Meanwhile, the foundation laid by Alan Turing, and also applicable to Church's Lambda Calculus
(stated earlier), was worked upon by Church's student and American logician, John Barkley Rosser.
The pure lambda calculus
is a well-known untyped system.
That set of mathematical rules is optimized to help people describe complex distributed systems comprised of multiple processes executing in parallel--unlike lambda calculus
A good intuition for the semantics is to imagine two copies of the simply typed lambda calculus
augmented with a new type t.
Some topics would benefit from a bit more follow-up, and others--like the lambda calculus
and the contravariant basis--could easily be omitted.
The following areas are currently covered by the members of the Editorial Board: Automata and Temporal Logic; Automated Deduction; Automated Verification; Commonsense and Nonmonotonic Reasoning; Constraint Programming; Finite Model Theory and Complexity of Logical Theories; Functional Programming and Lambda Calculus
; Concurrency Calculi and Tools; Logic and Machine Learning; Logical Aspects of Computational Complexity; Logical Aspects of Databases; Logic Programming; Logics of Uncertainty; Modal Logics, including Dynamic and Epistemic Logics; Model Checking; Program Development and Verification; Program Specification; Proof Theory; Term Rewriting Systems; and Type Theory and Logical Frameworks.
The authors start by describing how functions can really depend upon their arguments and how close this notion is to functions which art, typed by propositional relevance logic much like the Howard-Curry correspondence between intuitionistic logic and the lambda calculus
. Within the computer science community, this comes out as Scott's notion of "strictness".
The new C++14 standard allows lambda calculus
as we demonstrate in the applicative section of implementing conditionals, booleans and numbers.
The lazy lambda calculus
in a concurrency scenario.
The Lambda Calculus
. North Holland, Amsterdam, 1981.
The common framework considered here is a hierarchy of intermediate languages, all of which are subsets of the lambda calculus
. Our description of an implementation consists of a series of transformations [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], each one compiling a particular task by mapping an expression from one intermediate language into another.