scholarly journals Specifying theorem provers in a higher-order logic programming language

2005 ◽  
pp. 61-80 ◽  
Author(s):  
Amy Felty ◽  
Dale Miller
Keyword(s):  
Logic Programming ◽  
Programming Language ◽  
Higher Order ◽  
Order Logic ◽  
Higher Order Logic ◽  
Logic Programming Language ◽  
Theorem Provers

Extended natural semantics

1993 ◽  
Vol 3 (2) ◽  
pp. 123-152 ◽  
Author(s):  
John Hannan
Keyword(s):  
Logic Programming ◽  
Programming Language ◽  
Functional Programming ◽  
Higher Order ◽  
Order Logic ◽  
Inference Rules ◽  
Abstract Syntax ◽  
Higher Order Logic ◽  
First Order ◽  
Definition Of

AbstractWe extend the definition of natural semantics to include simply typed λ-terms, instead of first-order terms, for representing programs, and to include inference rules for the introduction and discharge of hypotheses and eigenvariables. This extension, which we call extended natural semantics, affords a higher-level notion of abstract syntax for representing programs and suitable mechanisms for manipulating this syntax. We present several examples of semantic specifications for a simple functional programming language and demonstrate how we achieve simple and elegant manipulations of bound variables in functional programs. All the examples have been implemented and tested in λProlog, a higher-order logic programming language that supports all of the features of extended natural semantics.

scholarly journals Making Automatic Theorem Provers more Versatile

10.29007/n6j7 ◽  
2018 ◽  
Author(s):  
Simon Cruanes
Keyword(s):  
Higher Order ◽  
Order Logic ◽  
Higher Order Logic ◽  
Research Directions ◽  
First Order ◽  
Theorem Provers ◽  
Smt Solvers ◽  
Automatic Theorem Provers ◽  
Automatic Theorem

We argue that automatic theorem provers should become more versatile and should be able to tackle problems expressed in richer input formats. Salient research directions include (i) developing tight combinations of SMT solvers and first-order provers; (ii) adding better handling of theories in first-order provers; (iii) adding support for inductive proving; (iv) adding support for user-defined theories and functions; and (v) bringing to the provers some basic abilities to deal with logics beyond first-order, such as higher-order logic.

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