Examples of using Combinatory in English and their translations into Ukrainian
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Combinatory terms.
Reduction in combinatory logic.
Combinatory calculi.
Some forms of combinatory logic;
The combinatory versions have T= K and F=(K I).
The Principal Type- Scheme of an Object in Combinatory Logic.
Combinatory logic can be given a variety of interpretations.
The Principal Type- Scheme of an Object in Combinatory Logic.
In combinatory logic, each primitive combinator comes with a reduction rule of the form.
Einstein described his scientific method as combinatory play.
Despite its simplicity, combinatory logic captures many essential features of computation.
Curry and Feys(1958), and Curry et al.(1972)survey the early history of combinatory logic.
Combinatory logic is a model of computation equivalent to lambda calculus, but without abstraction.
Dana Scott in the 1960s and1970s showed how to marry model theory and combinatory logic.
Combinatory logic is a notation to eliminate the need for quantified variables in mathematical logic.
In contrast, evaluating expressions in combinatory logic is much simpler, because there is no notion of substitution.
Combinatory logic was originally intended as a'pre-logic' that would clarify the role of quantified variables in logic, essentially by eliminating them.
It is undecidable whether a general combinatory term has a normal form; whether two combinatory terms are equivalent, etc.
Combinatory logic A concept which has many similarities to λ{\displaystyle\lambda}-calculus, but also important differences exist(e.g. fixed point combinator Y has normal form in combinatory logic but not in λ{\displaystyle\lambda}-calculus).
The question then is to ascertain whether language makes such combinatory operations possible or whether the operations evolve independently of language.
Hence combinatory logic has been used to model some non-strict functional programming languages and hardware.
In 1969,J. Roger Hindley publishes The Principal Type-Scheme of an Object in Combinatory Logic, later generalized into the Hindley- Milner type inference algorithm.
In computer science, combinatory logic is used as a simplified model of computation, used in computability theory and proof theory.
In 1969,J. Roger Hindley publishes The Principal Type-Scheme of an Object in Combinatory Logic, later generalized into the Hindley- Milner type inference algorithm.
A normal form is any combinatory term in which the primitive combinators that occur, if any, are not applied to enough arguments to be simplified.
The original inventor of combinatory logic, Moses Schönfinkel, published nothing on combinatory logic after his original 1924 paper.
While the expressive power of combinatory logic typically exceeds that of first-order logic, the expressive power of predicate functor logic is identical to that of first order logic(Quine 1960, 1966, 1976).
For a more modern treatment of combinatory logic and the lambda calculus together, see the book by Barendregt,[5] which reviews the models Dana Scott devised for combinatory logic in the 1960s and 1970s.
But taken from a psychological viewpoint, this combinatory play seems to be the essential feature in productive thought--before there is any connection with logical construction in words or other kinds of signs which can be communicated to others.