In Haskell, applicative functors are implemented in the `Applicative` type class.
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In the classification of programming languages, an applicative programming language is built out of functions applied to arguments. Applicative languages are functional, and applicative is often used as a synonym for functional. However, concatenative languages can be functional, while not being applicative. The semantics of applicative languages are based on beta reduction of terms, and side effects such as mutation of state are not permitted.
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' More recent learning materials refer to the ha- prefix as a superessive applicative marker, and the ho- prefix as an inessive applicative marker.
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The applicative it- may function as instrumental or intensifier. Additionally, the applicative prefix in Wamesa can also give aspectual meaning, which is unusual for applicatives. Regarding the use of the applicative as an instrumental, the instrument must not be human nor a human body part, and the applicative verb must agree with the subject, not the instrument. Aspectual information includes the indication that an action is either sudden or completed.
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In functional programming, an applicative functor is a structure intermediate between functors and monads, in that they allow sequencing of functorial computations (unlike plain functors) but without deciding on which computation to perform on the basis of the result of a previous computation (unlike monads). Applicative functors are the programming equivalent of lax monoidal functors with tensorial strength in category theory. Applicative functors were introduced in 2007 by Conor McBride and Ross Paterson in their paper Functional Pearl: applicative programming with effects. Applicative functors first appeared as a library feature in Haskell, but have since spread to other languages as well, including Idris, Agda, OCaml, Scala and F#. Both Glasgow Haskell and Idris now offer language features designed to ease programming with applicative functors.
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The applicative voice (abbreviated or ) is a grammatical voice that promotes an oblique argument of a verb to the core object argument. It is generally considered a valency-increasing morpheme. The Applicative is often found in agglutinative languages, such as the Bantu languagesJerro, Kyle Joseph. (2016). The Syntax and Semantics of Applicative Morphology in Bantu (Doctoral dissertation).
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Applicative computing systems, or ACS are the systems of object calculi founded on combinatory logic and lambda calculus.Wolfengagen V.E. Methods and means for computations with objects. Applicative Computational Systems. — M.: JurInfoR Ltd., «Center JurInfoR», 2004.
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Adjectives always follow nouns. Unlike verbs, they cannot take the applicative prefix.
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In constructions with the benefactive applicative -š(i)t (-bt), the argument indicated by the ergative is agent and that by accusative/absolutive the beneficiary. The benefactive applicative may also function to characterize an object as a recipient (Bischoff, 2011, p. 31).
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Applicative transitivizers introduce a third participant into the argument structure, and alter the role of the object. This means the participant represented by the object person marking morpheme serves as a possessor or dative with the possessor applicative transitivizer -łt (-pra) and as a beneficiary or dative with the benefactive transitivizer -š(i)t (-bt). There is also a third, much less frequent, applicative -tułt. can also indicate a dative construction, indicating the object to which something is given.
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Using applicative order, the expression KI\Omega = (\lambda x . \lambda y . x) (\lambda x . x)\Omega is reduced by first reducing \Omega to normal form (since it is the rightmost redex), but since \Omega has no normal form, applicative order fails to find a normal form for KI\Omega.
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The verbal prefixes convey information about the arguments of the verb: how many there are and their person and number features. The prefixes can be divided into three sorts: agreement markers, applicative markers, and anaphors (reflexives and reciprocals). The prefixes occur in the following order: agreement-anaphor-applicative-verb stem.
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The dative applicative -tułt is very rare, and the role of this applicative is uncertain other than that it introduces another participant into a sentence structure (Doak, 1997, p. 157). The only examples Doak gives only occur with third person or non-topic ergative person marking morphemes (Bischoff, 2011, p. 32).
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University of Texas at Austin. and Austronesian languages.Kikusawa, Ritsuko. (2012). On the Development of Applicative Constructions in Austronesian Languages.
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The positive tradeoff of using applicative order is that it does not cause unnecessary computation, if all arguments are used, because it never substitutes arguments containing redexes and hence never needs to copy them (which would duplicate work). In the above example, in applicative order `(λx.xx) ((λx.x)y)` reduces first to `(λx.
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If the reduction was done in an applicative order first, we save work because work is not duplicated: `(λx.xx) (II)` reduces to `(λx.xx) I`. On the other hand, using applicative order can result in redundant reductions or even possibly never reduce to normal form. For example, performing a β-reduction in normal order on `(λf.
