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Resolution and type theory

Leen Helmink
1991 Science of Computer Programming  
It combines the advantages of Horn clause resolution and higher order natural deduction style theorem proving.  ...  This rests on a mechanism that provides a simple clausal interpretation for the assumptions in a context. The method is not complete, due to the expressive power of type theory.  ...  Acknowledgements The author owes much gratitude to the referee and to Jan Bergstra, Loe Feijs, Bert Jutting, Ton Kalker, Frank van der Linden and Rob Wieringa for numerous suggestions and corrections.  ... 
doi:10.1016/0167-6423(91)90038-y fatcat:7m4ktl6y7rdqxk6vyqojuygd6y

The Formal System lambda-delta [article]

F. Guidi
2008 arXiv   pre-print
lambda calculi and some from the pure type systems, but differs from both in that it does not include the Pi construction while it provides for an abbreviation mechanism at the level of terms. lambda-delta  ...  The formal system lambda-delta is a typed lambda calculus that pursues the unification of terms, types, environments and contexts as the main goal. lambda-delta takes some features from the Automath-related  ...  The proofs are displayed correctly only selecting a font with Unicode support.  ... 
arXiv:cs/0611040v10 fatcat:f3uv6676gjcldlvl3awiosumh4

A Friendly Smoothed Analysis of the Simplex Method

Daniel Dadush, Sophie Huiberts
2020 SIAM journal on computing (Print)  
In this method, one simultaneously interpolates the objectives c \prime \rightar c and right-hand sides b \prime \rightar b, which has the effect of combining Phases I and II.  ...  We obtain our results via an improved shadow bound, key to earlier analyses as well, combined with improvements on algorithmic techniques of Vershynin.  ...  The authors would like to thank the Simons Institute program on``Bridging Continuous and Discrete Optimization,"" where some of this work was done.  ... 
doi:10.1137/18m1197205 fatcat:gbnr52kzwnam5haonc7z7co5mi

Expressive power of typed and type-free programming languages

Elfriede Fehr
1984 Theoretical Computer Science  
The times of type1 and type-free lambda-schemes are studied with respect to their use as control structures oi Ixogramming languages.  ...  We abbreviate I", to I if the corresponding domain A is clear from the context. For an index set K and a directed subset (NJ PC K) we write u" K a, for u (iZl.i vC K}.  ...  Special thanks are due to my colleague, Werner Damm, for his enthusiastic participation in discussions on the subject and for his many constructive comments.  ... 
doi:10.1016/0304-3975(84)90088-4 fatcat:e4dnihp66nfxpk34jaebk5liha

A Framework for Defining Logical Frameworks

Furio Honsell, Marina Lenisa, Luigi Liquori
2007 Electronical Notes in Theoretical Computer Science  
We investigate the metatheoretical properties of the calculus underpinning GLF and illustrate its expressive power. In particular, we focus on two interesting instantiations of GLF.  ...  lambda calculus, to lambda calculi with patterns.  ...  The last author would like to thank warmly Horatiu Cirstea and Claude Kirchner for many useful discussions, and for infecting him with the intellectual virus of blending term rewriting with lambda calculus  ... 
doi:10.1016/j.entcs.2007.02.014 fatcat:65vrsdecjbcbfdg2rt43petuvy

Abstract data type systems

Jean-Pierre Jouannaud, Mitsuhiro Okada
1997 Theoretical Computer Science  
ADTS generalize inductive types as they are defined in the calculus of constructions, by providing definitions of functions by pattern matching on the one hand, and relations among constructors of the  ...  This is shown to be the case for the polymorphic lambda calculus (with possibly subtypes) enriched by higher-order algebraic rules obeying a strong generalization of primitive recursion of higher type  ...  Acknowledgements To Maribel Fernandez and Ralph Matthes for scrutinizing several versions of this work.  ... 
doi:10.1016/s0304-3975(96)00161-2 fatcat:xmdsq2sawjgyfdv2k47npicjjm

A block rotation task: the application of multivariate and decision theory analysis for the prediction of organic brain disorder

P Satz
1966 The Psychological Monographs  
Cost efficiency probabilities of DF III for combinations of base rates P and Q when pi = .70 and pz = .10. pothesis Eq. 3).  ...  This particular visual-motor error tendency was first observed on the Goldstein-Scheerer Cube Test, which requires S to reproduce patterns with 1-inch colored cubes” (Gold- stein & Scheerer, 1941).  ... 
pmid:5968339 fatcat:z7chb45p6bbx3nljvn4ugleu5u

A block rotation task: The application of multivariate and decision theory analysis for the prediction of organic brain disorder

Paul Satz
1966 The Psychological Monographs  
Cost efficiency probabilities of DF III for combinations of base rates P and Q when pi = .70 and pz = .10. pothesis Eq. 3).  ...  This particular visual-motor error tendency was first observed on the Goldstein-Scheerer Cube Test, which requires S to reproduce patterns with 1-inch colored cubes” (Gold- stein & Scheerer, 1941).  ... 
doi:10.1037/h0093899 fatcat:jgdmgajotrgknfw73b4vz5fiee

