## Before we begin: Thank you, thank you, thank you,... Walter.WassollmanzudiesemMannnochsagen?

### BibTeX

@MISC{Müller_beforewe,

author = {Stefan Müller and Molekulare Strukturbiologie and Den Meisterdenkern and Peter Peter and Und Ivo and Den Gesellen Christoph and Stephan Und Alex and Den Lehrlingen Thomas and Andreas Günther Roman and Dagmar Und Michael Zusammenfassung},

title = {Before we begin: Thank you, thank you, thank you,... Walter.WassollmanzudiesemMannnochsagen?},

year = {}

}

### OpenURL

### Abstract

Doctor rerum naturalium

### Citations

3027 |
Genetic Programming: On the Programming of Computers by Means of Natural Selection
- Koza
- 1992
(Show Context)
Citation Context ...perspective, contrast it with approaches to adaptation based solely on population genetics or various flavorsIntroduction 4 of genetic algorithms [40], classifier systems [28] or genetic programming =-=[35]-=-. Like chemistry, many natural or artificial adaptive systems consist of a population dynamics involving objects of a combinatorial nature. These objects might be RNA sequences [19], neural networks, ... |

1561 |
An Introduction to Genetic Algorithms
- Mitchell
- 1997
(Show Context)
Citation Context ...rganization To place this framing in an evolutionary perspective, contrast it with approaches to adaptation based solely on population genetics or various flavorsIntroduction 4 of genetic algorithms =-=[40]-=-, classifier systems [28] or genetic programming [35]. Like chemistry, many natural or artificial adaptive systems consist of a population dynamics involving objects of a combinatorial nature. These o... |

1135 |
The Lambda-Calculus, its syntax and semantics
- Barendregt
- 1984
(Show Context)
Citation Context ...glue” consisting of cross-interaction products which do not belong to either component organization.3 λ-calculus In this presentation of the λ-calculus we follow the encyclopaedic book by Barendregt =-=[3]-=-, as well as the excellent textbook by Hankin [27]. 3.1 History The λ-calculus is a theory about functions as rules, rather than as graphs. “Functions as rules” is the old fashioned notion of function... |

958 | A theory of type polymorphism in programming
- Milner
(Show Context)
Citation Context ...nce, and a number of useful type systems have appeared in the literature (for a survey see [6]). We plan to study whether certain constraints of molecular interaction can be modeled by using System F =-=[39]-=- possibly augmented with union types and subtyping. Moreover, typed λ-calculus is a proof-theory of intuitionistic logic in natural deduction style [23]. This connection extends our previous view of c... |

694 |
The Genetical Theory of Natural Selection
- Fisher
- 1930
(Show Context)
Citation Context ... Mendelism and Darwinism, known as the “Modern Synthesis”, codified the evolutionary process as a problem in the dynamics of alleles (gene variants) governed jointly by fitness and transmission rules =-=[15, 26, 56]-=-. Yet concepts like gene and fitness depend on a functionally organized context known as organism (phenotype). Our current formal framework for theorizing about evolution assumes, therefore, the prior... |

574 | Term Rewriting Systems
- Klop
- 1992
(Show Context)
Citation Context ...k. These actions may, of course, depend on the context of a building block within a λ-term. The characterization of the functional relationships among building blocks yields a system of rewrite rules =-=[2, 32]-=-. This system can, in many cases, be exhaustively specified using Knuth-Bendix completion techniques [33, 34]. Rewrite systems which complete, permit a finite specification of all interactions among t... |

500 |
Simple word problems in universal algebras
- Knuth, Bendix
- 1970
(Show Context)
Citation Context ...tion of the functional relationships among building blocks yields a system of rewrite rules [2, 32]. This system can, in many cases, be exhaustively specified using Knuth-Bendix completion techniques =-=[33, 34]-=-. Rewrite systems which complete, permit a finite specification of all interactions among the elements of the subspace. This way they implicitly determine a grammar for its elements. The rewrite syste... |

333 |
The Calculi of Lambda Conversions
- Church
- 1941
(Show Context)
Citation Context ...ve (pure combinatory logic), but the logical part of this theory is too weak to be adequate as a foundation. After the Kleene-Rosser paradox Church was discouraged in his foundational program. Church =-=[8]-=- gave a consistent (as shown by the Church-Rosser theorem) subtheory of his original system dealing only with the functional part. This theory is the λI-calculus. Curry on the other hand did not want ... |

