(* Title: HOL/Tools/Function/fun_cases.ML
Author: Manuel Eberl, TU Muenchen
The fun_cases command for generating specialised elimination rules for
function package functions.
*)
signature FUN_CASES =
sig
val mk_fun_cases: Proof.context -> term -> thm
val fun_cases: (Attrib.binding * term list) list -> local_theory ->
thm list list * local_theory
val fun_cases_cmd: (Attrib.binding * string list) list -> local_theory ->
thm list list * local_theory
end;
structure Fun_Cases : FUN_CASES =
struct
local
val refl_thin =
Goal.prove_global @{theory HOL} [] [] @{prop "!!P. a = a ==> P ==> P"}
(fn _ => assume_tac 1);
val elim_rls = [asm_rl, FalseE, refl_thin, conjE, exE];
val elim_tac = REPEAT o Tactic.eresolve_tac elim_rls;
fun simp_case_tac ctxt i =
EVERY' [elim_tac, TRY o asm_full_simp_tac ctxt, elim_tac, REPEAT o bound_hyp_subst_tac ctxt] i;
in
fun mk_fun_cases ctxt prop =
let
val thy = Proof_Context.theory_of ctxt;
fun err () =
error (Pretty.string_of (Pretty.block
[Pretty.str "Proposition is not a function equation:",
Pretty.fbrk, Syntax.pretty_term ctxt prop]));
val ((f, _), _) =
Function_Elims.dest_funprop (HOLogic.dest_Trueprop prop)
handle TERM _ => err ();
val info = Function.get_info ctxt f handle List.Empty => err ();
val {elims, pelims, is_partial, ...} = info;
val elims = if is_partial then pelims else the elims;
val cprop = cterm_of thy prop;
val tac = ALLGOALS (simp_case_tac ctxt) THEN prune_params_tac;
fun mk_elim rl =
Thm.implies_intr cprop (Tactic.rule_by_tactic ctxt tac (Thm.assume cprop RS rl))
|> singleton (Variable.export (Variable.auto_fixes prop ctxt) ctxt);
in
(case get_first (try mk_elim) (flat elims) of
SOME r => r
| NONE => err ())
end;
end;
fun gen_fun_cases prep_att prep_prop args lthy =
let
val thy = Proof_Context.theory_of lthy;
val thmss =
map snd args
|> burrow (grouped 10 Par_List.map (mk_fun_cases lthy o prep_prop lthy));
val facts =
map2 (fn ((a, atts), _) => fn thms => ((a, map (prep_att thy) atts), [(thms, [])]))
args thmss;
in lthy |> Local_Theory.notes facts |>> map snd end;
val fun_cases = gen_fun_cases (K I) Syntax.check_prop;
val fun_cases_cmd = gen_fun_cases Attrib.intern_src Syntax.read_prop;
val _ =
Outer_Syntax.local_theory @{command_spec "fun_cases"}
"automatic derivation of simplified elimination rules for function equations"
(Parse.and_list1 Parse_Spec.specs >> (snd oo fun_cases_cmd));
end;