infix 1 then_cconv
infix 0 else_cconv
type cconv = conv
signature BASIC_CCONV =
sig
val then_cconv: cconv * cconv -> cconv
val else_cconv: cconv * cconv -> cconv
val CCONVERSION: cconv -> int -> tactic
end
signature CCONV =
sig
include BASIC_CCONV
val no_cconv: cconv
val all_cconv: cconv
val first_cconv: cconv list -> cconv
val abs_cconv: (cterm * Proof.context -> cconv) -> Proof.context -> cconv
val combination_cconv: cconv -> cconv -> cconv
val comb_cconv: cconv -> cconv
val arg_cconv: cconv -> cconv
val fun_cconv: cconv -> cconv
val arg1_cconv: cconv -> cconv
val fun2_cconv: cconv -> cconv
val rewr_cconv: thm -> cconv
val rewrs_cconv: thm list -> cconv
val params_cconv: int -> (Proof.context -> cconv) -> Proof.context -> cconv
val prems_cconv: int -> cconv -> cconv
val concl_cconv: int -> cconv -> cconv
val fconv_rule: cconv -> thm -> thm
val gconv_rule: cconv -> int -> thm -> thm
end
structure CConv : CCONV =
struct
val concl_lhs_of = Thm.cprop_of #> Drule.strip_imp_concl #> Thm.dest_equals_lhs
val concl_rhs_of = Thm.cprop_of #> Drule.strip_imp_concl #> Thm.dest_equals_rhs
fun transitive th1 th2 = Drule.transitive_thm OF [th1, th2]
val combination_thm =
let
val fg = @{cprop "f :: 'a :: {} \<Rightarrow> 'b :: {} \<equiv> g"}
val st = @{cprop "s :: 'a :: {} \<equiv> t"}
val thm = Thm.combination (Thm.assume fg) (Thm.assume st)
|> Thm.implies_intr st
|> Thm.implies_intr fg
in Drule.export_without_context thm end
fun abstract_rule_thm n =
let
val eq = @{cprop "\<And>x :: 'a :: {}. (s :: 'a \<Rightarrow> 'b :: {}) x \<equiv> t x"}
val x = @{cterm "x :: 'a :: {}"}
val thm = eq
|> Thm.assume
|> Thm.forall_elim x
|> Thm.abstract_rule n x
|> Thm.implies_intr eq
in Drule.export_without_context thm end
val no_cconv = Conv.no_conv
val all_cconv = Conv.all_conv
fun (cv1 else_cconv cv2) ct =
(cv1 ct
handle THM _ => cv2 ct
| CTERM _ => cv2 ct
| TERM _ => cv2 ct
| TYPE _ => cv2 ct)
fun (cv1 then_cconv cv2) ct =
let
val eq1 = cv1 ct
val eq2 = cv2 (concl_rhs_of eq1)
in
if Thm.is_reflexive eq1 then eq2
else if Thm.is_reflexive eq2 then eq1
else transitive eq1 eq2
end
fun first_cconv cvs = fold_rev (curry op else_cconv) cvs no_cconv
fun rewr_cconv rule ct =
let
val rule1 = Thm.incr_indexes (Thm.maxidx_of_cterm ct + 1) rule
val lhs = concl_lhs_of rule1
val rule2 = Thm.rename_boundvars (Thm.term_of lhs) (Thm.term_of ct) rule1
val rule3 = Thm.instantiate (Thm.match (lhs, ct)) rule2
handle Pattern.MATCH => raise CTERM ("rewr_cconv", [lhs, ct])
val rule4 =
if concl_lhs_of rule3 aconvc ct then rule3
else let val ceq = Thm.dest_fun2 (Thm.cprop_of rule3)
in rule3 COMP Thm.trivial (Thm.mk_binop ceq ct (concl_rhs_of rule3)) end
in
transitive rule4 (Thm.beta_conversion true (concl_rhs_of rule4))
end
fun rewrs_cconv rules = first_cconv (map rewr_cconv rules)
fun combination_cconv cv1 cv2 cterm =
let val (l, r) = Thm.dest_comb cterm
in combination_thm OF [cv1 l, cv2 r] end
fun comb_cconv cv = combination_cconv cv cv
fun fun_cconv conversion =
combination_cconv conversion all_cconv
fun arg_cconv conversion =
combination_cconv all_cconv conversion
fun abs_cconv cv ctxt ct =