249 |
Combinatory Reduction Systems
- Klop
- 1980
(Show Context)
Citation Context ...a redex is called a residual. In the above example there is no residual of the original redex in the final term; it has been reduced in the final step. A formal treatment of residuals can be found in =-=[31]-=-. Definition 3.59 A reduction sequence M0 ∆0 ∆1 ∆2 → M1 → M2 → ... is a standard reduction if ∀i ∀j <i:∆i is not a residual of a redex to the left of ∆j (in the term Mj). An alternative description of... |

210 | Type systems
- Cardelli
- 1996
(Show Context)
Citation Context ...gf, between two terms f and g from occurring. Type theory is a very active field of research in computer science, and a number of useful type systems have appeared in the literature (for a survey see =-=[6]-=-). We plan to study whether certain constraints of molecular interaction can be modeled by using System F [39] possibly augmented with union types and subtyping. Moreover, typed λ-calculus is a proof-... |

183 |
Evolutionary phenomena in simple dynamics
- Lindgren
- 1992
(Show Context)
Citation Context ...population dynamics involving objects of a combinatorial nature. These objects might be RNA sequences [19], neural networks, cellular automata [10], assembler code programs [46], strategies in a game =-=[37]-=- or any other kind of discrete structure. The combinatorial nature of these objects makes the set of possible variations astronomically large, such that typical population sizes can realize only a van... |

134 |
Correspondence between algol 60 and church’s lambda-notation: part i
- Landin
- 1965
(Show Context)
Citation Context ... Pascal, procedures can be arguments of procedures. In LISP the same is true and moreover a procedure can be the output of a procedure. For relations between λ-calculus and programming languages, see =-=[36, 42, 24]-=-. Because of the similarities of λ-calculus and some programming languages, ideas for the semantics of the former may be applied to the latter. Landin gave a semantics of Algol by translating this lan... |

131 |
Lambda-calculus models of programming languages
- Morris
- 1968
(Show Context)
Citation Context ... Pascal, procedures can be arguments of procedures. In LISP the same is true and moreover a procedure can be the output of a procedure. For relations between λ-calculus and programming languages, see =-=[36, 42, 24]-=-. Because of the similarities of λ-calculus and some programming languages, ideas for the semantics of the former may be applied to the latter. Landin gave a semantics of Algol by translating this lan... |

124 |
Functional Programming
- Field, Harrison
- 1988
(Show Context)
Citation Context ...stion by giving a reduction order which is guaranteed to terminate with normal form if any reduction sequence does, but if best is also meant to be optimal then the question is more complicated – see =-=[14]-=- for a more detailed discussion of this topic. 3.3.2 Notions of reduction Reduction may be viewed as a special form of relation on λ-terms. Why special? Recall the discussion of the constraints on equ... |

108 |
Recursive programming techniques
- Burge
- 1975
(Show Context)
Citation Context ...d to the latter. Landin gave a semantics of Algol by translating this language in λ-calculus and by describing an operational semantics for the latter. For further work on this kind of semantics, see =-=[44, 45, 43, 5]-=-. In the meantime there was a need for a denotational semantics of programming languages (in order to express what is the functional meaning of a program). A similar problem had occurred in a pure for... |

108 |
A set of postulates for the foundation of logic
- Church
- 1932
(Show Context)
Citation Context ...nders of combinatory logic, and it was also implicit in the work of Church founding the λ-calculus. Unfortunately all attempts to provide a foundation for mathematics failed. Church’s original system =-=[7]-=- was inconsistent as shown by Kleene and Rosser [30]. As was pointed out in [1], Frege’s well known inconsistent theory [21] essentially contains the λ-calculus; so that was in fact another failure. C... |

106 |
Proofs and Types. Cambridge Tracts
- Girard, Taylor, et al.
- 1989
(Show Context)
Citation Context ...ar interaction can be modeled by using System F [39] possibly augmented with union types and subtyping. Moreover, typed λ-calculus is a proof-theory of intuitionistic logic in natural deduction style =-=[23]-=-. This connection extends our previous view of chemistry to one in which molecular shapes are seen as propositions and physical molecules as proofs of propositions. A chemical reaction then literally ... |

105 | Continuity in Evolution: On the Nature of Transitions
- Fontana, Schuster
- 1998
(Show Context)
Citation Context ...enetic programming [35]. Like chemistry, many natural or artificial adaptive systems consist of a population dynamics involving objects of a combinatorial nature. These objects might be RNA sequences =-=[19]-=-, neural networks, cellular automata [10], assembler code programs [46], strategies in a game [37] or any other kind of discrete structure. The combinatorial nature of these objects makes the set of p... |