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Applicative universal grammar, or AUG, is a universal semantic metalanguage intended for studying the semantic processes in particular languages.Shaumyan S. A Semiotic Theory of Language. -- Bloomington and Indianapolis: Indiana University Press, 1987 This is a linguistic theory that views the formation of phrase in a form that is analogous to function application in an applicative programming language.
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W.B. Ackerman defines an applicative language as one which does all of its processing by means of operators applied to values.W.B. Ackerman, Data Flow Languages, Proceedings National Computer Conference, pp. 1087-1095, 1979 The earliest known applicative language was LISP. An FBP component can be regarded as a function transforming its input stream(s) into its output stream(s).
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Yagua is one language that has dedicated morphology for applicative uses. Here, the applicative suffix -ta shows that the locative or instrumental oblique is now a direct object: : : This same -ta suffix can be used with transitive verbs to create ditransitives: : : These behave identically as other lexical ditransitives, such as give and send in this language.
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In Common Lisp, arguments are evaluated in applicative order ('leftmost innermost'), while in Scheme order of arguments is undefined, leaving room for optimization by a compiler.
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For example, maŋga- 'laugh' becomes applicative maŋga-ŋa- 'laugh at' while warrŋgi- 'turn around' becomes causative warrŋgi-ŋa- 'turn something around'. The classes of verbs are not mutually exclusive however, so some words could have both meanings (bila- 'go in' becomes bila-ŋa- which translates either to applicative 'go in with' or causative 'put in'), which are disambiguated only through context.Dixon, R.M.W. (2000). "A Typology of Causatives: Form, Syntax, and Meaning".
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Doing the same but in applicative order yields `(λf.f I) (λy.y I (y I))`, `(λy.y I (y I)) I`, `I I (I I)`, and now work is duplicated.
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Linguistic Inquiry 36(3). 315–332. When a sentence involves an applicative, the word order is as follows: (subject) instrument verb (object), with the items in parentheses as optional.
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Unpublished ms, University of California, Berkeley. and Michaelis and Ruppenhofer 2001Michaelis, L. A., & Ruppenhofer, J. 2001. Beyond alternations: A constructional account of the applicative pattern in German. Stanford: CSLI Publications.
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A language may have multiple applicatives, each corresponding to such different roles as comitative, locative, instrumental, and benefactive. Sometimes various applicatives will be expressed by the same morphological exponence, such as in the Bantu language Chewa, where the suffix -ir- forms both instrumental and locative applicatives. Some languages, such as Luganda, permit a 'second applicative' (known in Luganda as the "augmentative applied"), formed by a double application of the suffix. In this case, the second applicative is used to give an alternative meaning.
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In the above example, in applicative order (\lambda x . xx) ((\lambda x . x)y) reduces first to (\lambda x . xx)y and then to the normal order yy, taking two steps instead of three.
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Amsterdam: John Benjamins. pp. 85-126. A similar construction known as dative shift, though different from true applicatives, occurs in other languages. Also, the benefactive case is commonly expressed by means of an applicative.
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Applicative order evaluation is an evaluation strategy in which an expression is evaluated by repeatedly evaluating its leftmost innermost reducible expression. This means that a function's arguments are evaluated before the function is applied.
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The German prefix be- is considered an applicative by some,Gronemeyer, Claire. (1995). Swedish applied verbs derived by the prefix be-. Working Papers in Linguistics (Lund University), 44, 21-40. but other analyses reject this view.
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Mycroft read Mathematics at Cambridge then moved to Edinburgh where he completed his Doctor of Philosophy degree with a thesis on the Abstract interpretation and optimising transformations for applicative programs supervised by Rod Burstall and Robin Milner.
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This entire expression contains only one redex, namely the whole expression; its reduct is again `Ω`. Since this is the only available reduction, `Ω` has no normal form (under any evaluation strategy). Using applicative order, the expression `KIΩ = (λx.λy.x) (λx.
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There are four morphemes modifying verbs. They are added to some verb root in the following order: # Reversive (-ol-) #: e.g.: kozinga to wrap and kozingola to develop # Causative (-is-) #: e.g. : koyéba to know and koyébisa to inform # Applicative (-el-) #: e.g.
