CZTOLJDEFGKJSKI calculus

CZTOLJDEFGKJSKI calculus

Paradigm(s)	functional
Designed by	User:Challenger5
Appeared in	2023
Computational class	Turing complete
Reference implementation	Unimplemented
Influenced by	Lazy K
File extension(s)	.cztoljdefgkjski

The CZTOLJDEFGKJSKI calculus is a derivative of Lazy K named after User:olus2000. Unlike Lazy K, it is (mostly) strictly evaluated (call-by-value) and uses a different set of combinators.

Combinators

Symbol	Name	Behavior (λ-term)
C	cardinal	λ a b c → a c b
Z	strict fixed point	λ a b → a (Z a) b
T	thrush	λ a b → b a
O	owl	λ a b → b (a b)
L	lark	λ a b → a (b b)
J	jay	λ a b c d → a b (a d c)
D	dove	λ a b c d → a b (c d)
E	eagle	λ a b c d e → a b (c d e)
F	finch	λ a b c → c b a
G	goldfinch	λ a b c d → a d (b c)
K	kestrel	λ a b → a
J	jota	λ a → a S K
S	starling	λ a b c → a c (b c)
K	lazy kestrel	λ a b → (eval b; eval a)
I	idiot	λ a → a

A few other differences from Lazy K:

• Only the Unlambda syntax can be used, but with capitalized combinator names.
• Note that some combinators have multiple definitions. The parser cycles through which definition is used every time the combinator appears in the program. So if you write ``GKK, the first use of K refers to the kestrel, but the second refers to the lazy kestrel.
• The lazy kestrel is the only combinator in the language which violates the call-by-value reduction model. When passed its first argument, it does not immediately evaluate it; instead, it waits for a second argument and evaluates that one first before finally evaluating and returning its first argument.