(* Title: HOL/MiniML/Maybe.ML
ID: $Id$
Author: Wolfgang Naraschewski and Tobias Nipkow
Copyright 1996 TU Muenchen
*)
(* constructor laws for option_bind *)
goalw thy [option_bind_def] "option_bind (Some s) f = (f s)";
by (Simp_tac 1);
qed "option_bind_Some";
goalw thy [option_bind_def] "option_bind None f = None";
by (Simp_tac 1);
qed "option_bind_None";
Addsimps [option_bind_Some,option_bind_None];
(* expansion of option_bind *)
goal thy
"P(option_bind res f) = ((res = None --> P None) & (!s. res = Some s --> P(f s)))";
by (option.induct_tac "res" 1);
by (fast_tac (HOL_cs addss !simpset) 1);
by (Asm_simp_tac 1);
qed "expand_option_bind";
goal thy
"((option_bind m f) = None) = ((m=None) | (? p. m = Some p & f p = None))";
by(simp_tac (!simpset setloop (split_tac [expand_option_bind])) 1);
qed "option_bind_eq_None";
Addsimps [option_bind_eq_None];
(* auxiliary lemma *)
goal Maybe.thy "(y = Some x) = (Some x = y)";
by( simp_tac (!simpset addsimps [eq_sym_conv]) 1);
qed "rotate_Some";