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SASL (from St Andrews Static Language, alternatively St Andrews Standard Language) is a purely functional programming language developed by David Turner at the University of St Andrews in 1972, based on the applicative subset of ISWIM.Turner, An implementation of SASL In 1976 Turner redesigned and reimplemented it as a non-strict (lazy) language.Turner , A New Implementation Technique for Applicative Languages, pages 31-49 In this form it was the foundation of Turner's later languages KRC and Miranda, but SASL appears to be untyped whereas Miranda has polymorphic types. Burroughs Corporation used SASL to write a compiler and operating system.
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Called in practical contexts "lazy evaluation". In implementations this "name" takes the form of a pointer, with the redex represented by a thunk. Applicative order is not a normalising strategy. The usual counterexample is as follows: define `Ω = ωω` where `ω = λx.xx`.
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Maay Maay is fairly agglutinative. It has complex verb forms, inflecting at least for tense/aspect and person/number of both subject and object. There is also a prefix indicating negation. In addition, verbs exhibit derivational morphology, including a causative and an applicative.
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Functors are very useful in modeling functional effects to apply a function to computations that did not yet finish. Functors form a base for more complex abstractions like Applicative, Monad, Comonad. In C++, the name functor refers to a function object instead of this definition.
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The Spaceborne Hyperspectral Applicative Land and Ocean Mission (SHALOM), a joint mission by Israel (ISA) and the Italy Space Agency (ASI) has a budget of $116 million. The budget allocated annually for the Israeli military program as well as commercial programs are managed on different budgets.
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The same Atlantic–Congo languages which have noun classes also have a set of verb applicatives and other verbal extensions, such as the reciprocal suffix -na (Swahili penda 'to love', pendana 'to love each other'; also applicative pendea 'to love for' and causative pendeza 'to please').
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The applicative suffix is identical in form with the past tense suffix, with which it should not be confused. For example: (12) Íbè nye-re-re m Ógù ákwụkwọ. : Ibe give-PRF-APPL 1sg Ogu book : 'Ibe gave the book to Ogu for me.' (12) also illustrates Igbo ditransitive word order.
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Hope is a small functional programming language developed in the 1970s at the University of Edinburgh.Burstall R.M, MacQueen D.B, Sannella D.T. (1980) Hope: An Experimental Applicative Language. Conference Record of the 1980 LISP Conference, Stanford University, pp. 136-143. It predates Miranda and Haskell and is contemporaneous with ML, also developed at the University.
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Applicative order is not a normalising strategy. The usual counterexample is as follows: define \Omega = \omega\omega where \omega = \lambda x . xx. This entire expression contains only one redex, namely the whole expression; its reduct is again \Omega. Since this is the only available reduction, \Omega has no normal form (under any evaluation strategy).
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The ACL2 programming language is an applicative (side-effect free) variant of Common Lisp. ACL2 is untyped. All ACL2 functions are total — that is, every function maps each object in the ACL2 universe to another object in its universe. ACL2's base theory axiomatizes the semantics of its programming language and its built-in functions.
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Wamesa has an applicative (it), causative (on), and essive (ve-). Additional affixes include markers for plural (-si ), singular (-i ), and 3rd plural human (-sia). Wamesa's clitics include the topicalizer =ma, focus =ya, =ye, =e; and the proximal (=ne), default/medial (=pa), and distal (=wa) definite determiners. Note that Wamesa clitics are only phonological and not syntactic.
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Spaceborne Hyperspectral Applicative Land and Ocean Mission (SHALOM) is a joint mission by the Israeli Space Agency and the Italian Space Agency to develop a hyperspectral satellite. The mission was agreed upon in late 2010. and was originally intended to build two commercial hyperspectral satellites. Preliminary studies for the program started in 2012, with Phase A completed in 2013.
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ACT 3NSG 3UND3= help this :So now you help them like this, :hok haib u- ebeer u- ihin =e nang? :some danger VI- die VI- lost =FOC NEG :do any die from danger or not? The applicative verbal prefix mi- allows an added Undergoer argument as well, but this Undergoer can only be an Instrument. :(5) Na lam. :1SG.
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Though rarer in computer science, one can use category theory directly, which defines a monad as a functor with two additional natural transformations. So to begin, a structure requires a higher-order function (or "functional") named map to qualify as a functor: This is not always a major issue, however, especially when a monad is derived from a pre-existing functor, whereupon the monad inherits automatically. (For historical reasons, this `map` is instead called `fmap` in Haskell.) A monad's first transformation is actually the same from the Kleisli triple, but following the hierarchy of structures closely, it turns out characterizes an applicative functor, an intermediate structure between a monad and a basic functor. In the applicative context, is sometimes referred to as pure but is still the same function.
