# Theory Pattern_Nits

theory Pattern_Nits
imports Main
(*  Title:      HOL/Nitpick_Examples/Pattern_Nits.thy
Author:     Jasmin Blanchette, TU Muenchen

Examples featuring Nitpick's "destroy_constrs" optimization.
*)

section ‹Examples Featuring Nitpick's \textit{destroy\_constrs} Optimization›

theory Pattern_Nits
imports Main
begin

nitpick_params [verbose, card = 8, max_potential = 0, sat_solver = MiniSat_JNI,
max_threads = 1, timeout = 240]

lemma "x = (case u of () ⇒ y)"
nitpick [expect = genuine]
oops

lemma "x = (case b of True ⇒ x | False ⇒ y)"
nitpick [expect = genuine]
oops

lemma "x = (case p of (x, y) ⇒ y)"
nitpick [expect = genuine]
oops

lemma "x = (case n of 0 ⇒ x | Suc n ⇒ n)"
nitpick [expect = genuine]
oops

lemma "x = (case opt of None ⇒ x | Some y ⇒ y)"
nitpick [expect = genuine]
oops

lemma "x = (case xs of [] ⇒ x | y # ys ⇒ y)"
nitpick [expect = genuine]
oops

lemma "x = (case xs of
[] ⇒ x
| y # ys ⇒
(case ys of
[] ⇒ x
| z # zs ⇒
(case z of
None ⇒ x
| Some p ⇒
(case p of
(a, b) ⇒ b))))"
nitpick [expect = genuine]
oops

fun f1 where
"f1 x () = x"

lemma "x = f1 y u"
nitpick [expect = genuine]
oops

fun f2 where
"f2 x _ True = x" |
"f2 _ y False = y"

lemma "x = f2 x y b"
nitpick [expect = genuine]
oops

fun f3 where
"f3 (_, y) = y"

lemma "x = f3 p"
nitpick [expect = genuine]
oops

fun f4 where
"f4 x 0 = x" |
"f4 _ (Suc n) = n"

lemma "x = f4 x n"
nitpick [expect = genuine]
oops

fun f5 where
"f5 x None = x" |
"f5 _ (Some y) = y"

lemma "x = f5 x opt"
nitpick [expect = genuine]
oops

fun f6 where
"f6 x [] = x" |
"f6 _ (y # ys) = y"

lemma "x = f6 x xs"
nitpick [expect = genuine]
oops

fun f7 where
"f7 _ (y # Some (a, b) # zs) = b" |
"f7 x (y # None # zs) = x" |
"f7 x [y] = x" |
"f7 x [] = x"

lemma "x = f7 x xs"
nitpick [expect = genuine]
oops

lemma "u = ()"
nitpick [expect = none]
sorry

lemma "∃y. (b::bool) = y"
nitpick [expect = none]
sorry

lemma "∃x y. p = (x, y)"
nitpick [expect = none]
sorry

lemma "∃x. n = Suc x"
nitpick [expect = genuine]
oops

lemma "∃y. x = Some y"
nitpick [expect = genuine]
oops

lemma "∃y ys. xs = y # ys"
nitpick [expect = genuine]
oops

lemma "∃y a b zs. x = y # Some (a, b) # zs"
nitpick [expect = genuine]
oops

end