[PDF] Top 20 A Classical Sequent Calculus with Dependent Types

... and dependent types Originally created to deepen the connection between programming and logic, dependent types are now a key feature of numerous functional programming ...programming, ... Voir le document complet

... and dependent types Originally created to deepen the connection between programming and logic, dependent types are now a key feature of numerous functional programming ...programming, ... Voir le document complet

... Abstract. Dependent types are a key feature of type systems, typically used in the context of both richly-typed programming languages and proof ...connected with classical logic along ... Voir le document complet

... of a sequent calculus, which we call dLPA ω ...quent calculus presentations of a calculus usually provides good in- termediate steps for CPS translations [9, 22, 23] since they ... Voir le document complet

... of a coinductive defined infinite conjunction ν 0 Xn (∃P(0, y) ∧ X(n + 1)), we cannot afford to pre-evaluate each of its components, and then have to use a lazy call-by-value evaluation ...prove a ... Voir le document complet

... Implicit Calculus of Constructions encompasses some features of Curry-style systems in an otherwise Church-style Calculus of ...Implicit Calculus only structural polymorphism is ...adds a ... Voir le document complet

... as a “call-by- name” calculus and it is its use in computer programming languages that motivated the theoretical study of its more intricate 5 call-by-value counterpart, thanks successively to Plotkin [32], ... Voir le document complet

... is a formal method mainly used in the railway industry to specify and develop safety-critical ...of a B project, one decisive challenge is to show correct a large amount of proof obligations, which ... Voir le document complet

... not a type theory formulated with a typed equality judgement, which makes it hard to define its models [ Miquel 2000 ]Ðwe wish not to go there, but stay within the framework of Martin-Löf Type Theory ... Voir le document complet

... of types is the characterization of retractions in a given logical ...be a difficult problem for the λ-calculus ...of types in usual Linear Logic. Balat and Di Cosmo have given a ... Voir le document complet

... to classical propositional logic: (i) the distribution axiom schema, that now has the form: [α](A → B) → ([α]A → [α]B), for each program α; (ii) modus ponens and the rule of necessitation; and (iii) ... Voir le document complet

... for a higher-order π- ...defines a notion of causal complexity in π-calculus and gives a type system characterizing processes with polynomial ...to a particular complexity class ... Voir le document complet

... ⊃ A ⊃ B. Otherwise there would exist a term which behaves both as I and as ...as a relevant arrow type → r . As explained in [3], it can be viewed as a special case of im- plication whose ... Voir le document complet

... the relations Prop ≤ Type 1 and Type i ≤ Type i+1 (i ≥ 1). In both constructions λx : T . M and Πx : T . U , the symbols λ and Π are binders, which bind all the free occurrences of the variable x in M and U , but no ... Voir le document complet

... LKF, a version of LLF for classical ...Gentzen’s sequent calculus Gentzen [ Gen35 ] introduced the sequent calculus as a formalism of mathematical logic and reason- ing, ... Voir le document complet

... is a natural extension of the classical heat equation to the path- dependent ...associated with Brownian motion viewed as a real valued process, then the path-dependent heat ... Voir le document complet

... requires a new induction; however, since we have already proved Corollary ...together with the trivial statement for terms and commands saying that if T → T ′ , then true (this amounts to saying that we are ... Voir le document complet

... on classical logic in proof theory, it is now well-established that continuation- passing style (CPS) translations in call by name and call by value correspond to different polarisations of formulae ( Girard , ... Voir le document complet

... 1) With these rules, the rst proof above is not directly a proof in the restriction: the axiom rule of LJ has to be encoded in the restriction by an axiom rule followed by a contraction ...2)This ... Voir le document complet

... for a strongly non-confluent ...in a similar form in ...by a strategy limits the obtainable normal ...obtaining a confluent calculus, see e.g. [7, 23], to be used as a ... Voir le document complet