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A Linear Logical Framework
, 1996
"... We present the linear type theory LLF as the forAppeared in the proceedings of the Eleventh Annual IEEE Symposium on Logic in Computer Science  LICS'96 (E. Clarke editor), pp. 264275, New Brunswick, NJ, July 2730 1996. mal basis for a conservative extension of the LF logical framework. ..."
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Cited by 222 (45 self)
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We present the linear type theory LLF as the forAppeared in the proceedings of the Eleventh Annual IEEE Symposium on Logic in Computer Science  LICS'96 (E. Clarke editor), pp. 264275, New Brunswick, NJ, July 2730 1996. mal basis for a conservative extension of the LF logical framework. LLF combines the expressive power of dependent types with linear logic to permit the natural and concise representation of a whole new class of deductive systems, namely those dealing with state. As an example we encode a version of MiniML with references including its type system, its operational semantics, and a proof of type preservation. Another example is the encoding of a sequent calculus for classical linear logic and its cut elimination theorem. LLF can also be given an operational interpretation as a logic programming language under which the representations above can be used for type inference, evaluation and cutelimination. 1 Introduction A logical framework is a formal system desig...
Automated Equational Reasoning in Nondeterministic λCalculi Modulo Theories H*
, 2009
"... In this thesis I study four extensions of untyped λcalculi all under the maximally coarse semantics of the theory H ∗ (observable equality), and implement a system for reasoning about and storing abstract knowledge expressible in languages with these extensions. The extensions are: (1) a semilattic ..."
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In this thesis I study four extensions of untyped λcalculi all under the maximally coarse semantics of the theory H ∗ (observable equality), and implement a system for reasoning about and storing abstract knowledge expressible in languages with these extensions. The extensions are: (1) a semilattice operation J, the join w.r.t the Scott ordering; (2) a random mixture R for stochastic λcalculus; (3) a computational comonad 〈code,apply,eval,quote, {−}〉 for Gödel codes modulo provable equality; and (4) a Π 1 1complete oracle O. I develop three languages from combinations of these extensions. The syntax of these languages is always simple: each is a finitely generated combinatory algebra. The semantics of these languages are various fragments of Dana Scott’s D ∞ models. Although the languages use ideas