combinatory logic

E588865
branch of mathematical logic formal system model of computation theory of computation

Combinatory logic is a foundational formal system in mathematical logic and computer science that eliminates variables by expressing computation through the combination of a small set of primitive functions.

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Observed surface forms (2)

Surface form Occurrences
Curry’s combinator 1
Curry’s combinators 1

Statements (46)

Predicate Object
instanceOf branch of mathematical logic ⓘ
formal system ⓘ
model of computation ⓘ
theory of computation ⓘ
aimsTo provide a basis for mathematics without bound variables ⓘ
basedOn combination of primitive combinators ⓘ
developedBy Haskell Curry NERFINISHED ⓘ
Moses Schönfinkel NERFINISHED ⓘ
documentedIn "Combinatory Logic" by Haskell Curry and Robert Feys NERFINISHED ⓘ
fieldOfStudy lambda calculus NERFINISHED ⓘ
mathematical logic ⓘ
proof theory ⓘ
theoretical computer science ⓘ
formalizedIn equational logic ⓘ
hasApplication categorical combinatory logic ⓘ
hasGoal eliminate variables from formal expressions ⓘ
hasHistoricalPeriod early 20th century ⓘ
hasNormalFormConcept normal form of a combinatory term ⓘ
hasNotation juxtaposition for application ⓘ
hasOperation combinator abstraction ⓘ
function application ⓘ
hasPrimitive I combinator ⓘ
K combinator NERFINISHED ⓘ
S combinator ⓘ
hasProblem decidability of equality of combinatory terms ⓘ
hasProperty Turing complete ⓘ
equivalent in expressive power to lambda calculus ⓘ
variable-free notation ⓘ
hasSubfield typed combinatory logic ⓘ
untyped combinatory logic ⓘ
influenced combinator-based programming languages ⓘ
functional programming ⓘ
proof assistants ⓘ
type theory ⓘ
relatedTo SKI combinator calculus NERFINISHED ⓘ
lambda calculus ⓘ
logic combinators ⓘ
studiedIn denotational semantics ⓘ
foundations of mathematics ⓘ
supports representation of functions without variables ⓘ
usedFor analyzing functional programs ⓘ
constructing models of lambda calculus ⓘ
studying foundations of computation ⓘ
usesConcept application ⓘ
combinator ⓘ
reduction ⓘ

Referenced by (4)

Full triples — surface form annotated when it differs from this entity's canonical label.

Curry encoding → influencedBy → combinatory logic ⓘ
Haskell Curry → notableWork → combinatory logic ⓘ
Haskell Curry → knownFor → combinatory logic ⓘ
this entity surface form: Curry’s combinators
Haskell Curry → hasConceptNamedAfter → combinatory logic ⓘ
this entity surface form: Curry’s combinator