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mathematical logic, specifically in realizability, a partial combinatory algebra (pca) is an algebraic structure which abstracts a model of computation.
Partial_combinatory_algebra
Topics referred to by the same term
polyphenol antioxidant Pyroglutamic acid, an amino acid derivative Partial combinatory algebra, an abstraction of a model of computation in mathematical logic
PCA
Church–Turing sense. Instead, assemblies are defined over a specific partial combinatory algebra, which abstracts the model of computation. It is a set equipped
Assembly_(realizability)
Reasoning about equations with free variables
called "Boolean algebras with operators." Algebraic formalisms going beyond first-order logic in at least some respects include: Combinatory logic, having
Algebraic_logic
congruency. The λ-algebra describing the algebraic structure of the lambda-calculus is found to be an extension of the combinatory algebra, with an element
Computable_topology
Sequence of operations for a task
Procedures and Algorithms. Infinite machines. Post, Emil (1936). "Finite Combinatory Processes, Formulation I". The Journal of Symbolic Logic. 1 (3): 103–105
Algorithm
Transforming a function in such a way that it only takes a single argument
cartesian categories (such as the category of sets, complete partial orders or Heyting algebras) is just the Cartesian product; it is interpreted as an ordered
Currying
Element mapped to itself by a mathematical function
its greatest fixed point coincides with its greatest postfixpoint). In combinatory logic for computer science, a fixed-point combinator is a higher-order
Fixed_point_(mathematics)
theoretical framework. The topos is based on the partial combinatory algebra given by Kleene's first algebra K 1 {\displaystyle {\mathcal {K}}_{1}} . In Kleene's
Effective_topos
Academic subfield of computer science
point combinator Y has normal form in combinatory logic but not in λ {\displaystyle \lambda } -calculus). Combinatory logic was developed with great ambitions:
Theory_of_computation
Programming paradigm based on applying and composing functions
functional programming languages. An equivalent theoretical formulation, combinatory logic, was developed by Moses Schönfinkel and Haskell Curry in the 1920s
Functional_programming
Overview of and topical guide to logic
Boolean algebra Free Boolean algebra Monadic Boolean algebra Residuated Boolean algebra Two-element Boolean algebra Modal algebra Derivative algebra (abstract
Outline_of_logic
Operation on mathematical functions
\circ. Cobweb plot – a graphical technique for functional composition Combinatory logic Composition ring, a formal axiomatization of the composition operation
Function_composition
Square array with symbols that each occur once per row and column
Oxford Camb. Dublin Messenger of Math. 19: 85–239. MacMahon, P.A. (1915). Combinatory Analysis. Cambridge University Press. p. 300. Frolov, M. (1890). "Sur
Latin_square
Symbols for constants, special functions
transport Ψ {\displaystyle \Psi } represents: a quaternary combinator in combinatory logic a symbol for psychology the wave function in the Schrödinger equation
Greek letters used in mathematics, science, and engineering
Greek_letters_used_in_mathematics,_science,_and_engineering
Category theory
Essays in Combinatory Logic. Balmer, Paul; Schlichting, Marco (2001), "Idempotent completion of triangulated categories" (PDF), Journal of Algebra, 236 (2):
Karoubi_envelope
and articles that criticised socialism Moses Schönfinkel, inventor of combinatory logic Sara Shakulova, first female mathematician of Tatar descent Yakov
List of Russian mathematicians
List_of_Russian_mathematicians
Datatype Algebraic data type (generalized) Type variable First-class value Polymorphism Calculus of constructions Domain theory Directed complete partial order
List of functional programming topics
List_of_functional_programming_topics
American logician (born 1932)
paradigm to programming languages as well as to construct models of Curry's combinatory logic and Church's calculus of lambda conversion; and The 2001 Bolzano
Dana_Scott
Problem in computer science
recursive functions. 7 October 1936 (1936-10-07): Emil Post's paper "Finite Combinatory Processes. Formulation I" is received. Post adds to his "process" an
Halting_problem
Generalization of the concept of category that allows morphisms of multiple arity
in the OEIS), integer partitions (sequence A063834 in the OEIS), and combinatory separations (sequence A269134 in the OEIS). The triangles (or compositions)
Multicategory
representation theory, algebraic geometry, and mathematical physics Hans Freudenthal (1905–1990), algebraic topology Avner Friedman (born 1932), partial differential
