FIT-PROLOG : a functional/relational language comparison

The programming languages FIT and PROLOG are compared as examples of functional and relational programming, respectively. This leads to some proposals concerning both languages. As an introductory tutorial, PROLOG facts, questions, variables, conjunctions, and rules are reformulated in FIT. A natural equivalence between functions and relations is exploited for their interchangeable FIT use. An ESCVAL operator is proposed which causes relation calls to return values of request variables and thus permits their function-like nesting. Function calls with request variables are introduced, showing a sense in which FIT functions are more general than PROLOG relations. Higher-order functions and relations are demonstrated to be available in FIT but not in PROLOG. PROLOG structures and FIT compounds differ mainly in the fixed arity of the former and the variable length of the latter. FIT's compounds can also be interpreted as function calls that return themselves in normalized form. Pattern matching in PROLOG [FIT] treats list heads and tails asymmetrically [symmetrically] and doesn't [does] allow for non-deterministic results. While PROLOG generalizes pattern-data matching to pattern-pattern unification. FIT generalizes it to adapter-data fitting. PROLOG's Horn clauses in FIT become implicit fitters: Facts become special implicit adapters and rules become special implicit transformers; for PROLOG II constraints, transformers with LOCAL bodies or invocation adapters with COM[POSE-TRA]FO expressions can be used. While PROLOG interprets clauses in textual order, FIT interprets them in a specificity order which is modifiable by a SECURE operator. Although PROLOG's cut operator is not used in FIT, a proposal is made to distinguish the specification of clause ordering [by FIT's SECURE operator] and the specification of clause abandoning [by an EXCLUSIVE operator corresponding to 'initial'-restricted cuts]. EXCLUSIVE-marked COMFO-constrained rules are then used for functional and relational representations of guarded commands. A comparison of the list processing capabilities of both languages exemplifies how FIT's adapters can make relational programming more concise than PROLOG’s Horn clauses. The representation of sets as lists without duplicates leads to difficulties with PROLOG's standard intersection and union predicates, which can be overcome by representing them as the self-normalizing CLASS data structure in FIT. Possible reasons for the poor readability of Warren's PROLOG serialise predicate are discussed and an alternative FIT function is formulated which shows the inherent simplicity of this problem. McDermott's PROLOG quadrat predicate is transformed into a more concise and readable ESCVAL form, which in turn is transformed into a corresponding FIT ESCVAL form and into a functional FIT form. Fermat's equation is formulated relationally, showing that for principal reasons some relations can not be used in all ways allowed by PROLOG's notation, a problem that does not arise in a corresponding functional FIT formulation

Interval linear constraint solving in constraint logic programming.

by Chong-kan Chiu.Thesis (M.Phil.)--Chinese University of Hong Kong, 1994.Includes bibliographical references (leaves 97-103).Chapter 1 --- Introduction --- p.1Chapter 1.1 --- Related Work --- p.2Chapter 1.2 --- Organizations of the Dissertation --- p.4Chapter 1.3 --- Notations --- p.4Chapter 2 --- Overview of ICLP(R) --- p.6Chapter 2.1 --- Basics of Interval Arithmetic --- p.6Chapter 2.2 --- Relational Interval Arithmetic --- p.8Chapter 2.2.1 --- Interval Reduction --- p.8Chapter 2.2.2 --- Arithmetic Primitives --- p.10Chapter 2.2.3 --- Interval Narrowing and Interval Splitting --- p.13Chapter 2.3 --- Syntax and Semantics --- p.16Chapter 3 --- Limitations of Interval Narrowing --- p.18Chapter 3.1 --- Computation Inefficiency --- p.18Chapter 3.2 --- Inability to Detect Inconsistency --- p.23Chapter 3.3 --- The Newton Language --- p.27Chapter 4 --- Design of CIAL --- p.30Chapter 4.1 --- The CIAL Architecture --- p.30Chapter 4.2 --- The Inference Engine --- p.31Chapter 4.2.1 --- Interval Variables --- p.31Chapter 4.2.2 --- Extended Unification Algorithm --- p.33Chapter 4.3 --- The Solver Interface and Constraint Decomposition --- p.34Chapter 4.4 --- The Linear and the Non-linear Solvers --- p.37Chapter 5 --- The Linear Solver --- p.40Chapter 5.1 --- An Interval Gaussian Elimination Solver --- p.41Chapter 5.1.1 --- Naive Interval Gaussian Elimination --- p.41Chapter 5.1.2 --- Generalized Interval Gaussian Elimination --- p.43Chapter 5.1.3 --- Incrementality of Generalized Gaussian Elimination --- p.47Chapter 5.1.4 --- Solvers Interaction --- p.50Chapter 5.2 --- An Interval Gauss-Seidel Solver --- p.52Chapter 5.2.1 --- Interval Gauss-Seidel Method --- p.52Chapter 5.2.2 --- Preconditioning --- p.55Chapter 5.2.3 --- Increment ality of Preconditioned Gauss-Seidel Method --- p.58Chapter 5.2.4 --- Solver Interaction --- p.71Chapter 5.3 --- Comparisons --- p.72Chapter 5.3.1 --- Time Complexity --- p.72Chapter 5.3.2 --- Storage Complexity --- p.73Chapter 5.3.3 --- Others --- p.74Chapter 6 --- Benchmarkings --- p.76Chapter 6.1 --- Mortgage --- p.78Chapter 6.2 --- Simple Linear Simultaneous Equations --- p.79Chapter 6.3 --- Analysis of DC Circuit --- p.80Chapter 6.4 --- Inconsistent Simultaneous Equations --- p.82Chapter 6.5 --- Collision Problem --- p.82Chapter 6.6 --- Wilkinson Polynomial --- p.85Chapter 6.7 --- Summary and Discussion --- p.86Chapter 6.8 --- Large System of Simultaneous Equations --- p.87Chapter 6.9 --- Comparisons Between the Incremental and the Non-Incremental Preconditioning --- p.89Chapter 7 --- Concluding Remarks --- p.93Chapter 7.1 --- Summary and Contributions --- p.93Chapter 7.2 --- Future Work --- p.95Bibliography --- p.9

