By D. A. Wolfram
This e-book provides the theoretical starting place of a higher-order good judgment programming language with equality, in line with the clausal thought of varieties. A long-sought objective of common sense programming, the clausal concept of varieties is a good judgment programming language that enables practical computation as a primitive operation whereas having rigorous, sound, and whole declarative and operational semantics. The language is particularly robust, assisting higher-order equational deduction and practical computation. Its greater order syntax makes it concise and expressive, summary information varieties will be expressed in it, and looking for a number of options is a easy operation. the writer proves a few vital and fabulous effects: a Skolem-Herbrand-Gödel theorem for higher-order good judgment; a Higher-Order answer Theorem, consisting of as particular circumstances a few formerly unproven conjectures approximately equational matching and higher-order matching.