List_of_Jewish_mathematicians
Extension of linear logic
terms of partial permutations. It also has a denotational semantics in which formulas are interpreted by modules over some specific Hopf algebras. By extension
Noncommutative_logic
Subfield of mathematics
intuitionistic logic. Formal calculi such as the lambda calculus and combinatory logic are now studied as idealized programming languages. Computer science
Mathematical_logic
Subpermutation of a longer permutation
factorial if and only if π avoids 1324 and 21354. MacMahon, Percy A. (1915), Combinatory Analysis, London: Cambridge University Press, Volume I, Section III,
Permutation_pattern
German mathematician (1928–2022)
Kombinatorik und Wahrscheinlichkeitsrechnung auf der Primarstufe (Elementary combinatory and probability games) (in German). Klett. p. 167. ISBN 978-3-12-902000-5
Arthur_Engel_(mathematician)
Software programming optimization technique
memoization on a class webpage. Memoization in Combinatory Logic – A web service to reduce Combinatory Logic while memoizing every step in a database
Memoization
Thesis on the nature of computability
close cousin to the modern notion of the computer. Other models include combinatory logic and Markov algorithms. Gurevich adds the pointer machine model
Church–Turing_thesis
Bronze medal awarded by the Royal Society (London)
contributions to combinatory topology, Boolean algebras and mathematical logic." 1961 Philip Hall British "For his distinguished researches in algebra." 1964 Mary
Sylvester_Medal
correspondence with reality or facts. combinator A function or expression in combinatory logic that acts on arguments to produce results without the need for
Glossary_of_logic
Subset of lambda calculus
introduced the term "functional completeness" in the context of combinatory algebra. Kappa calculus arose out of efforts by Lambek to formulate an appropriate
Kappa_calculus
System responsible for combining morphemes into complex structures
in which constituents combine as function and argument, according to combinatory possibilities specified in their syntactic categories. For example, other
Syntax
About mathematical functions
that Haskell Curry (1958) carried this work forward "under the head of combinatory logic". By 1925 Abraham Fraenkel (1922) and Thoralf Skolem (1922) had
History of the function concept
History_of_the_function_concept
Relation specifying a rewrite for each object, compatible with a reduction relation
323. ISBN 978-3-540-20861-7. Curry, Haskell B.; Feys, Robert (1958). Combinatory Logic. Vol. I. Amsterdam: North Holland. pp. 139–142. ISBN 0-7204-2208-6
Reduction_strategy
Computation model defining an abstract machine
(4): 533–546. doi:10.1145/321356.321362. Post, Emil (1936). "Finite Combinatory Processes—Formulation 1". Journal of Symbolic Logic. 1: 103–105. doi:10
Turing_machine
Type system used in computer programming and mathematics
Hindley, J. Roger (1969). "The Principal Type-Scheme of an Object in Combinatory Logic". Transactions of the American Mathematical Society. 146: 29–60
Hindley–Milner_type_system
Representation of data of various types in lambda calculus
contain algebraic data types. Nonetheless Church encoding is often used in theoretical arguments, as it is a natural representation for partial evaluation
Church_encoding
Measure of algorithmic complexity
"Review of Li Vitányi 1997". Tromp, John. "John's Lambda Calculus and Combinatory Logic Playground". Tromp's lambda calculus computer model offers a concrete
Kolmogorov_complexity
Branch of type theory
assignment for the strongly normalizable λ-terms. To HB Curry: essays on combinatory logic, lambda calculus and formalism, 561-577. Coppo, Mario; Dezani-Ciancaglini
Intersection_type_discipline
Varying application boundaries
of a definite cut-off point along an implied scale (in contrast to "combinatory vagueness" caused by a term that has a number of logically independent
Fuzzy_concept
topology and Schnirelmann density of numbers Moses Schönfinkel, inventor of combinatory logic Yakov Sinai, developed the Kolmogorov–Sinai entropy and Sinai billiard
List_of_Russian_scientists
Formal power series
Laplace [..]. He applied this mathematical tool to several problems in Combinatory Analysis and the Theory of Numbers. A generating function is a device
Generating_function
topology and Schnirelmann density of numbers Moses Schönfinkel, inventor of combinatory logic Yakov Sinai, developed the Kolmogorov–Sinai entropy and Sinai billiard
List_of_Russian_people
PARTIAL COMBINATORY-ALGEBRA
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PARTIAL COMBINATORY-ALGEBRA