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Linear Sized Types in the Calculus of Constructions [chapter]

Jorge Luis Sacchini
2014 Lecture Notes in Computer Science  
Concretely, we present a type system with linear sized types for the Calculus of Constructions extended with one inductive type (natural numbers) and one coinductive type (streams).  ...  In this paper, we study sized types with linear annotations of the form n · α + m with n and m natural numbers.  ...  The statements made herein are solely the responsibility of the author.  ... 
doi:10.1007/978-3-319-07151-0_11 fatcat:comunxcnnrb7roqf2ojtgzitoq

Decidability of Type-Checking in the Calculus of Algebraic Constructions with Size Annotations [chapter]

Frédéric Blanqui
2005 Lecture Notes in Computer Science  
First, we prove that, in the Calculus of Algebraic Constructions with size annotations, the problems of type inference and type-checking are decidable, provided that the sets of constraints generated by  ...  rewriting paradigms, culminating in the Calculus of Algebraic Constructions.  ...  I would like to thank very much Miki Hermann, Hongwei Xi, Christophe Ringeissen and Andreas Abel for their comments on a previous version of this paper.  ... 
doi:10.1007/11538363_11 fatcat:4bygivrqkncv3lumwpcptyja74

An expressive, scalable type theory for certified code

Karl Crary, Joseph C. Vanderwaart
2002 Proceedings of the seventh ACM SIGPLAN international conference on Functional programming - ICFP '02  
The inclusion of explicit proofs allows the type system to guarantee properties that would otherwise be incompatible with decidable type checking.  ...  We present the type theory LTT, intended to form a basis for typed target languages, providing an internal notion of logical proposition and proof.  ...  We conjecture that an extension of SSTP with linear typing constructs would have similar expressive power, but the metatheory of the Calculus of Inductive Constructions with linearity has not been investigated  ... 
doi:10.1145/581478.581497 dblp:conf/icfp/CraryV02 fatcat:ojq22xmtwrcoregppjbbphpi7q

An expressive, scalable type theory for certified code

Karl Crary, Joseph C. Vanderwaart
2002 SIGPLAN notices  
The inclusion of explicit proofs allows the type system to guarantee properties that would otherwise be incompatible with decidable type checking.  ...  We present the type theory LTT, intended to form a basis for typed target languages, providing an internal notion of logical proposition and proof.  ...  We conjecture that an extension of SSTP with linear typing constructs would have similar expressive power, but the metatheory of the Calculus of Inductive Constructions with linearity has not been investigated  ... 
doi:10.1145/583852.581497 fatcat:x3rvrbttfbe7xjlfuk23xrusxq

Lower End of the Linial-Post Spectrum

Andrej Dudenhefner, Jakob Rehof, Michael Wagner
2018 Types for Proofs and Programs  
Contrary to the above result, axiomatizations of the Hilbert-style calculus containing only the axiom a → (b → b) are recognizable in linear time.  ...  We show that recognizing axiomatizations of the Hilbert-style calculus containing only the axiom a → (b → a) is undecidable (a reduction from the Post correspondence problem is formalized in the Lean theorem  ...  calculus containing only the axiom a → a are recognizable in linear time.  ... 
doi:10.4230/lipics.types.2017.2 dblp:conf/types/DudenhefnerR17 fatcat:3fxjgsei7zaetdu7itmergeq7q

Ludics is a Model for the Finitary Linear Pi-Calculus [chapter]

Claudia Faggian, Mauro Piccolo
2007 Lecture Notes in Computer Science  
The calculus In this section we describe the finitary fragment of the linear π-calculus ([NYB01], [LH06]). We first discuss the untyped syntax and then introduce the typed setting.  ...  Hence typed π−calculus, Linear Logic, proof-nets, linear strategies fit together as aspects of the same broader picture.  ...  The linear π-calculus is a typed version of asynchronous π-calculus introduced by Yoshida, Honda and Berger. We interpret π-processes of the finitary fragment of the calculus into linear strategies.  ... 
doi:10.1007/978-3-540-73228-0_12 fatcat:ms5aqiitofaq5diksfzqwystci

From Proof-Nets to Linear Logic Type Systems for Polynomial Time Computing [chapter]

