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The Maude system is an implementation of rewriting logic. It is similar in its general approach to Joseph Goguen's OBJ3 implementation of equational logic, but based on rewriting logic rather than order-sorted equational logic, and with a heavy emphasis on powerful metaprogramming based on reflection.
Going further, for every proof in the logic, there was a matching function (term) in the programming language. One of Curry's examples was the correspondence between simply typed lambda calculus and intuitionistic logic. [2] Predicate logic is an extension of propositional logic, adding quantifiers.
In logic, a logical framework provides a means to define (or present) a logic as a signature in a higher-order type theory in such a way that provability of a formula in the original logic reduces to a type inhabitation problem in the framework type theory. [1] [2] This approach has been used successfully for (interactive) automated theorem ...
The quantifier {M:nat} can be read as "for all M of type nat". The constant plus_succ defines the case for when the second argument is the successor of some other number N (see pattern matching). The result is the successor of P, where P is the sum of M and N. This recursive call is made via the subgoal plus M N P, introduced with <-.
Mustache-1 was inspired by ctemplate and et, [3] and began as a GitHub distribution at the end of 2009. A first version of the template engine was implemented with Ruby, running YAML template texts. The (preserved) main principles were: Logic-less: no explicit control flow statements, all control driven by data.
Constraint logic programming is a form of constraint programming, in which logic programming is extended to include concepts from constraint satisfaction. A constraint logic program is a logic program that contains constraints in the body of clauses. An example of a clause including a constraint is A (X, Y):-X + Y > 0, B (X), C (Y).
The belief–desire–intention software model (BDI) is a software model developed for programming intelligent agents.Superficially characterized by the implementation of an agent's beliefs, desires and intentions, it actually uses these concepts to solve a particular problem in agent programming.
Typed lambda calculi are closely related to mathematical logic and proof theory via the Curry–Howard isomorphism and they can be considered as the internal language of certain classes of categories. For example, the simply typed lambda calculus is the language of Cartesian closed categories (CCCs). [2]