,
URL : https://hal.archives-ouvertes.fr/hal-01329609
Modular specification of monads through higher-order presentations, Proc. 4th ,
URL : https://hal.archives-ouvertes.fr/hal-02307998
, Int. Conf. on Formal Structures for Comp. and Deduction, LIPIcs. Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik, 2019.
Reduction monads and their signatures, 2020. ,
URL : https://hal.archives-ouvertes.fr/hal-02380682
Monads need not be endofunctors, Logical Methods in Computer Science, vol.11, issue.1, 2015. ,
A categorical semantics for inductive-inductive definitions, Proc. 4th Alg. and Coalgebra in Comp. Sci., volume 6859 of LNCS, pp.70-84, 2011. ,
GSOS for probabilistic transition systems: (extended abstract), Coalgebraic Methods in Computer Science, vol.65, issue.1, pp.29-53, 2002. ,
Bisimulation can't be traced, J. ACM, vol.42, issue.1, pp.232-268, 1995. ,
A cellular Howe theorem, Proc. 35th ACM/IEEE Logic in Comp. Sci. ACM, 2020 ,
URL : https://hal.archives-ouvertes.fr/hal-02880876
The differential lambda-calculus, TCS, vol.309, pp.1-41, 2003. ,
URL : https://hal.archives-ouvertes.fr/hal-00150572
Second-order equational logic, Proceedings of the 19th EACSL Annual Conference on Computer Science Logic (CSL 2010), 2010. ,
On the construction of free algebras for equational systems, TCS, vol.410, pp.1704-1729, 2009. ,
Second-order and dependently-sorted abstract syntax, Proc. 23rd Logic in Comp. Sci, pp.57-68, 2008. ,
A congruence rule format for name-passing process calculi from mathematical structural operational semantics, Proc. 21st Logic in Comp. Sci, pp.49-58, 2006. ,
Semantics of name and value passing, Proc. 16th Logic in Comp. Sci, pp.93-104, 2001. ,
Combinatorial structure of type dependency, Journal of Pure and Applied Algebra, vol.219, issue.6, pp.1885-1914, 2015. ,
Term rewriting with variable binding: An initial algebra approach, Proc. 5th Princ. and Practice of Decl. Prog. ACM, 2003. ,
Séquents qu'on calcule: de l'interprétation du calcul des séquents comme calcul de lambda-termes et comme calcul de stratégies gagnantes, 1995. ,
Modules over monads and linearity, WoLLIC, vol.4576, pp.218-237, 2007. ,
Cartesian closed 2-categories and permutation equivalence in higher-order rewriting, LMCS, vol.9, issue.3, p.2013 ,
URL : https://hal.archives-ouvertes.fr/hal-00540205
Signatures and models for syntax and operational semantics in the presence of variable binding, 2019. ,
Call-by-value solvability, RAIRO -Theor. Inf. and Applic, vol.33, issue.6, pp.507-534, 1999. ,
URL : https://hal.archives-ouvertes.fr/hal-00780358
A left adjoint construction related to free triples, JPAA, vol.10, pp.57-71, 1977. ,
The ?-calculus -a theory of mobile processes, 2001. ,
General structural operational semantics through categorical logic, Proc. 23rd Logic in Comp. Sci, pp.166-177, 2008. ,
Towards a mathematical operational semantics, Proc. 12th Logic in Comp. Sci, pp.280-291, 1997. ,
, Lionel Vaux. ?-calcul différentiel et logique classique : interactions calculatoires, 2007.
, At this stage, we can already deduce uniqueness of the desired morphism, T is the initial algebra of ? ? + Id, as a (finitary) endofunctor on [Set, Set] f . By inspecting the colimit of the relevant initial chains, it can be shown that T (1) is the initial algebra of ? ? + Id +1 . Given the data, M has (? ? + Id +1)-algebra structure: the natural transformation Id ? M is merely the composite Id ? T ? M with the unit of T . By initiality, we have a unique (? ? + Id +1)-algebra morphism i : T (1) ? M as functors, such that i ? j = m
, the above adjunction, we get a (? ? + 1)-algebra morphism T (1) ? M , and thus in particular a T -module morphism T (1) ? M . We now apply this recipe to define unary multiterm substitution