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Processes in Lingua Cosmica
Acta Astronautica 71 (2012) 170–172
Contents lists available at SciVerse ScienceDirect
Acta Astronautica journal homepage: www.elsevier.com/locate/actaastro
Academy Transactions Note
Processes in Lingua Cosmica Alexander Ollongren n Leiden Institute of Advanced Computer Science, Niels Bohrweg 1, 2333 CA Leiden, Holland
a r t i c l e in f o
abstract
Article history: Received 1 March 2011 Accepted 29 September 2011 Available online 28 October 2011
In a sequence of papers on the topic of message construction for interstellar communication by means of a cosmic language, representations of various kinds of concepts of reality in a Lingua Cosmica system [1]. Those studied were logic relations of a static character. The present contribution contains an important, fundamental extension: groundwork is done for the purpose of interpreting (dynamic) processes of various sorts in the linguistic system. Individual processes are abstracted in a logic sense and provided with basic properties as termination and communication functions. They can be combined into kinds of processes: sequential and parallel ones represented by only one inductive definition in logic. Based on concepts from the so-called process algebra, processes are provided with channels mapping them to their states. State vectors are introduced to represent states of conglomerates of processes. Communication between processes (locally or globally) is effectuated by means of state transitions. Together with a programmed arbitration function, state vectors play a crucial role in representing communication. With these ingredients possibilities for general interpretations of a wide range of processes in the Lingua Cosmica system come in view. & 2011 Published by Elsevier Ltd.
Keywords: Communication Interstellar Interspecies
1. Basics The present contribution is concerned with the nontrivial matter of incorporating descriptions of sequential processes or processes running in parallel without reference to time in a linguistic system for interstellar message construction. The linguistic system used in the present note is the new lingua cosmica system [1,2], referred to as LINCOS. The system is based on constructive logic and its terms (logical forms) are represented as types, see also [3]. Processes to be discussed in the present paper are represented by a map in the form of an inductive type DEFINE Proc :¼ seq : Proc-Proc-Proc9 par : Proc-Proc-Proc9 arb : Proc-Proc:
n
Tel.: þ 31 715 173 169. E-mail address: [email protected]
0094-5765/$ - see front matter & 2011 Published by Elsevier Ltd. doi:10.1016/j.actaastro.2011.09.017
This injective, total map represents either a sequential process, or a process, which operates in parallel with another one, or an arbitration. The selectors seq, par and arb identify the terms belonging to the three distinct cases. A process s of type Proc, written s:Proc, occurring in a sequence is supposed to ‘do something’, carry out an action (an elementary step), and then is either followed by a process because (seq s) Proc-Proc, or it terminates. If u is next after s in a sequence, (seq s u):Proc. Processes occurring in parallel, all of type Proc, are supposed to be linearly ordered in some sense. However if p is in the ordering (par p) is not the next in the ordering. In addition if p and q are in the ordering, (par p q):Proc, p and q both do something but they are not supposed to interfere with one another. It is also supposed that there is no difference between (par p q) and (par q p). A process occurring in parallel can also terminate. Finally no process can occur in parallel with itself.
A. Ollongren / Acta Astronautica 71 (2012) 170–172
The arbitration process is included for the purpose of treating communication between processes, in the present treaty subjected to a communication program. 2. Parallel processes
171
program DEFINE program1 : Proc-Proc :¼ ½* : ð:pq:Þðrs:Þ: Then because (arb (:p q:)):Proc, we have (program1 (arb (:p q:))):Proc, and additionally ðprogram1 ðarb ð:p q:ÞÞÞ ¼ ð:rs:Þ:
Let p:Proc and q:Proc be two unequal terms in the linear ordering of processes, which do something simultaneously (in parallel) without interfering with one another. We have seen (par p q):Proc. We shall use for a pair like (par p q) the expression :p q: or (:p q:) if it is required to indicate that it is to be an element of a state vector. This type of vector, introduced briefly in a previous paper [3] in the context of LINCOS, is considered to consist of one or more silent processes of type Proc. Note that the silent process :p q: is the same as :q p:. In other words, : : commutes. A silent process does not do something, but it carries information. Furthermore we assume that to any (parallel) process a channel is associated, mapping a process to its element of the state vector DEFINE channel : Proc-Proc :¼ ½x : ProcJxJ This definition is supplemented by a return, mapping a vector element to the corresponding process DEFINE return : Proc-Proc :¼ ½JxJ : Procx: Here [:x::Proc]x means that :x: is l-bound to the type Proc [see 2,3] and the l-term is applied to x. The resulting term is of type Proc-Proc. If p:Proc we agree on the conventions (channel p) ¼:p:, (return :p:)¼ p and then find (return (channel p)) ¼p, using the so-called (mathematical) b-conversion available in LINCOS. In the case of two parallel processes p and q, (par p q) can be transformed to :p q: by applying the channel to (p q), so we write (channel (par p q))¼ :p q:. The vector element :p q: is transformed back to (p q) by the application (return :p q:)¼(par p q). As a result we have ðreturnðchannel ðpar p qÞÞ ¼ ðparðp qÞÞ Let r and s be two parallel processes so that (channel (par r s)) ¼:r s:. The state vector of the four processes p, q, r, s, is then :p q r s: or some other permutation. This four tulple is by agreement also considered to be a silent process of type Proc. We require ðreturn:p q r s:Þ ¼ ðpar pðpar qðpar r sÞÞÞ: These representations have been chosen in order to admit the modeling in LINCOS of interrupts in processes. This is achieved by means of an arbiter program. 3. The arbiter We have by definition arb:Proc-Proc, but we will restrict the domain of this map to the state vectors of silent processes, for example (arb :p q:):Proc. The arbiter will be used to organize processing in a predetermined way. That goal is achieved by programming the arbiter term. We explain this with an example. Let it be required that the state vector element :p q: is to change to :r s:. This is achieved by the following
Note that in this case the variable l-bound to :p q: is not needed in :r s::Proc, so it is not given a name, and we write n instead. Here again the b-reduction from the l-calculus is used. Strictly speaking this reduction should be formulated separately. A program can be used to change an element of a state vector (but also a complete one), into another. For example DEFINE program2 : Proc-Proc :¼ ½* : ð:p q r s:Þð:t u v w:Þ: ðprogram2 ðarbð:p q r s:ÞÞÞ ¼ ð:t u v w:Þ:
4. Application Using the theory explained above we show now how actions in ‘reality’ can be modeled in LINCOS. As an example we consider the processes occurring in the opening act of Shakespeare’s HAMLET, PRINCE OF DENMARK, SCENE,– ELSINORE. ACT I. A platform before the Castle. After a while there are four persons on the platform: FRANSISCO, BERNARDO, HORATIO and MARCELLUS. They are engaged in conversation when the Ghost enters. Here is Shakespeare’s text leading to that event: FRANSISCO at his post. Enter to him BERNARDO. Ber. Who’s there? Fran. Nay, answer me: stand and unfold Yourself. Ber. Long live the king! Fran. Bernardo? Ber. He. Fran. You come most carefully upon your hour. Ber. ‘Tis now struck twelve; get thee to bed, Francisco. Fran. For this relief much thanks: ‘tis bitter cold. And I am sick at heart. Ber. Have you had quiet guard? Fran. Not a mouse stirring. Ber. Well, good night. If you do meet Horatio and Marcellus, The rivals of my watch, bid them make haste. Fran. I think I hear them. —Stand, ho! Who is there? Enter HORATIO and MARCELLUS. Hor. Friends to this ground. Mar. And liegemen to the Dane. Fran. Give you good-night. Mar. O, farewell, honest soldier: Who hath reliev’d you? Fran. Bernardo has my place. Give you good-night. [Exit]. Mar. Holla! Bernardo! Ber. Say. What, is Horatio there? Hor. A piece of him. Ber. Welcome, Horatio:- welcome, good Marcellus. Mar. What, has this thing appear’d again to-night? Ber. I have seen nothing.
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A. Ollongren / Acta Astronautica 71 (2012) 170–172
y.. Mar. Peace, break thee off; look where it comes again! Enter Ghost, armed. y..