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In Ganda, direct and indirect pronominal objects may be incorporated into the verb as object infixes. For example: In the second example, the applicative suffix -ira converts the (usually monotransitive) verb gamba to a ditransitive. While agreement with a verbal subject is compulsory, agreement with an object is required only when the object is omitted. Many other Bantu languages exhibit this feature.
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The affix -Vli- means 'do while going' and the affix -Vlda- means 'do while coming'. It is for this reason that they cannot be added to the verbs gali- 'go' or gada- 'come'. Therefore, the word magiilinyu means 'went up, climbing' and magiildanyu means 'came up, climbing'. One morpheme, -ŋa, is an applicative in some verbs and a causative in others.
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In transitive constructions with the possessor applicative -łt (-pra), the object marking on the predicate indicates the possessor, rather than the possessed, such as in Examples 1a and 1b below. In some cases, as in Example 1c below, -łt (-pra) serves to indicate a dative construction. In these cases, the role of the object shifts to dative (Bischoff, 2011, p. 30-31).
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Verbs inflect for aspects and moods as well as for person and number of the subject and the object. There are also a number of suffixes expressing shape, position, or body parts that affect or are affected by the verbal action. Transitivity is manipulated by suffixes forming transitive verbs with applicative or causative meaning or intransitives with passive or inchoative meanings.
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To paraphrase: attachment begets entitlement in a non-logical, non-physical sense. Given the above, the boundary that is requisite for entitlement to exist on the non-logical, non- physical level is outside of non-possession's scope. This is not the case for aparigraha. Non-stealing is a necessary component in addition to non- possession because of Satyagraha's applicative nature.
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R.M. Burstall, D.B. MacQueen and D.T. Sannella. HOPE: an experimental applicative language. Proc. 1980 LISP Conference, Stanford, 136–143 (1980). ML eventually developed into several dialects, the most common of which are now OCaml and Standard ML. In the 1970s, Guy L. Steele and Gerald Jay Sussman developed Scheme, as described in the Lambda Papers and the 1985 textbook Structure and Interpretation of Computer Programs.
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Tboli, like other Philippine languages, makes a distinction between transitive and intransitive verbs. Intransitive verbs are marked with the affix me- while transitive verbs are marked with ne-. Unlike Philippine languages, applicative affixes are not used in Tboli though prepositions are used instead. Furthermore, aspect marking is not marked on the verb but with preverbal aspect markers such as deng (completed actions) and angat (incomplete action).
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Gunbarlang has been proposed to be included into the marne group of Gunwinyguan family, making its closest relatives the Central Gunwinyguan languages Bininj Kunwok and Dalabon. The label marne refers to the phonological shape of the benefactive applicative affix common to all three languages (as opposed to the bak languages to the east, e.g. Rembarrnga, Ngandi and Wubuy/Nunggubuyu).Alpher, B., Evans, N. & Harvey, M. 2003.
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With regard to verbs, phrases must adhere to the following rules: # Subject agreement (person and number) must be marked on each verb and only on verbs. # If direction is involved in the sentence, it must be marked on the verb. # If there is an essive, it must attach to the verb that is describing a trait of the subject. # The applicative must attach to the verb, not the instrument.
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Khwe is a suffixing language, and thus has a rich inventory of head-marking suffixes on nouns and verbs. Verbs take tense-aspect-mood suffixes (TAMs), marking for causative, applicative, comitative, locative, passive, reflexive and reciprocal. Nouns are marked with person-gender-number suffixes (PGNs). Gender division in Khwe is based on sex, and is expressed by PGNs, with gender being marked even in first-person dual and plural.
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This is done essentially using applicative order, call by value reduction (see below), but usually called "eager evaluation". ; Normal order: The leftmost, outermost redex is always reduced first. That is, whenever possible the arguments are substituted into the body of an abstraction before the arguments are reduced. ; : Only the outermost redexes are reduced: a redex is reduced only when its right hand side has reduced to a value (variable or abstraction).
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Simon Peyton Jones, Alastair Reid, Fergus Henderson, Tony Hoare, and Simon Marlow. "A semantics for imprecise exceptions" Conference on Programming Language Design and Implementation. 1999. The semantics of these languages is compositional in that the meaning of a phrase depends on the meanings of its subphrases. For example, the meaning of the applicative expression f(E1,E2) is defined in terms of semantics of its subphrases f, E1 and E2.
