TPS: A theorem-proving system for classical type theory

System Description: TPS: A Theorem Proving System for Type Theory

The TPS Theorem Proving System

When one is seeking an expansion proof for a theorem of higher-order logic, not all necessary substitution terms can be generated by unification of formulas already present, so certain expansion options [5] are applied, and then a search for a p-acceptable mating [2] is made, using Huet's higher-order unification algorithm [8] to generate all remaining substitution terms. The expansion options ...

Theorem Proving in Type Theory

As one aspect of the endeavor to c r e a te new i n t e l l e c t u a l t o o l s f o r mankind, we w ish to enable computers to p rove , and t o a s s i s t i n the p roo f s o f , theorems o f mathematics and ( e v e n t u a l l y ) o t h e r d i s c i p l i n e s which have ach ieved the r e q u i s i t e l o g i c a l p r e c i s i o n . For t h i s purpose, a p a r t i c u l a r l y s u i ...

Proving Theorems of Type Theory Automatically with TPS

Reasoning plays an important role in many activities which involve intelligence, and it may be anticipated that automated reasoning will play a significant role in many applications of artificial intelligence. The importance of developing methods of automating reasoning has been recognized since the inception of research on artificial intelligence. One fruitful approach to this problem is to us...

TPS: An Interactive and Automatic Tool for Proving Theorems of Type Theory

This is a demonstration of TPS, a theorem proving system for classical type theory (Church’s typed λ-calculus). TPS can be used interactively or automatically, or in a combination of these modes. An important feature of TPS is the ability to translate between expansion proofs and natural deduction proofs. CATEGORY: Demonstration