42 lines
1.6 KiB
Text
42 lines
1.6 KiB
Text
|
import cast
|
||
|
|
variable vec : Nat → Type
|
||
|
|
variable concat {n m : Nat} (v : vec n) (w : vec m) : vec (n + m)
|
||
|
|
infixl 65 ; : concat
|
||
|
|
axiom concat_assoc {n1 n2 n3 : Nat} (v1 : vec n1) (v2 : vec n2) (v3 : vec n3) :
|
||
|
|
(v1 ; v2) ; v3 = cast (congr2 vec (symm (Nat::add_assoc n1 n2 n3)))
|
||
|
|
(v1 ; (v2 ; v3))
|
||
|
|
variable empty : vec 0
|
||
|
|
axiom concat_empty {n : Nat} (v : vec n) :
|
||
|
|
v ; empty = cast (congr2 vec (symm (Nat::add_zeror n)))
|
||
|
|
v
|
||
|
|
|
||
|
|
rewrite_set simple
|
||
|
|
add_rewrite Nat::add_assoc Nat::add_zeror eq_id : simple
|
||
|
|
add_rewrite concat_assoc concat_empty Nat::add_assoc Nat::add_zeror : simple
|
||
|
|
|
||
|
|
variable f {A : Type} : A → A
|
||
|
|
|
||
|
|
(*
|
||
|
|
local m = simplifier_monitor(nil, nil, nil,
|
||
|
|
function (s, e, i, k)
|
||
|
|
print("App simplification failure, argument #" .. i)
|
||
|
|
print("Kind: " .. k)
|
||
|
|
print("-----------")
|
||
|
|
end,
|
||
|
|
function (s, e, ceq, ceq_id, i, k)
|
||
|
|
print("Rewrite failure: " .. tostring(e))
|
||
|
|
end,
|
||
|
|
function (s, e, k)
|
||
|
|
print("Abst failure: " .. tostring(e))
|
||
|
|
end
|
||
|
|
)
|
||
|
|
local s = simplifier("simple", options(), m)
|
||
|
|
local t = parse_lean('λ val : Nat, (λ n : Nat, λ v : vec (n + 0), (f v) ; empty) val == (λ n : Nat, λ v : vec (n + 0), v) val')
|
||
|
|
print(t)
|
||
|
|
print("=====>")
|
||
|
|
local t2, pr = s(t)
|
||
|
|
print(t2)
|
||
|
|
-- print(pr)
|
||
|
|
get_environment():type_check(pr)
|
||
|
|
*)
|