scholarly journals The Grail Theorem Prover: Type Theory for Syntax and Semantics

2017 ◽  
pp. 247-277 ◽  
Author(s):  
Richard Moot
Keyword(s):  
Type Theory ◽  
Theorem Prover

scholarly journals Constructing Infinitary Quotient-Inductive Types

2020 ◽  
pp. 257-276
Author(s):  
Marcelo P. Fiore ◽  
Andrew M. Pitts ◽  
S. C. Steenkamp
Keyword(s):  
Type Theory ◽  
Theorem Prover ◽  
Dependent Type Theory ◽  
Inductive Definitions ◽  
Inductive Types ◽  
Recursive Definitions ◽  
Dependent Type

AbstractThis paper introduces an expressive class of quotient-inductive types, called QW-types. We show that in dependent type theory with uniqueness of identity proofs, even the infinitary case of QW-types can be encoded using the combination of inductive-inductive definitions involving strictly positive occurrences of Hofmann-style quotient types, and Abel’s size types. The latter, which provide a convenient constructive abstraction of what classically would be accomplished with transfinite ordinals, are used to prove termination of the recursive definitions of the elimination and computation properties of our encoding of QW-types. The development is formalized using the Agda theorem prover.

2OBJ: a metalogical framework theroem prover based on equational logic

1992 ◽  
Vol 339 (1652) ◽  
pp. 69-86 ◽  
Keyword(s):  
Type Theory ◽  
Term Rewriting ◽  
Order Type ◽  
Theorem Prover ◽  
Abstract Data Type ◽  
Equational Logic ◽  
Window User ◽  
Abstract Data ◽  
Definition Of ◽  
Module System

This paper describes 2OBJ, a tactic-based generic theorem prover that encodes object logics into equational logic via an abstract data type of object logic sentences and proofs. 2OBJ is built upon OBJ3, a term rewriting implementation of (order sorted conditional) equational logic. Because object logic proofs are explicitly represented, 2OBJ can not only reason with them, but also about them, as in arguments by symmetry and other metalogical devices of ordinary mathematics; this motivates the 'meta’ of ‘metalogical’ in the title. First-order equational logic has advantages in simplicity and efficiency over more complex framework logics, such as intuitionistic higher-order type theory, and also facilitates the definition of tactic languages. In addition, 2OBJ benefits from OBJ3’s powerful parametrized module system, and it has a convenient X window user interface. The paper concludes with a sketch of some semantic foundations based upon ruled parchments, charters, and institutions.

Basic Simple Type Theory

1997 ◽  
Author(s):  
J. Roger Hindley
Keyword(s):  
Type Theory ◽  
Simple Type ◽  
Simple Type Theory

Type Theory and Formal Proof

2009 ◽  
Author(s):  
Rob Nederpelt ◽  
Herman Geuvers
Keyword(s):  
Type Theory ◽  
Formal Proof

Computational Models for Multilayered Composite Shells with Application to Tires

1996 ◽  
Vol 24 (1) ◽  
pp. 11-38 ◽  
Author(s):  
G. M. Kulikov
Keyword(s):  
Type Theory ◽  
Computational Models ◽  
Geometrical Nonlinearity ◽  
Higher Order ◽  
Stress Strain ◽  
Strain Fields ◽  
First Order ◽  
Timoshenko Type ◽  
Joint Influence ◽  
Discrete Layer

Abstract This paper focuses on four tire computational models based on two-dimensional shear deformation theories, namely, the first-order Timoshenko-type theory, the higher-order Timoshenko-type theory, the first-order discrete-layer theory, and the higher-order discrete-layer theory. The joint influence of anisotropy, geometrical nonlinearity, and laminated material response on the tire stress-strain fields is examined. The comparative analysis of stresses and strains of the cord-rubber tire on the basis of these four shell computational models is given. Results show that neglecting the effect of anisotropy leads to an incorrect description of the stress-strain fields even in bias-ply tires.

Evaluation Opportunities in Mechanized Theories

10.29007/7kx8 ◽  
2018 ◽  
Author(s):  
Joe Hurd
Keyword(s):  
Mathematical Theory ◽  
Theorem Prover ◽  
Mechanized Mathematics ◽  
Reasoning Tasks

This invited talk will look at logic solvers through the application lens of constructing and processing a theory library of mechanized mathematics. In fact, constructing and processing theories are two distinct applications, and each will be considered in turn. Construction is carried out by formalizing a mathematical theory using an interactive theorem prover, and logic solvers can remove much of the drudgery by automating common reasoning tasks. At the theory library level, logic solvers can provide assistance with theory engineering tasks such as compressing theories, managing dependencies, and constructing new theories from reusable theory components.

Campus Social Climate Correlates of Environmental Type Dimensions

NASPA Journal ◽  
2004 ◽  
Vol 41 (4) ◽  
Author(s):  
Daniel W. Salter ◽  
Reynol Junco ◽  
Summer D. Irvin
Keyword(s):  
Work Environment ◽  
Personal Growth ◽  
Type Theory ◽  
General Purpose ◽  
Myers Briggs Type Indicator ◽  
Environment Scale ◽  
Type Indicator ◽  
Group Environment ◽  
System Maintenance ◽  
Environment Type

To address the ability of the Salter Environment Type Assessment (SETA) to measure different kinds of campus environments, data from three studies of the SETA with the Work Environment Scale, Group Environment Scale, and University Residence Environment Scale were reexamined (n = 534). Relationship dimension scales were very consistent with extraversion and feeling from environmental type theory. System maintenance and systems change scales were associated with judging and perception on the SETA, respectively. Results from the SETA and personal growth dimension scales were mixed. Based on this analysis, the SETA may serve as a general purpose environmental assessment for use with the Myers-Briggs Type Indicator.

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