Patrick Baillot
2007 Lecture Notes in Computer Science  
We stress the importance of proof-nets from Light linear logic for the design of this type system and for a result establishing that typable lambda-terms can be evaluated efficiently with optimal reduction  ...  We also discuss the issue of DLAL type inference, which can be performed in polynomial time for system F terms.  ...  This resolution procedure is correct and complete and it can be performed in polynomial time w.r.t. the size of the original system F term.  ... 
doi:10.1007/978-3-540-73228-0_2 fatcat:7axovijfpfbbxhxe5umqljqnku

Page 4624 of Mathematical Reviews Vol. , Issue 2002G [page]

2002 Mathematical Reviews  
The author studies Church’s 4d-calculus in a typed fashion. For each pair of (simple) types A,B a constant d:A —~ A— B > B — B is considered.  ...  In this work we define a tableau calculus that is sound and complete with respect to k-validity, when the initial formula and the bound k on the size of the temporal models are given as input.  ... 

On the complexity of the linear-time μ-calculus for Petri Nets [chapter]

Peter Habermehl
1997 Lecture Notes in Computer Science  
Esparza has shown in 5] that it is decidable, but the space complexity of his algorithm is exponential in the size of the system and double exponential in the size of the formula.  ...  We study the complexity of model-checking Petri Nets w.r.t. the propositional linear-time -calculus.  ...  Acknowledgement: The author would like to thank Javier Esparza for very helpful discussions on this topic.  ... 
doi:10.1007/3-540-63139-9_32 fatcat:lblieccp4zf2fiimqqtkli72ny

Page 6074 of Mathematical Reviews Vol. , Issue 2001I [page]

2001 Mathematical Reviews  
We show that the standard encod- ing of the PHP as a monotone sequent admits quasipolynomial- size proofs in this system.  ...  Using this relationship, we prove nearly linear (Q(n/logn) vs. O(1)) separations between Nullstellensatz and PC degree, for a family of explicitly constructed contradictory 3CNF formulas.  ... 

Page 5971 of Mathematical Reviews Vol. , Issue 2004h [page]

2004 Mathematical Reviews  
A linear map reducing the degree of polynomials in F [x] by one is defined as a difference-tial operator. The factorial n! is generalized first to n,,!  ...  In general, w(q)- calculus is in fact M. Ward’s ‘calculus of sequences’ [Amer. J. Math. 58 (1936), 255-266; Zbl 0014.05603] in Rota’s finite op- erator calculus form.  ... 

A Fresh Look at the lambda-Calculus (Invited Talk)

Beniamino Accattoli, Michael Wagner
2019 International Conference on Rewriting Techniques and Applications  
The paper is a bird's eye view of the questions the author worked on in the last few years: how to measure the complexity of λ-terms, how to decompose their evaluation, how to implement it, and how all  ...  The (untyped) λ-calculus is almost 90 years old. And yet -we argue here -its study is far from being over.  ...  Framework or the Calculus of Constructions, as well as for unification modulo βη in simply typed frameworks like λ-prolog.  ... 
doi:10.4230/lipics.fscd.2019.1 dblp:conf/rta/Accattoli19 fatcat:75swok72vvb6fdfl3fx5lu5sey

Linear Numeral Systems

Ian Mackie
2018 Journal of automated reasoning  
We investigate numeral systems in the lambda calculus; specifically in the linear lambda calculus where terms cannot be copied or erased.  ...  This paper defines systems that address these points, and in addition provides a characterisation of linear numeral systems.  ...  Copying can never be simulated in the linear λ-calculus because of Lemma 3, Part 3: reduction reduces the size of the term, so there is no way to build a term of arbitrary size.  ... 
doi:10.1007/s10817-018-9456-6 fatcat:awpzudwwprblfkxn2x67ee36ey

PhD Abstracts

GRAHAM HUTTON
2015 Journal of functional programming  
A dissertation is eligible if parts of it have or could have appeared in JFP, that is, if it is in the general area of functional programming. The abstracts are not reviewed.  ...  As a service to the community, JFP recently launched a new feature, in the form of a regular publication of abstracts from PhD dissertations that were completed during the previous year.  ...  computed in time polynomial w.r.t. the input size.  ... 
doi:10.1017/s0956796815000040 fatcat:g7yt23qxivevte45fkiqv6xwna

Page 2889 of Mathematical Reviews Vol. , Issue 2001E [page]

2001 Mathematical Reviews  
The first part of the pa- per is a summary of the paper “Yet another constructivization of classical logic” [in Twenty-five years of constructive type the-  ...  Constructive classical logic as CPS-calculus.  ... 
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