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ACL2 ("A Computational Logic for Applicative Common Lisp") is a software system consisting of a programming language, an extensible theory in a first- order logic, and an automated theorem prover. ACL2 is designed to support automated reasoning in inductive logical theories, mostly for the purpose of software and hardware verification. The input language and implementation of ACL2 are written in Common Lisp. ACL2 is free and open-source software.
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If a function takes, for example, 2 arguments, any extras are ignored. For user defined functions, if too few arguments are provided, additional one are added with the value of the empty string (""). A function may have a maximum of 62 arguments. As with other applicative programming languages, a TTM function may be recursive and may be defined as the result of the invocation of a sequence of other function calls.
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This is done essentially using applicative order, call by value reduction (see below), but usually called "eager evaluation". ;Normal order: The leftmost, outermost redex is always reduced first. That is, whenever possible the arguments are substituted into the body of an abstraction before the arguments are reduced. ;Call by value: Only the outermost redexes are reduced: a redex is reduced only when its right hand side has reduced to a value (variable or lambda abstraction).
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This working process is advantageous in terms of the choice of color base for systemic products that are either of heterogeneous origin or are considered OEM products. The latter, even if characterized by different forms, can be connoted with the base colors or materials that are representative of the brand due to CMF design. Since CMF design manuals and the color matrix have a prescriptive role, the designers who create them are rarely involved in the applicative distribution either of colors, materials or finishes of individual products.
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Sahaptin has a split ergative syntax, with direct-inverse voicing and several applicative constructions.Rude, 2009. The ergative case inflects third-person nominals only when the direct object is first- or second-person (the examples below are from the Umatilla dialect): ;1) i-q̓ínu-šana yáka paanáy :3nom-see-asp bear 3acc.sg :‘the bear saw him’ ;2) i-q̓ínu-šana=aš yáka-nɨm :3nom-see-asp=1sg bear-erg :‘the bear saw me’ The direct-inverse contrast can be elicited with examples such as the following.
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The main task of this institution is to equip graduates with knowledge and skills for individual managing of small family business in the area of biotechnology. This Faculty is the only one of its kind in the country. The higher education activities of the Faculty of Biotechnical Sciences are organized on different levels of higher education: graduate studies, postgraduate studies, and studies at doctoral level. The Faculty also undertakes fundamental, developmental and applicative research, and runs courses, seminars and workshops for staff and students.
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Infinitive verbs have the form gʊ-object-ext-ROOT-ext-V- locative, where ext stands for any of various grammatical 'extensions', and -V is the final vowel. For example, with roots in bold and tone omitted, :gũ-n- tĩn-ĩl-a :'To cut for him/her' :gwĩ-tĩn-ĩl-a :'To cut for each other' -ĩl is the applicative suffix, translated as 'for'. The reciprocal prefix ĩ has fused into the infinitive gũ. :gũ-fum-a-mo :'To get out there' -mo is a locative 'inside', as in class 18 nominal concord.
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The objects generated in these systems are the functional entities with the following features: # the number of argument places, or object arity is not fixed but is enabling step by step in interoperations with other objects; # in a process of generating the compound object one of its counterparts—function—is applied to other one—argument—but in other contexts they can change their roles, i.e. functions and arguments are considered on the equal rights; # the self-applying of functions is allowed, i.e. any object can be applied to itself. ACS give a sound ground for applicative approach to programming.
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Northwest Caucasian languages have rather simple noun systems, with only a handful of cases at the most, coupled with highly agglutinative verbal systems that can contain almost the entire syntactic structure of the sentence. All finite verbs are marked for agreement with three arguments: absolutive, ergative, and indirect object,Nichols, Johanna (1986) and there are also a wide range of applicative constructions. There is a split between "dynamic" and "stative" verbs, with dynamic verbs having an especially complex morphology. A verb's morphemes indicate the subject's and object's person, place, time, manner of action, negative, and other types of grammatical categories.
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W.H. Burge, Recursive Programming Techniques, Addison-Wesley, Reading, MA, 1975 In FBP, it is necessary to be able to describe and process structured data chunks (FBP IPs). Furthermore, most applicative systems assume that all the data is available in memory at the same time, whereas FBP applications need to be able to process long- running streams of data while still using finite resources. Friedman and Wise suggested a way to do this by adding the concept of "lazy cons" to Burge's work. This removed the requirement that both of the arguments of "cons" be available at the same instant of time.