(case Thm.term_of ct of
Abs (x, _, _) =>
let
(* Instantiate the rule properly and apply it to the eq theorem. *)
fun abstract_rule u v eq =
let
(* Take a variable v and an equality theorem of form:
P1 Pure.imp ... Pure.imp Pn Pure.imp L v == R v
And build a term of form:
!!v. (%x. L x) v == (%x. R x) v *)
fun mk_concl var eq =
let
val certify = Thm.cterm_of ctxt
fun abs term = (Term.lambda var term) $ var
fun equals_cong f t =
Logic.dest_equals t
|> (fn (a, b) => (f a, f b))
|> Logic.mk_equals
in
Thm.concl_of eq
|> equals_cong abs
|> Logic.all var |> certify
end
val rule = abstract_rule_thm x
val inst = Thm.match (Drule.cprems_of rule |> hd, mk_concl (Thm.term_of v) eq)
in
(Drule.instantiate_normalize inst rule OF [Drule.generalize ([], [u]) eq])
|> Drule.zero_var_indexes
end
(* Destruct the abstraction and apply the conversion. *)
val (u, ctxt') = yield_singleton Variable.variant_fixes Name.uu ctxt
val (v, ct') = Thm.dest_abs (SOME u) ct
val eq = cv (v, ctxt') ct'
in
if Thm.is_reflexive eq
then all_cconv ct
else abstract_rule u v eq
end
| _ => raise CTERM ("abs_cconv", [ct]))
val arg1_cconv = fun_cconv o arg_cconv
val fun2_cconv = fun_cconv o fun_cconv
(* conversions on HHF rules *)
(*rewrite B in !!x1 ... xn. B*)
fun params_cconv n cv ctxt ct =
if n <> 0 andalso Logic.is_all (Thm.term_of ct)
then arg_cconv (abs_cconv (params_cconv (n - 1) cv o #2) ctxt) ct
else cv ctxt ct
(* TODO: This code behaves not exactly like Conv.prems_cconv does.
Fix this! *)
(*rewrite the A's in A1 Pure.imp ... Pure.imp An Pure.imp B*)
fun prems_cconv 0 cv ct = cv ct
| prems_cconv n cv ct =
(case ct |> Thm.term_of of
(Const (@{const_name "Pure.imp"}, _) $ _) $ _ => ((if n = 1 then fun_cconv else I) o arg_cconv) (prems_cconv (n-1) cv) ct
| _ => cv ct)
(*rewrite B in A1 Pure.imp ... Pure.imp An Pure.imp B*)
fun concl_cconv 0 cv ct = cv ct
| concl_cconv n cv ct =
(case ct |> Thm.term_of of
(Const (@{const_name "Pure.imp"}, _) $ _) $ _ => arg_cconv (concl_cconv (n-1) cv) ct
| _ => cv ct)
(*forward conversion, cf. FCONV_RULE in LCF*)
fun fconv_rule cv th =
let
val eq = cv (Thm.cprop_of th)
in
if Thm.is_reflexive eq then th
else th COMP (Thm.permute_prems 0 (Thm.nprems_of eq) (eq RS Drule.equal_elim_rule1))
end
(*goal conversion*)
fun gconv_rule cv i th =
(case try (Thm.cprem_of th) i of
SOME ct =>
let
val eq = cv ct
(* Drule.with_subgoal assumes that there are no new premises generated
and thus rotates the premises wrongly. *)
fun with_subgoal i f thm =
let
val num_prems = Thm.nprems_of thm
val rotate_to_front = rotate_prems (i - 1)
fun rotate_back thm = rotate_prems (1 - i + num_prems - Thm.nprems_of thm) thm
in
thm |> rotate_to_front |> f |> rotate_back
end
in
if Thm.is_reflexive eq then th
else with_subgoal i (fconv_rule (arg1_cconv (K eq))) th
end
| NONE => raise THM ("gconv_rule", i, [th]))
(* Conditional conversions as tactics. *)
fun CCONVERSION cv i st = Seq.single (gconv_rule cv i st)
handle THM _ => Seq.empty
| CTERM _ => Seq.empty
| TERM _ => Seq.empty
| TYPE _ => Seq.empty
end
structure Basic_CConv: BASIC_CCONV = CConv
open Basic_CConv