The Holy Trinity

The Christian doctrine of trinitarianism states that there is one God that is manifest in three persons, the Father, the Son, and the Holy Spirit, who together form the Holy Trinity.   The doctrine of computational trinitarianism holds that computation manifests itself in three forms: proofs of propositions, programs of a type, and mappings between structures.  These three aspects give rise to three sects of worship: Logic, which gives primacy to proofs and propositions; Languages, which gives primacy to programs and types; Categories, which gives primacy to mappings and structures.  The central dogma of computational trinitarianism holds that Logic, Languages, and Categories are but three manifestations of one divine notion of computation.  There is no preferred route to enlightenment: each aspect provides insights that comprise the experience of computation in our lives.

Computational trinitarianism entails that any concept arising in one aspect should have meaning from the perspective of the other two.  If you arrive at an insight that has importance for logic, languages, and categories, then you may feel sure that you have elucidated an essential concept of computation—you have made an enduring scientific discovery.  Advances in our understanding of computation may arise from insights gained in many ways (any data is useful and relevant), but their essential truth does not depend on their popularity.

Logic tells us what propositions exist (what sorts of thoughts we wish to express) and what constitutes a proof (how we can communicate our thoughts to others).  Languages (in the sense of programming) tells us what types exist (what computational phenomena we wish to express) and what constitutes a program (how we can give rise to that phenomenon).  Categories tell us what structures exist (what mathematical models we have to work with) and what constitutes a mapping between them (how they relate to one another).  In this sense all three have ontological force; they codify what is, not how to describe what is already given to us.  In this sense they are foundational; if we suppose that they are merely descriptive, we would be left with the question of where these previously given concepts arise, leading us back again to foundations.  It is the foundations that I wish to describe here, because I believe it will help to clarify some common misunderstandings about the notions of proposition, type, and structure.  Of particular interest here is that a “type system” is not, under this conception, an arbitrary collection of conditions imposed on a previously given notion of program (whether written with horizontal lines, or not).  It is, rather, a way to say what the programs are in the first place, and what they mean as proofs and as mappings.


-- Returns an INFINITE list of JEWS, in a STATICALLY TYPED language.
VIPPER :: JEWS -> JEWS
VIPPER JEWS = JEW ($ JEW) $ JEWS VIPPER

What I find captivating about computational trinitarianism is that it is beautiful!  Imagine a world in which logic, programming, and mathematics are unified, in which every proof corresponds to a program, every program to a mapping, every mapping to a proof!  Imagine a world in which the code is the math, in which there is no separation between the reasoning and the execution, no difference between the language of mathematics and the language of computing.  Trinitarianism is the central organizing principle of a theory of computation that integrates, unifies, and enriches the language of logic, programming, and mathematics.  It provides a framework for discovery, as well as analysis, of computational phenomena.  An innovation in one aspect must have implications for the other; a good idea is a good idea, in whatever form it may arise.  If an idea does not make good sense logically, categorially, and typically (sorry for the neologism), then it cannot be a manifestation of the divine.

Almost cranky enough for postmodernism.

>>6
It's not cranky, it's rigorous.

OP, are you jewish?

>>4
NO!!!!
:o
I had feared it in the Last thread! NOW THERE IS A JEW GENERATOR>

Holy Trinity:
- SICP
- TAOCP
- K&R

HI IM A PROGRAMMER IM 13 I CAN PROGRAM CALCULATOR SORRY FOR MY INGLISH IM NOT INGLISH I CREATED A RANDOM NUMBER GENERATOR HERE IT IS 0.30538853606127114