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The Kosova National Art Gallery was established in 1979 as a cultural institution to present visual arts, and to preserve and collect valuable works of art. It is named after one of the most prominent Kosovan artists, Muslim Mulliqi. It was established as a necessity for the visual presentation of Kosovan culture, as the only art institutions before it were the Art High School in Pejë in 1949, the Higher Pedagogical School in Pristina, and the Academy of Arts, founded in 1973, from which more than 1000 artists have graduated. Nearly 500 of them are active these days in the fields of painting, sculpture, graphic and applicative arts.
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While Waldinger's thesis had dealt with the synthesis of applicative programs, which return an output but produce no side effects, Waldinger then turned to the synthesis of imperative programs, which do both. To deal with the problem of achieving simultaneously goals that interfere with each other, he introduced the notion of goal regression, which was obtained from earlier work in program verification by Floyd, King, Hoare, and Dijkstra. Since imperative programs are analogous to plans, the approach was also applicable to classical AI planning problems. In collaboration with Zohar Manna, of Stanford University, Waldinger developed nonclausal resolution, a form of resolution that did not require the translation of logical sentences into a restricted clausal form.
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In particular, Haskell used a problematic "lazy stream" model up through v1.2 to reconcile I/O with lazy evaluation, until switching over to a more flexible monadic interface. The Haskell community would go on to apply monads to many problems in functional programming, and researchers working with Haskell eventually generalized the monad pattern into a wider hierarchy of structures, including applicative functors and arrows. At first, programming with monads was largely confined to Haskell and its derivatives, but as functional programming has influenced other paradigms, many languages have incorporated a monad pattern (in spirit if not in name). Formulations now exist in Scheme, Perl, Python, Racket, Clojure, Scala, F#, and have also been considered for a new ML standard.
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These functions are then combined to make more complex transformations, as shown here: Two functions feeding one If we label streams, as shown, with lower case letters, then the above diagram can be represented succinctly as follows: c = G(F(a),F(b)); Just as in functional notation F can be used twice because it only works with values, and therefore has no side effects, in FBP two instances of a given component may be running concurrently with each other, and therefore FBP components must not have side-effects either. Functional notation could clearly be used to represent at least a part of an FBP network. The question then arises whether FBP components can themselves be expressed using functional notation. W.H. Burge showed how stream expressions can be developed using a recursive, applicative style of programming, but this work was in terms of (streams of) atomic values.
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For example, a sequence of operations in an applicative language like the following: y = foo(x) z = bar(y) w = baz(z) ...is written in a concatenative language as a sequence of functions, without parameters: foo bar baz Functions and procedures written in concatenative style are not value level, i.e. they typically do not represent the data structures they operate on with explicit names or identifiers; instead they are function level - a function is defined as a pipeline, a sequence of operations that take parameters from an implicit data structure on which all functions operate, and return the function results to that shared structure so that it will be used by the next operator. The combination of a compositional semantics with a syntax that mirrors such a semantics makes concatenative languages highly amenable to algebraic manipulation of programs; although it may be difficult to write mathematical expressions directly in them. Concatenative languages can be implemented in an efficient way with a stack machine, and are commonly present implicitly in virtual machines in the form of their instruction sets.
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However, a procedure to apply any simple function over the whole list, in other words , is straight- forward: (map φ) xlist = [ φ(x1), φ(x2), ..., φ(xn) ] Now, these two procedures already promote `List` to an applicative functor. To fully qualify as a monad, only a correct notion of to flatten repeated structure is needed, but for lists, that just means unwrapping an outer list to append the inner ones that contain values: join(xlistlist) = join([xlist1, xlist2, ..., xlistn]) = xlist1 ++ xlist2 ++ ... ++ xlistn The resulting monad is not only a list, but one that automatically resizes and condenses itself as functions are applied. can now also be derived with just a formula, then used to feed `List` values through a pipeline of monadic functions: (xlist >>= f) = join ∘ (map f) xlist One application for this monadic list is representing nondeterministic computation. `List` can hold results for all execution paths in an algorithm, then condense itself at each step to "forget" which paths led to which results (a sometimes important distinction from deterministic, exhaustive algorithms).
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