Ppt Soft Linear Logic Lambda Calculus And Intersection Types This paper introduces a typed functional language Λ! and a categorical model for it. the terms of Λ! encode a version of natural deduction for intuitionistic linear logic such that linear. This paper explores the interplay between lambda calculus and intuitionistic linear logic through the lens of the curry howard isomorphism. it emphasizes how this relationship can be used to model computational environments specifically focusing on resource management.
The Logic Philosophy And History Of The Lambda Calculus Softarchive First of all, lafont [13] defined a calculus of combinators, corresponding to the intuitionistic linear logic (ill in the following), where combinators were suggested from the categorical interpretation of the logic. then, he defined a linear abstract machine for the evaluation of his calculus. Abstract. the in tro duction of linear logic extends the curry ho w ard isomorphism to in tensional asp ects of the t yp ed functional programming. in particular, ev ery form ula of linear logic tells whether the term it is a t yp e for, can b e either erased duplicated or not, during a computation. The terms of a1 encode a version of natural deduction for intuitionistic linear logic such that linear and non linear assumptions are managed multiplicatively and additively, respectively. These features can be effectively studied using a language corresponding to the intuitionistic fragment of the linear logic, through the curry howard isomorphism. until now, some languages inspired by this isomorphism have been designed.
Figure 1 From A Linear Linear Lambda Calculus Semantic Scholar The terms of a1 encode a version of natural deduction for intuitionistic linear logic such that linear and non linear assumptions are managed multiplicatively and additively, respectively. These features can be effectively studied using a language corresponding to the intuitionistic fragment of the linear logic, through the curry howard isomorphism. until now, some languages inspired by this isomorphism have been designed. We introduce the ! calculus, a linear lambda calculus extended with scalar multiplication and term addition, that acts as a proof language for intuitionistic linear logic (ill). Models of moggi's computational metalanguage. we use the adjoint presentation of these models and the associated adjoint calculus to show that three transla tions, due mainly to moggi, of the lambda calculus into the computational metalanguage (direct, call by name and call by value) correspond exactly to three transla tions, due mainly to. Intuition istic logic. section 2 describes how the curry howard correspondence relates this l gic to lambda calculus. section 3 ntroduces linear logic. section 4 uses the curry howard correspondence to derive a linear lambda calculus, and out lines its applications. section 5 discusses rel ted work and concludes. it is worth not. This work introduces two lambda calculi: a parallel lambda calculus and an algebraic lambda calculus, both extending full propositional intuitionistic logic and proposes a novel set theoretic interpretation based on the union of the disjoint union and the cartesian product.
Comments are closed.