:Fran-p Fran-c:-:Fran-ex:, soldier FRANSISCO leaves the platform :Ber-c Hor-c:- empty, officers BERNARDO and HORATIO are speechless
We use following abbreviations for the processes. Fran-p¼Fran on platform, Fran-c¼ Fran conversing, Fran-ex¼Fran leaving Ber-e¼Ber entering, Ber-p¼Ber on platform, Ber-c ¼Ber conversing Hor-e ¼Hor entering, Hor-p¼Hor on platform, Hor-c ¼Hor conversing Mar-e ¼Mar entering, Mar-p¼Mar on platform, Mar-c ¼Mar conversing, Mar-! ¼Mar exclaims Ghost-e¼ the Ghost entering The sequence of state vectors is during the beginning of Act I: :Fran-p : :Fran-p Ber-e : :Fran-p Ber-p : :Fran-p Fran-c Ber-p Ber-c : :Fran-p Fran-c Ber-p Ber-c Hor-e : :Fran-p Fran-c Ber-p Ber-c Hor-p Mar-e : :Fran-p Fran-c Ber-p Ber-c Hor-p Mar-p : :Fran-p Fran-c Ber-p Ber-c Hor-p Hor-c Mar-p Mar-c : :Fran-ex Ber-p Hor-p Mar-p Mar-! Ghost-e :
:Mar-c:-:Mar-!:, HAMLET’s friend MARCELLUS sees the Ghost! At the same time it is seen that :Ber-p Hor-p Mar-p: is kept in the new state vector—BERNARDO, MARCELLUS and HORATIO are in place on the platform. This state vector is necessary. Should we have left out one of these, the person would have disappeared! That would be all right (later on) for the Ghost, but not for the officers and HAMLET’s friend! 5. Conclusion The present extensive note explains how processes running in parallel, subjected to interrupts, can be modeled in a satisfactory manner in terms of the Lingua Cosmica. There is no reference to time. Processes carry out elementary steps, either sequentially or in parallel, not related to time intervals. The same applies to interrupts, modeled as changes in state vectors. References
In order to model this in LINCOS we need eight programs. The last one is DEFINE program8:Proc-Proc:¼ [*::Fran-p Fran-c Ber-p Ber-c Hor-p Hor-c Mar-p Mar-c:] (:Fran-ex Ber-p Hor-p Mar-p Mar-! Ghost-e:). Note that the following changes are registered with program8.
[1] A. Ollongren, Large-size message construction for ETI, Papers Presented at Congresses of the International Astronautical Academy 1998–2008, Cf. Acta Astronautica and Science.Direct.com. [2] A. Ollongren, Astrolinguistics, Logic design of a system for interstellar communication, LINCOS, a monograph (in review for publication 2011–12), Chapter 5.1, Representing Sequential Processes. [3] A. Ollongren, D. Vakoch, Processes in Lingua Cosmica, Paper in AbSciCon 2010, Session ‘Search for Intelligent Life’, Topic ‘Interstellar Message Construction: Can We Make Ourselves Understood?’ SUNY, April 2011, submitted for publication.
Contents lists available at SciVerse ScienceDirect
Acta Astronautica journal homepage: www.elsevier.com/locate/actaastro
Academy Transactions Note
Processes in Lingua Cosmica Alexander Ollongren n Leiden Institute of Advanced Computer Science, Niels Bohrweg 1, 2333 CA Leiden, Holland
a r t i c l e in f o
abstract
Article history: Received 1 March 2011 Accepted 29 September 2011 Available online 28 October 2011
In a sequence of papers on the topic of message construction for interstellar communication by means of a cosmic language, representations of various kinds of concepts of reality in a Lingua Cosmica system [1]. Those studied were logic relations of a static character. The present contribution contains an important, fundamental extension: groundwork is done for the purpose of interpreting (dynamic) processes of various sorts in the linguistic system. Individual processes are abstracted in a logic sense and provided with basic properties as termination and communication functions. They can be combined into kinds of processes: sequential and parallel ones represented by only one inductive definition in logic. Based on concepts from the so-called process algebra, processes are provided with channels mapping them to their states. State vectors are introduced to represent states of conglomerates of processes. Communication between processes (locally or globally) is effectuated by means of state transitions. Together with a programmed arbitration function, state vectors play a crucial role in representing communication. With these ingredients possibilities for general interpretations of a wide range of processes in the Lingua Cosmica system come in view. & 2011 Published by Elsevier Ltd.
Keywords: Communication Interstellar Interspecies
1. Basics The present contribution is concerned with the nontrivial matter of incorporating descriptions of sequential processes or processes running in parallel without reference to time in a linguistic system for interstellar message construction. The linguistic system used in the present note is the new lingua cosmica system [1,2], referred to as LINCOS. The system is based on constructive logic and its terms (logical forms) are represented as types, see also [3]. Processes to be discussed in the present paper are represented by a map in the form of an inductive type DEFINE Proc :¼ seq : Proc-Proc-Proc9 par : Proc-Proc-Proc9 arb : Proc-Proc:
n
Tel.: þ 31 715 173 169. E-mail address: [email protected]
0094-5765/$ - see front matter & 2011 Published by Elsevier Ltd. doi:10.1016/j.actaastro.2011.09.017
This injective, total map represents either a sequential process, or a process, which operates in parallel with another one, or an arbitration. The selectors seq, par and arb identify the terms belonging to the three distinct cases. A process s of type Proc, written s:Proc, occurring in a sequence is supposed to ‘do something’, carry out an action (an elementary step), and then is either followed by a process because (seq s) Proc-Proc, or it terminates. If u is next after s in a sequence, (seq s u):Proc. Processes occurring in parallel, all of type Proc, are supposed to be linearly ordered in some sense. However if p is in the ordering (par p) is not the next in the ordering. In addition if p and q are in the ordering, (par p q):Proc, p and q both do something but they are not supposed to interfere with one another. It is also supposed that there is no difference between (par p q) and (par q p). A process occurring in parallel can also terminate. Finally no process can occur in parallel with itself.
