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##
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Linear Sized Types in the Calculus of Constructions
[chapter]

2014
*
Lecture Notes in Computer Science
*

Concretely, we present a

doi:10.1007/978-3-319-07151-0_11
fatcat:comunxcnnrb7roqf2ojtgzitoq
*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. ...##
###
Decidability of Type-Checking in the Calculus of Algebraic Constructions with Size Annotations
[chapter]

2005
*
Lecture Notes in Computer Science
*

First, we prove that,

doi:10.1007/11538363_11
fatcat:4bygivrqkncv3lumwpcptyja74
*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. ...##
###
An expressive, scalable type theory for certified code

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 ...

##
###
An expressive, scalable type theory for certified code

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 ...

##
###
Lower End of the Linial-Post Spectrum

2018
*
Types for Proofs and Programs
*

Contrary to

doi:10.4230/lipics.types.2017.2
dblp:conf/types/DudenhefnerR17
fatcat:3fxjgsei7zaetdu7itmergeq7q
*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. ...##
###
Ludics is a Model for the Finitary Linear Pi-Calculus
[chapter]

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. ...

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

2007
*
Lecture Notes in Computer Science
*

We stress

doi:10.1007/978-3-540-73228-0_2
fatcat:7axovijfpfbbxhxe5umqljqnku
*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. ...##
###
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]

1997
*
Lecture Notes in Computer Science
*

Esparza has shown

doi:10.1007/3-540-63139-9_32
fatcat:lblieccp4zf2fiimqqtkli72ny
*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. ...##
###
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)

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. ...

##
###
Linear Numeral Systems

2018
*
Journal of automated reasoning
*

We investigate numeral systems

doi:10.1007/s10817-018-9456-6
fatcat:awpzudwwprblfkxn2x67ee36ey
*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*. ...##
###
PhD Abstracts

2015
*
Journal of functional programming
*

A dissertation is eligible if parts

doi:10.1017/s0956796815000040
fatcat:g7yt23qxivevte45fkiqv6xwna
*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*. ...##
###
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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