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Here we study the confluence properties of (CCL, CCLpqSP) and of several of its subsystems, and the relationship between untyped Lambda-calculi and (CCL, CCLpqSP) as rewriting systems. ... The Strong Categorical Combinatory Logic (CCL, CCLpqSP), developed by Curien (1986) is, when typed and augmented with a rule defining a terminal object, a presentation of Cartesian Closed Categories. ... The Strong Categorical Combinatory Logic Upon the idea that semantics can be made akin to syntax, Curien introduced the Categorical Combinatory Logic, called CCL. ...doi:10.1016/0304-3975(89)90105-9 fatcat:skfsyolxrzf5db3vgmrmr7elpe
Lecture Notes in Computer Science
Starting from natural deduction for the conjunction-implication fragment of intuitionistic logic we design a corresponding deep inference system together with reduction rules on proofs that allow a fine-grained ... We set out to find something that corresponds to deep inference in the same way that the lambda-calculus corresponds to natural deduction. ... The confluence proofs for Curien's systems, that we know of, use strong normalisation of the subsystem which carries out substitutions, so they do not seem to directly apply in our setting. ...doi:10.1007/978-3-540-89439-1_34 fatcat:s2onuy4y3fh35avd64ngy3y67q
Lecture Notes in Computer Science
We prove here confluence, strong-normalization in presence of a typing system, and present a model of the typed calculus. ... This calculus remains very close to lambda-calculus, and keeps most of its properties. ... As a result, strong normalization extends to simply typed transformation calculus. ...doi:10.1007/3-540-60692-0_46 fatcat:j4ztlaffbngrhodhzmf3wof6w4
normalization, 1158, 1301, 1552, 2689, 3204, 3324.3580 for the polymorphic lambda calculus, 1552 result, 2321 strong NP-completeness, 249, 3306 NP-complete problems, 249 polymorphic typing, ... , type -, 882 relation, 1219 test, 2037 subsumption-equivalence, 2796 subsystem equivalent -, 768 SLp of CCLpq SP, 1236 subsystems, 2639, 2765 ergodic -. 2350 of CCL, 1236 subtask, 2729 subtasks ...doi:10.1016/s0304-3975(98)00319-3 fatcat:s22ud3iiqjht7lfbtc3zctk7zm
., 91b:68105 Hardin, Thérese Confluence results for the pure strong categorical logic CCL. A-calculi as subsystems of CCL. 91h:03021 Hennessy, Matthew (with Ingélfsdottir, A.) ... and (Not in MR) Streicher, Thomas Independence results for calculi of dependent types. 91a:68184 Surzhko, S. ...
Starting from natural deduction for the conjunction-implication fragment of intuitionistic logic we design a corresponding deep inference system together with reduction rules on proofs that allow a fine-grained ... We set out to find something that corresponds to deep inference in the same way that the lambda-calculus corresponds to natural deduction. ... The confluence proofs for Curien's systems, that we know of, use strong normalisation of the subsystem which carries out substitutions, so they do not seem to directly apply in our setting. ...doi:10.7892/boris.37187 fatcat:7arr5legjvbkfee5tz3aba3iaq
In the case of Intuitionistic linear logic, this leads to a refinement of the lambda calculus, giving finer control over order of evaluation and storage allocation, while maintaining the logical content ... We study Guard's linear logic from the point of view of giving a concrete computational interpretation of the logic, based on the Curry-Howard isomorphism. ... The two major results for system F are undoubtedly that it satisfies the ChurchPRosser and strong normalization properties [ 151. These results concern reduction, and apply to all strategies. ...doi:10.1016/0304-3975(93)90181-r fatcat:jbsbpzpmjvejhbi3ic24jzbvey
Laville, Proof of termination of the rewriting system SUBST on CCL (Note) 46 (2-3) (1986) 305-312 Hardin, T.. Confluence results for the pure Strong Categorical Logic CCL. ... A-calculi as subsystems of CLL 65 (3) (1989) 291-342 Hare], D., Proving the correctness of regular deterministic programs: A unifying survey using dy, T. and M. ...doi:10.1016/0304-3975(92)90292-n fatcat:ekwes6owtrco3lkfkiqagnketq
Second, we justify our choice of realisation and mechanise a proof of convergence of the σ SP -calculus, a calculus of explicit substitutions that is complete for equality of the de Bruijn algebra corresponding ... Third, to demonstrate the practical usefulness of our approach, we provide concise, transparent, and accessible mechanised proofs for a variety of case studies refined to de Bruijn substitutions. ... First, I want to thank my advisor Gert Smolka for both his invaluable advice and the great amount of freedom given in his group. ...doi:10.22028/d291-30298 fatcat:7sjtq3piinbrncwv5wdverv42y