Programming Language Theory: Difference between revisions

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* Formal functional system (<tt>ffp</tt>): Extensible functional forms, functions represented by objects, translation of object representation to applicable form, formal semantics
* Formal functional system (<tt>ffp</tt>): Extensible functional forms, functions represented by objects, translation of object representation to applicable form, formal semantics
* Applicative state transition system (<tt>ast</tt>): <tt>ffp</tt> plus mutable state and coarse-grained operations thereupon
* Applicative state transition system (<tt>ast</tt>): <tt>ffp</tt> plus mutable state and coarse-grained operations thereupon
''Higher-order functions'' map one or more functions to a function.
===Combinatory Logic===
===Combinatory Logic===
====The Y (Fixed-Point) Combinator====
====Fixed-Point Combinators====
Higher-order functions which compute the fixed points of their inputs. Curry's ''Y-combinator'' was the first:
* <tt>Y ≡ λf. (λx. f (x x)) (λx. f (x x))</tt>


===Untyped λ-calculus===
===Untyped λ-calculus===