Kind/book/Kind.reduce.op2.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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Kind.reduce.op2
: ∀(opr: Kind.Oper) ∀(fst: Kind.Term) ∀(snd: Kind.Term)
Kind.Term
= λopr λfst λsnd
use P = ∀(snd: Kind.Term) Kind.Term
use Y = λfst_val λsnd
use P = ∀(fst_val: #U60) Kind.Term
use Y = λsnd_val λfst_val
use P = λx ∀(fst_val: #U60) ∀(snd_val: #U60) Kind.Term
use add = λfst_val λsnd_val (Kind.num #(+ fst_val snd_val))
use mul = λfst_val λsnd_val (Kind.num #(* fst_val snd_val))
use sub = λfst_val λsnd_val (Kind.num #(- fst_val snd_val))
use div = λfst_val λsnd_val (Kind.num #(/ fst_val snd_val))
use mod = λfst_val λsnd_val (Kind.num #(% fst_val snd_val))
use eq = λfst_val λsnd_val (Kind.num #(== fst_val snd_val))
use ne = λfst_val λsnd_val (Kind.num #(!= fst_val snd_val))
use lt = λfst_val λsnd_val (Kind.num #(< fst_val snd_val))
use gt = λfst_val λsnd_val (Kind.num #(> fst_val snd_val))
use lte = λfst_val λsnd_val (Kind.num #(<= fst_val snd_val))
use gte = λfst_val λsnd_val (Kind.num #(>= fst_val snd_val))
use and = λfst_val λsnd_val (Kind.num #(& fst_val snd_val))
use or = λfst_val λsnd_val (Kind.num #(| fst_val snd_val))
use xor = λfst_val λsnd_val (Kind.num #(^ fst_val snd_val))
use lsh = λfst_val λsnd_val (Kind.num #(<< fst_val snd_val))
use rsh = λfst_val λsnd_val (Kind.num #(>> fst_val snd_val))
(~opr
P
add
mul
sub
div
mod
eq
ne
lt
gt
lte
gte
and
or
xor
lsh
rsh
fst_val
snd_val
)
use N = λsnd λfst_val (Kind.op2 opr (Kind.num fst_val) snd)
(Kind.if.num snd P Y N fst_val)
use N = λfst λsnd (Kind.op2 opr fst snd)
(Kind.if.num fst P Y N snd)