Computation as Logic
Logic plays an important role in the two areas of computer science - reduction and resolution respectively associated with functional programming and logic programming. This book illustrates that logic is not only a language in which one can accurately state facts or knowledge (as in artificial intelligence) but also that programming itself is a logical activity.
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A-calculus A-terms abstraction algebra algorithm allows application arbitrary arithmetic arity assumption atoms axioms binary Boolean bound calculus called clause closed terms complete computer science confluence constant constructed critical pair Curry-Howard correspondence defined domain E-algebra elements encoding equivalent evaluation example exists finite terms first-order fixpoint formula ip functional programming graph h ip hence Herbrand induction inference system infinite integers interpretation intuitionistic intuitionistic logic iteration lemma literal logic programming minimal morphism multisets natural deduction negation notation obtained occurrence operator partial function Peano arithmetic polynomial predicate primitive recursive primitive recursive functions problem programming languages Prolog proof proposition prove quantifiers query recursive set redex reduction relation result rewriting system rule rx val satisfies semantics sequence sequent calculus signature solution solved Standard ML subset substitution subterm supercombinator symbol syntactic theorem theory transformation Ts[X Turing machine unary undecidable unification var(M written
The Significance of Complexity: Approaching a Complex World Through Science ...
Kees van Kooten Niekerk,Hans Buhl
No preview available - 2004