97 | The evolution of emergent computation
- Mitchell, Crutchfield
- 1994
(Show Context)
Citation Context ...many natural or artificial adaptive systems consist of a population dynamics involving objects of a combinatorial nature. These objects might be RNA sequences [19], neural networks, cellular automata =-=[10]-=-, assembler code programs [46], strategies in a game [37] or any other kind of discrete structure. The combinatorial nature of these objects makes the set of possible variations astronomically large, ... |

84 |
M.,The Denotational description of programming languages
- Gordon
- 1979
(Show Context)
Citation Context ...nal semantics for programming languages. This is because Scott’s method is powerful enough to give also a meaning to the following two features of programming languages: recursion and data types. See =-=[51, 38, 53, 25]-=-. 3.1.3 Pure λ-calculus λ-calculus, as treated in the rest of this section, is not directed towards applications as above, but is studied for its own interest. The formal (type free) λ-calculus, a the... |

83 |
the arrival of the fittest”:towards a theory of biological organisation
- Fontana, Buss
- 1994
(Show Context)
Citation Context ...the dynamical aspect of the base model (chapter 6).2 A model of functional organization In the following we provide an executive summary of the published work which established this area of research =-=[16, 17, 18]-=-. 2.1 Chemistry as a calculus Chemistry deals with structures that encode potential actions. The reactive interaction of one structure with another triggers a specific joint action which yields furthe... |

63 |
Frege structures and the notion of proposition, truth and set
- Aczel
- 1980
(Show Context)
Citation Context ...ding the λ-calculus. Unfortunately all attempts to provide a foundation for mathematics failed. Church’s original system [7] was inconsistent as shown by Kleene and Rosser [30]. As was pointed out in =-=[1]-=-, Frege’s well known inconsistent theory [21] essentially contains the λ-calculus; so that was in fact another failure. Curry [11] did provide a consistent theory fulfilling the first point above (pur... |

57 | What would be conserved if ‘the tape were played twice
- Fontana, Buss
- 1994
(Show Context)
Citation Context ...the dynamical aspect of the base model (chapter 6).2 A model of functional organization In the following we provide an executive summary of the published work which established this area of research =-=[16, 17, 18]-=-. 2.1 Chemistry as a calculus Chemistry deals with structures that encode potential actions. The reactive interaction of one structure with another triggers a specific joint action which yields furthe... |

51 |
Grundgesetze der Arithmetik, Begriffschriftlich Abgeleitet, Viena (1893/1903
- Frege
(Show Context)
Citation Context ...pts to provide a foundation for mathematics failed. Church’s original system [7] was inconsistent as shown by Kleene and Rosser [30]. As was pointed out in [1], Frege’s well known inconsistent theory =-=[21]-=- essentially contains the λ-calculus; so that was in fact another failure. Curry [11] did provide a consistent theory fulfilling the first point above (pure combinatory logic), but the logical part of... |

51 |
Lambda-definability and recursiveness
- Kleene
- 1936
(Show Context)
Citation Context ...lculus dealing only with functions turned out to be quite successful. Using this theory Church proposed a formalization of the notion “effectively computable” by the concept of λ-definability. Kleene =-=[29]-=- showed that λ-definability is equivalent to (partial) recursiveness and in the meantime Church formulated his thesis, stating that recursiveness is the proper formalization of effective computability... |

49 |
The barrier of objects: from dynamical systems to bounded organizations
- Fontana, Buss
- 1996
(Show Context)
Citation Context ...the dynamical aspect of the base model (chapter 6).2 A model of functional organization In the following we provide an executive summary of the published work which established this area of research =-=[16, 17, 18]-=-. 2.1 Chemistry as a calculus Chemistry deals with structures that encode potential actions. The reactive interaction of one structure with another triggers a specific joint action which yields furthe... |

41 |
Grundlagen der kombinatorischen Logik
- Curry
- 1930
(Show Context)
Citation Context ...inconsistent as shown by Kleene and Rosser [30]. As was pointed out in [1], Frege’s well known inconsistent theory [21] essentially contains the λ-calculus; so that was in fact another failure. Curry =-=[11]-=- did provide a consistent theory fulfilling the first point above (pure combinatory logic), but the logical part of this theory is too weak to be adequate as a foundation. After the Kleene-Rosser para... |

30 | Beyond digital naturalism
- Fontana, Wagner, et al.
- 1994
(Show Context)
Citation Context ...nd which features are curiosities derived from particular initial conditions, parameter settings, or a particular chemical stance. The distinction is between what has been called “digital naturalism” =-=[20]-=- and the claim for a theory of self-maintenance. (3) As emphasized at the outset, an abstract theory of objects plays a role analogous to that of differential equations. The analysis of a dynamical sy... |