Connection Machine Lisp

Guy L. Steele, W. Daniel Hillis
1986 Proceedings of the 1986 ACM conference on LISP and functional programming - LFP '86  
Ths symbol fl is used to indicate permutation and reduction of sets of data. Connection Machine Lisp in practice leans heavily on APL and FP and their descendants.  ...  The symbols st and • are used, in a manner syntactically reminiscent of the backquote notation used in Common Lisp, to indicate what parts of an expression are to be executed in parallel.  ...  We are grateful for many comments from Michael Berry, Ted Tablceki, and others within Thinking Machines Corporation, and from the referees.  ... 
doi:10.1145/319838.319870 fatcat:5cdr4uxoj5aizk6ugkyc3nitaq

Irrelevance, Heterogeneous Equality, and Call-by-value Dependent Type Systems

Vilhelm Sjöberg, Chris Casinghino, Ki Yung Ahn, Nathan Collins, Harley D. Eades III, Peng Fu, Garrin Kimmell, Tim Sheard, Aaron Stump, Stephanie Weirich
2012 Electronic Proceedings in Theoretical Computer Science  
We present a full-spectrum dependently typed core language which includes both nontermination and computational irrelevance (a.k.a. erasure), a combination which has not been studied before.  ...  Our language design is strongly influenced by the choice of CBV evaluation, and by our novel treatment of propositional equality which has a heterogeneous, completely erased elimination form.  ...  Acknowledgments This work was supported by the National Science Foundation (NSF grant 0910500).  ... 
doi:10.4204/eptcs.76.9 fatcat:lv4inpdztvdufhcxki7z2oxtny

Categorial Type Logics [chapter]

Michael Moortgat
1997 Handbook of Logic and Language  
SBR-9510706, and on research conducted in the context of the Esprit BRA project 6852 'Dynamic interpretation of natural language'.  ...  Acknowledgements This chapter is based in part on work supported by the National Science Foundation under Grant No.  ...  (7) in Prop 2.18, and use X as an abbreviation Example 2.19 Deriving (one half of) Associativity from (one directional instantiation of) Geach.  ... 
doi:10.1016/b978-044481714-3/50005-9 fatcat:xseh4iz55vesfnm3daywvb7gyu

Categorial Type Logics [chapter]

Michael Moortgat
2011 Handbook of Logic and Language  
SBR-9510706, and on research conducted in the context of the Esprit BRA project 6852 'Dynamic interpretation of natural language'.  ...  Acknowledgements This chapter is based in part on work supported by the National Science Foundation under Grant No.  ...  (7) in Prop 2.18, and use X as an abbreviation Example 2.19 Deriving (one half of) Associativity from (one directional instantiation of) Geach.  ... 
doi:10.1016/b978-0-444-53726-3.00002-5 fatcat:mg4b3coyyfhgrcztbtkglsigry

D1.1 - State of the Art Analysis

Danilo Ardagna
2021 Zenodo  
The aim of this deliverable is to review the state-of-the-art in techniques used in the development and operation of AI applications in computing continua and the related technologies.  ...  The deliverable starts with an overview of AI applications and edge computing market trends.  ...  , especially in combination with AI and IoT.  ... 
doi:10.5281/zenodo.6372377 fatcat:f6ldfuwivbcltew4smiiwphfty

Algebraic theories of power operations [article]

William Balderrama
2022 arXiv   pre-print
By combining this general algebra with obstruction-theoretic machinery, we obtain tools for computing with 𝔼_∞ algebras over 𝔽_p and over Lubin-Tate spectra.  ...  In particular, we consider Quillen cohomology in the context of algebras over algebraic theories, plethories, and Koszul resolutions for algebras over additive theories.  ...  The P-module Γ (P1,...,Pn) is isomorphic to the total fiber of the n-cube obtained by tensoring together the maps ∆ + − η ⊗ P i − P i ⊗ η : Λ Pi → Λ PiPi Λ Pi ⊗ Λ Pi . Proof.  ... 
arXiv:2108.06802v2 fatcat:uuozpojq7vdx5n4273gw2nuyoi

A Modular Hierarchy of Logical Frameworks [chapter]

Robin Adams
2004 Lecture Notes in Computer Science  
Considered as a type system, it is one of the members of the lambda-cube; λP , to be precise.  ...  , MSB93] and ALF [Mag95] , based on inductive definitions; and Pi, based on partial inductive definitions [Hal91, Eri93, Eri94] .  ...  So: Proof We deal with cases 7 and 8; each case is similar to one of these. 7 .  ... 
doi:10.1007/978-3-540-24849-1_1 fatcat:q34oliqmmzfw5dvzejss2eeu7a
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