Causal Notation.

Purpose.

This is a Causal Notation's initial draft, it's intended to have uses in Causal Proofs, Causal Analysis,
Causal Modelling, Causal Design, Causal Programming & Causal Automated Tests.


Additional practical notes.

This model is not detached from Reality, it applies to concurrent, non-realtime systems. Hence, we consider unknown delays in model & notation.

Are realtime systems detached from Reality?

Generally they are not - but for many solutions they are too expensive and slow to make. Hence, in many niches and solutions they are too unreal to be worthwhile.

Proving that programs or program parts will complete in a given maximum amount of time, is not possible using these tools. Using statistical-allowance of errors, including completion-time-related errors and forming contracts that way might be possible, but there's always a risk.

While time is counted very precisely by computer clocks, there are delays caused by code execution - every instruction takes a time to perform. Exact amount of delay depends on instruction(s), on processor(s) and on operating system and other software layers, if there are any.

Therefore, clock-events, objects creation and interaction are associated with delays, and response to clock-events usually is associated with delays.

Profilers, either built-in a programming language, or added manually or provided by thrid-party tools - are a good way of measuring average, worst and best delays statistically on a given hardware-software infrastructure unit.

See also, if You wish: Correctness.


Types.

Ca: a cause,
R: a result, an abstract object type that can evaluate to a boolean value,
De: discrete event, either a cause or result,
Co: a condition,
Te: a timeframe.
Cns: a conditions set,
B: a boolean expression,
Cto: a clock-events bound condition; it's state contains exact time of appearance and time of disappearance,
t: a time measured in milliseconds since beginning of year 1 A.D.
O: observer object - observes clock events, causes & conditions appearance, existence and disappearance, as well as origination, hold time, and cessation, then reacts with events that can result in cause(s) and/or condition(s) appearance and disappearance, as well as origination and cessation.


Definitions.

Cto := (t₁, t₂) - - Condition that appears at time t₁ or a little later, and disappears at t₂ or a little later,
Cto := (t, ...) - Condition that appears at a time t or a little later, and disappears when program stops,
Cto := (..., t) - Condition that appears during program's initialization, and disappears at time t or a little later,
Te_n := Co_m - a timeframe Te_n is defined as in-between of a condition Co_m appearance and disappearance.
Cns_n := Co_n1, Co_n2, ... - a conditions set Co_n is defined as a collection of conditions Co_n1, Co_n2, ...
Cns_n := Cns_m1, Cns_m2, ..., Co_p1, Co_p2, ... - a conditions set Cns_n,
  is defined as a collection of:
  * conditions Co_p1, Co_p2, ...,
  * conditions from conditions sets Cns_m1, Cns_m2, ...

Origination - an objects starts to affect Reality.
Hold - an object keeps affecting Reality.
Cessation - an object ceases to affect Reality.

Appearance - an object appears in Reality.
Existence - an object exists in Reaiity.
Disappearance - an object disappears from Reality.

In different sources - Buddhist or other - these ideas might be defined differently.

In many cases, but not all:
* appearance means origination,
* existence means hold,
* disappearance means cessation.

Can object exist and not affect Reality?
* depends on how we define a Reality,
* a part of Reality is also a Reality,
* we can play with ideas of objects with or without meaning,
* we can play with ideas of physical and nonmaterial objects,
* we can play with ideas of redefining what 'affecting' means, and with 'affecting threshold',
* does observation affect Reality?,
* ...

This has uses in modelling, for example, as models are simplified representation of interresting Reality's parts.


Appearance, Existence, Disappearance, Origination, Hold & Cessation.

Ca_n := App De_m - a discrete event De_m makes a cause Ca_n to appear.
Ca_n := App Co_m - a condition Co_m makes a cause Ca_n to appear.
Ca_n := App Cns_m - a conditions set Cns_m makes a cause Ca_n to appear.

when B_n : Co_m - condition Co_m appears and exists for as long as B_n is true.

R_n := Ap De_m in Te_p - a result R_n evaluates to true if a discrete event De_m appears in a timeframe Te_p.
R_n := Ap Co_m in Te_p - a result R_n evaluates to true if a condition Co_m appears in a timeframe Te_p.
R_n := Ap Cns_m in Te_p - a result R_n evaluates to true if a conditions set Cns_m appears in a timeframe Te_p.
R_n := Dis Ca_m in Te_p - a result R_n evaluates to true if a cause Ca_m disappears in a timeframe Te_p.
R_n := Dis Co_m in Te_p - a result R_n evaluates to true if a condition Co_m disappears in a timeframe Te_p.
R_n := Dis Cns_m in Te_p - a result R_n evaluates to true if a condition set Cns_m disappears in a timeframe Te_p.
R_n := Ex Ca_m in Te_p - a result R_n evaluates to true if a cause Ca_m exists in a timeframe Te_p.
R_n := Ex Co_m in Te_p - a result R_n evaluates to true if a condition Co_m exists in a timeframe Te_p.
R_n := Ex Cns_m in Te_p - a result R_n evaluates to true if a condition set Cns_m exists in a timeframe Te_p.

R_n := Ori De_m in Te_p - a result R_n evaluates to true if a cause De_m originates in a timeframe Te_p.
R_n := Ori Co_m in Te_p - a result R_n evaluates to true if a condition Co_m originates in a timeframe Te_p.
R_n := Ori Cns_m in Te_p - a result R_n evaluates to true if a conditions set Cns_m originates in a timeframe Te_p.
R_n := Ces Ca_m in Te_p - a result R_n evaluates to true if a cause Ca_m ceases in a timeframe Te_p.
R_n := Ces Co_m in Te_p - a result R_n evaluates to true if a condition Co_m ceases in a timeframe Te_p.
R_n := Ces Cns_m in Te_p - a result R_n evaluates to true if a condition set Cns_m ceases in a timeframe Te_p.
R_n := H Ca_m in Te_p - a result R_n evaluates to true if a cause Ca_m holds in a timeframe Te_p.
R_n := H Co_m in Te_p - a result R_n evaluates to true if a condition Co_m holds in a timeframe Te_p.
R_n := H Cns_m in Te_p - a result R_n evaluates to true if a condition set Cns_m holds in a timeframe Te_p.



Links.

See also, if You wish:
* The 'Causal Programming Paradigm'.
* Causal Automated Tests.