A. Ollongren / Acta Astronautica 71 (2012) 170–172
The arbitration process is included for the purpose of treating communication between processes, in the present treaty subjected to a communication program. 2. Parallel processes
171
program DEFINE program1 : Proc-Proc :¼ ½* : ð:pq:Þðrs:Þ: Then because (arb (:p q:)):Proc, we have (program1 (arb (:p q:))):Proc, and additionally ðprogram1 ðarb ð:p q:ÞÞÞ ¼ ð:rs:Þ:
Let p:Proc and q:Proc be two unequal terms in the linear ordering of processes, which do something simultaneously (in parallel) without interfering with one another. We have seen (par p q):Proc. We shall use for a pair like (par p q) the expression :p q: or (:p q:) if it is required to indicate that it is to be an element of a state vector. This type of vector, introduced briefly in a previous paper [3] in the context of LINCOS, is considered to consist of one or more silent processes of type Proc. Note that the silent process :p q: is the same as :q p:. In other words, : : commutes. A silent process does not do something, but it carries information. Furthermore we assume that to any (parallel) process a channel is associated, mapping a process to its element of the state vector DEFINE channel : Proc-Proc :¼ ½x : ProcJxJ This definition is supplemented by a return, mapping a vector element to the corresponding process DEFINE return : Proc-Proc :¼ ½JxJ : Procx: Here [:x::Proc]x means that :x: is l-bound to the type Proc [see 2,3] and the l-term is applied to x. The resulting term is of type Proc-Proc. If p:Proc we agree on the conventions (channel p) ¼:p:, (return :p:)¼ p and then find (return (channel p)) ¼p, using the so-called (mathematical) b-conversion available in LINCOS. In the case of two parallel processes p and q, (par p q) can be transformed to :p q: by applying the channel to (p q), so we write (channel (par p q))¼ :p q:. The vector element :p q: is transformed back to (p q) by the application (return :p q:)¼(par p q). As a result we have ðreturnðchannel ðpar p qÞÞ ¼ ðparðp qÞÞ Let r and s be two parallel processes so that (channel (par r s)) ¼:r s:. The state vector of the four processes p, q, r, s, is then :p q r s: or some other permutation. This four tulple is by agreement also considered to be a silent process of type Proc. We require ðreturn:p q r s:Þ ¼ ðpar pðpar qðpar r sÞÞÞ: These representations have been chosen in order to admit the modeling in LINCOS of interrupts in processes. This is achieved by means of an arbiter program. 3. The arbiter We have by definition arb:Proc-Proc, but we will restrict the domain of this map to the state vectors of silent processes, for example (arb :p q:):Proc. The arbiter will be used to organize processing in a predetermined way. That goal is achieved by programming the arbiter term. We explain this with an example. Let it be required that the state vector element :p q: is to change to :r s:. This is achieved by the following
Note that in this case the variable l-bound to :p q: is not needed in :r s::Proc, so it is not given a name, and we write n instead. Here again the b-reduction from the l-calculus is used. Strictly speaking this reduction should be formulated separately. A program can be used to change an element of a state vector (but also a complete one), into another. For example DEFINE program2 : Proc-Proc :¼ ½* : ð:p q r s:Þð:t u v w:Þ: ðprogram2 ðarbð:p q r s:ÞÞÞ ¼ ð:t u v w:Þ:
4. Application Using the theory explained above we show now how actions in ‘reality’ can be modeled in LINCOS. As an example we consider the processes occurring in the opening act of Shakespeare’s HAMLET, PRINCE OF DENMARK, SCENE,– ELSINORE. ACT I. A platform before the Castle. After a while there are four persons on the platform: FRANSISCO, BERNARDO, HORATIO and MARCELLUS. They are engaged in conversation when the Ghost enters. Here is Shakespeare’s text leading to that event: FRANSISCO at his post. Enter to him BERNARDO. Ber. Who’s there? Fran. Nay, answer me: stand and unfold Yourself. Ber. Long live the king! Fran. Bernardo? Ber. He. Fran. You come most carefully upon your hour. Ber. ‘Tis now struck twelve; get thee to bed, Francisco. Fran. For this relief much thanks: ‘tis bitter cold. And I am sick at heart. Ber. Have you had quiet guard? Fran. Not a mouse stirring. Ber. Well, good night. If you do meet Horatio and Marcellus, The rivals of my watch, bid them make haste. Fran. I think I hear them. —Stand, ho! Who is there? Enter HORATIO and MARCELLUS. Hor. Friends to this ground. Mar. And liegemen to the Dane. Fran. Give you good-night. Mar. O, farewell, honest soldier: Who hath reliev’d you? Fran. Bernardo has my place. Give you good-night. [Exit]. Mar. Holla! Bernardo! Ber. Say. What, is Horatio there? Hor. A piece of him. Ber. Welcome, Horatio:- welcome, good Marcellus. Mar. What, has this thing appear’d again to-night? Ber. I have seen nothing.
