Kind/book/BBT.get.kind2
Victor Taelin 85ad65b026 use-notation
Now, there are two local binders:

let x = ...
use x = ...

The 'let' binder will create a local definition, type-check it, and
assign a name to it. When compiled, it will create 'dup' nodes.

The 'use' binder is just an alias. It will not bind a new variable, and,
when compiled, will create inline copies. Also, for type-checking, it
allows creating aliases that are definitionaly equal for the checker.
2024-03-08 17:39:37 -03:00

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BBT.get
: ∀(K: *)
∀(V: *)
∀(cmp: ∀(a: K) ∀(b: K) Cmp)
∀(key: K)
∀(map: (BBT K V))
(Maybe V)
= λK λV λcmp λkey λmap
use P = λx (Maybe V)
use bin = λ_size λnext.key λnext.val λnext.lft λnext.rgt
use P = λx
∀(cmp: ∀(a: K) ∀(b: K) Cmp) ∀(key: K) (Maybe V)
use ltn = λcmp λkey (BBT.get K V cmp key next.lft)
use eql = λcmp λkey (Maybe.some V next.val)
use gtn = λcmp λkey (BBT.get K V cmp key next.rgt)
(~(cmp key next.key) P ltn eql gtn cmp key)
use tip = (Maybe.none V)
(~map P bin tip)