The Church of Christ in early Bernicia: forerunners and foundation

A firmly multidlsciplinary approach starts from a theological definition of the Church as the Body of Christ, and Christians as empowered by the Holy Spirit, the possibility of miracle, and the reality of warfare with demons are taken seriously, and scholarly belief in them defended. They are made the subject of excursuses. Hagiographic writings are treated with cautious respect. Bernicia, land and people, and its relationship to its neighbours are considered. In a demographic excursus the view that Dark Age life-span was short is rebuffed. Part two discusses the life and mission of the Church in sub-Roman Britain. In our area evidence for this proves to be largely limited to the shadowy activities of Ninian and Kentigern, therefore further evidence of the status of the British church in the fifth and sixth centuries is sought in Patrick’s Confession and Gildas's De Excidlo Britɸmniae. A new model for the latter - the sermon of the protomartyr Stephen - is proposed; as is a new exegesis of D. E. B. c.69, which may have Implications for our understanding of the persistence of Pelagian beliefs. An excursus considers the significance of white stones in association with Christian burial. The origins of the mission of Augustine are considered briefly. Part three considers the mission of Paulinus in detail, in particular the reasons for its collapse; in contrasting it with the Celtic mission misslological principles are cited. A reappraisal of Paulinus's retreat, more favourable to him than that normally held, is reached by invoking wartime experience. The discipline of obstetrics is involved to advance the theory that /Ethelburh's delivery was premature; also earlier to re-examine the Herbert Ian account of Kentigern's conception, where the 'something contrary to sound doctrine' is identified, against the hitherto standard view, as the apparent approval, by Servanus, of extramarital coitus. The final establishment of the Church in Bernicia is seen as occurring principally as the result of Aidan's mission, but with valid contributions from the British and Roman traditions. That Simeon of Durham gave the credit for this foundation to Oswald is found Justifiable. A new genealogical tree of Oswy has been constructed, and maps have been provided

Mission: Vol. 20, Nos. 1 and 2

Mission: Vol. 20, Nos. 1 and 2. The articles in this issue include: A Thread of Faith from the Editor, Coping With Change In Religious Belief: Genesis and Overview by Herbert A. Marlowe, Jr., On Not Jumping Without a Parachute: Transitions, Tensions and Traumas of Active Faith by Kathy J. Pulley, Coping When Different by Dwayne D. Simmons, Changing Without Leaving by Mary Lou Walden, Dear Diary: Snapshots of Transition by Diana Caillouet, PERSONAL RESPONSES TO EDITOR\u27S REQUEST: We Have Chosen to Stay by Larry and Jacquelyn Floyd, and God is Bigger Than The Problems by Everett and Helen Champney. Everlasting Life by Karen Lashley, Falling But Believing by David Henderson, and Voices of Concern: A Book Whose Time Had Come by David N. Elkins. A WORD FOR OUR TIMES: Experiencing the Stages of Love by Harold Straughn, History Bears Out More Than Fiction by Neil DeCarlo, A Fast Day by Paul Fromberg, and Our Outrageous God by Larry James. Mission and the Church: The Quest For Unity by Robert M. Randolph, and Forum

An Analytical, Critical And Comparative Study Of Anglican Mission In The Dioceses Of Nakuru And Mount Kenya East, Kenya, From 1975.

Distinctive and common approaches in the local mission theologies of the Anglican dioceses of Nakuru and Mount Kenya East/Kirinyaga, Kenya during the period from 1975 are compared with other Protestant forms and Roman Catholicism, Pentecostal-type churches and African Instituted Churches. Specific analysis of Anglican liturgy reveals that issues of social justice and political concern have had a major impact on liturgical development and pinpoint the link between mission and worship. The mission of the Anglican Church in Kenya was at its inception Evangelical but has acquired a Catholic emphasis which has affected the use of liturgy. Appropriate theories from Anglican mission and sociology highlight aspects of recent Kenyan history (e.g. independence, decolonialization, ethnic identity, land disputes, development) which influence the course of the CPK (Church of the Province of Kenya) in the areas of Kirinyaga and Nakuru dioceses. The distinctive expression of the East African Revival Movement (Balokole) constitutes areas of commonality in mission theology between Anglicans, Methodists and Presbyterians in the diocesan areas. Anglican distinctiveness is also evident in training contexts and expressed in church leadership and communities by means of the theory and practice of wholistic mission and catechetics in relation to urban and rural cultures. It is argued that a study of the sociology and history of worship aids an understanding of a Kenyan Anglican theory of the church in mission. Various views are critiqued in focusing on the relationship between mission and liturgy. Correlations between the history of liturgical renewal, mission history, and between liturgy and sociology and secularity are examined. These demonstrate the originality of Kenyan Anglican wholistic mission through liturgy. A practical analysis of processes of liturgical change in the CPK, and other churches (using case studies) signals the extent to which the theory and practice of contextualised African Anglican liturgies in the diocesan areas have become indices of the formation of distinctive ecclesiological communities in mission. Therefore the CPK is distinctive in mission among the churches of Kenya through a unique combination of theology, training, ecclesiology, and culture-sensitive liturgy