172
A. Ollongren / Acta Astronautica 71 (2012) 170–172
y.. Mar. Peace, break thee off; look where it comes again! Enter Ghost, armed. y..
:Fran-p Fran-c:-:Fran-ex:, soldier FRANSISCO leaves the platform :Ber-c Hor-c:- empty, officers BERNARDO and HORATIO are speechless
We use following abbreviations for the processes. Fran-p¼Fran on platform, Fran-c¼ Fran conversing, Fran-ex¼Fran leaving Ber-e¼Ber entering, Ber-p¼Ber on platform, Ber-c ¼Ber conversing Hor-e ¼Hor entering, Hor-p¼Hor on platform, Hor-c ¼Hor conversing Mar-e ¼Mar entering, Mar-p¼Mar on platform, Mar-c ¼Mar conversing, Mar-! ¼Mar exclaims Ghost-e¼ the Ghost entering The sequence of state vectors is during the beginning of Act I: :Fran-p : :Fran-p Ber-e : :Fran-p Ber-p : :Fran-p Fran-c Ber-p Ber-c : :Fran-p Fran-c Ber-p Ber-c Hor-e : :Fran-p Fran-c Ber-p Ber-c Hor-p Mar-e : :Fran-p Fran-c Ber-p Ber-c Hor-p Mar-p : :Fran-p Fran-c Ber-p Ber-c Hor-p Hor-c Mar-p Mar-c : :Fran-ex Ber-p Hor-p Mar-p Mar-! Ghost-e :
:Mar-c:-:Mar-!:, HAMLET’s friend MARCELLUS sees the Ghost! At the same time it is seen that :Ber-p Hor-p Mar-p: is kept in the new state vector—BERNARDO, MARCELLUS and HORATIO are in place on the platform. This state vector is necessary. Should we have left out one of these, the person would have disappeared! That would be all right (later on) for the Ghost, but not for the officers and HAMLET’s friend! 5. Conclusion The present extensive note explains how processes running in parallel, subjected to interrupts, can be modeled in a satisfactory manner in terms of the Lingua Cosmica. There is no reference to time. Processes carry out elementary steps, either sequentially or in parallel, not related to time intervals. The same applies to interrupts, modeled as changes in state vectors. References
In order to model this in LINCOS we need eight programs. The last one is DEFINE program8:Proc-Proc:¼ [*::Fran-p Fran-c Ber-p Ber-c Hor-p Hor-c Mar-p Mar-c:] (:Fran-ex Ber-p Hor-p Mar-p Mar-! Ghost-e:). Note that the following changes are registered with program8.
[1] A. Ollongren, Large-size message construction for ETI, Papers Presented at Congresses of the International Astronautical Academy 1998–2008, Cf. Acta Astronautica and Science.Direct.com. [2] A. Ollongren, Astrolinguistics, Logic design of a system for interstellar communication, LINCOS, a monograph (in review for publication 2011–12), Chapter 5.1, Representing Sequential Processes. [3] A. Ollongren, D. Vakoch, Processes in Lingua Cosmica, Paper in AbSciCon 2010, Session ‘Search for Intelligent Life’, Topic ‘Interstellar Message Construction: Can We Make Ourselves Understood?’ SUNY, April 2011, submitted for publication.