26 |
Lambda calculi: a guide for computer scientists
- Hankin
- 1994
(Show Context)
Citation Context ...ich do not belong to either component organization.3 λ-calculus In this presentation of the λ-calculus we follow the encyclopaedic book by Barendregt [3], as well as the excellent textbook by Hankin =-=[27]-=-. 3.1 History The λ-calculus is a theory about functions as rules, rather than as graphs. “Functions as rules” is the old fashioned notion of function and refers to the process of going from argument ... |

22 |
The inconsistency of certain formal logics
- Kleene, Rosser
- 1935
(Show Context)
Citation Context ...t in the work of Church founding the λ-calculus. Unfortunately all attempts to provide a foundation for mathematics failed. Church’s original system [7] was inconsistent as shown by Kleene and Rosser =-=[30]-=-. As was pointed out in [1], Frege’s well known inconsistent theory [21] essentially contains the λ-calculus; so that was in fact another failure. Curry [11] did provide a consistent theory fulfilling... |

16 |
The Causes of Evolution. Longmans
- Haldane
- 1932
(Show Context)
Citation Context ... Mendelism and Darwinism, known as the “Modern Synthesis”, codified the evolutionary process as a problem in the dynamics of alleles (gene variants) governed jointly by fitness and transmission rules =-=[15, 26, 56]-=-. Yet concepts like gene and fitness depend on a functionally organized context known as organism (phenotype). Our current formal framework for theorizing about evolution assumes, therefore, the prior... |

6 |
Computing in Systems Described by Equations. Lecture Notes in Computer Science 58
- O’Donnell
- 1977
(Show Context)
Citation Context ...d to the latter. Landin gave a semantics of Algol by translating this language in λ-calculus and by describing an operational semantics for the latter. For further work on this kind of semantics, see =-=[44, 45, 43, 5]-=-. In the meantime there was a need for a denotational semantics of programming languages (in order to express what is the functional meaning of a program). A similar problem had occurred in a pure for... |

4 |
An Introduction to Knuth-Bendix Completion
- Klop, Middeldorp
- 1988
(Show Context)
Citation Context ...tion of the functional relationships among building blocks yields a system of rewrite rules [2, 32]. This system can, in many cases, be exhaustively specified using Knuth-Bendix completion techniques =-=[33, 34]-=-. Rewrite systems which complete, permit a finite specification of all interactions among the elements of the subspace. This way they implicitly determine a grammar for its elements. The rewrite syste... |

3 |
Artificial life in real chemical reaction systems. Book manuscript in preparation (contact address
- Bro
- 1995
(Show Context)
Citation Context ...a semiotic unit as a device for natural language interpretation, and interpretation of terms-as-molecules as germane to a blueprint for the design of a self-maintaining chemical manufacturing process =-=[4]-=-, as it is to a metabolic cycle in a cell or a system of cell-cell communications defining an organ. The origin of such specifications from a research program in artifical chemistry or in experimental... |

2 |
Evaluation and Denotation of Pure LISP. A Worked Example in Semantics
- Gordon
- 1973
(Show Context)
Citation Context ... Pascal, procedures can be arguments of procedures. In LISP the same is true and moreover a procedure can be the output of a procedure. For relations between λ-calculus and programming languages, see =-=[36, 42, 24]-=-. Because of the similarities of λ-calculus and some programming languages, ideas for the semantics of the former may be applied to the latter. Landin gave a semantics of Algol by translating this lan... |

2 |
A Theory of Programming Language Semantics (2 vols
- MILNE, STRACHEY
- 1976
(Show Context)
Citation Context ...nal semantics for programming languages. This is because Scott’s method is powerful enough to give also a meaning to the following two features of programming languages: recursion and data types. See =-=[51, 38, 53, 25]-=-. 3.1.3 Pure λ-calculus λ-calculus, as treated in the rest of this section, is not directed towards applications as above, but is studied for its own interest. The formal (type free) λ-calculus, a the... |

1 |
Rechnen und Schließen in gleichungsdefinierten Strukturen
- Reduktionssysteme
- 1995
(Show Context)
Citation Context ...k. These actions may, of course, depend on the context of a building block within a λ-term. The characterization of the functional relationships among building blocks yields a system of rewrite rules =-=[2, 32]-=-. This system can, in many cases, be exhaustively specified using Knuth-Bendix completion techniques [33, 34]. Rewrite systems which complete, permit a finite specification of all interactions among t... |

1 | 119, emphasis by the author - Chance, page - 1971 |