author | wenzelm |
Thu, 14 Jul 2005 19:28:24 +0200 | |
changeset 16842 | 5979c46853d1 |
parent 16778 | 2162c0de4673 |
child 17811 | 10ebcd7032c1 |
permissions | -rw-r--r-- |
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(* Title: HOLCF/domain/axioms.ML |
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ID: $Id$ |
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Author: David von Oheimb |
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Syntax generator for domain section. |
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*) |
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structure Domain_Axioms = struct |
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local |
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open Domain_Library; |
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infixr 0 ===>;infixr 0 ==>;infix 0 == ; |
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infix 1 ===; infix 1 ~= ; infix 1 <<; infix 1 ~<<; |
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infix 9 ` ; infix 9 `% ; infix 9 `%%; infixr 9 oo; |
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fun infer_types thy' = map (inferT_axm (sign_of thy')); |
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fun calc_axioms comp_dname (eqs : eq list) n (((dname,_),cons) : eq)= |
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let |
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(* ----- axioms and definitions concerning the isomorphism ------------------ *) |
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val dc_abs = %%:(dname^"_abs"); |
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val dc_rep = %%:(dname^"_rep"); |
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val x_name'= "x"; |
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val x_name = idx_name eqs x_name' (n+1); |
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val dnam = Sign.base_name dname; |
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val abs_iso_ax = ("abs_iso" ,mk_trp(dc_rep`(dc_abs`%x_name')=== %:x_name')); |
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val rep_iso_ax = ("rep_iso" ,mk_trp(dc_abs`(dc_rep`%x_name')=== %:x_name')); |
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val when_def = ("when_def",%%:(dname^"_when") == |
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foldr (uncurry /\ ) (/\x_name'((when_body cons (fn (x,y) => |
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Bound(1+length cons+x-y)))`(dc_rep`Bound 0))) (when_funs cons)); |
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fun con_def outer recu m n (_,args) = let |
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fun idxs z x arg = (if is_lazy arg then fn t => %%:upN`t else I) |
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(if recu andalso is_rec arg then (cproj (Bound z) eqs |
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(rec_of arg))`Bound(z-x) else Bound(z-x)); |
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fun parms [] = %%:ONE_N |
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| parms vs = foldr'(fn(x,t)=> %%:spairN`x`t)(mapn (idxs(length vs))1 vs); |
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fun inj y 1 _ = y |
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| inj y _ 0 = %%:sinlN`y |
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| inj y i j = %%:sinrN`(inj y (i-1) (j-1)); |
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in foldr /\# (outer (inj (parms args) m n)) args end; |
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val copy_def = ("copy_def", %%:(dname^"_copy") == /\"f" (dc_abs oo |
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Library.foldl (op `) (%%:(dname^"_when") , |
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mapn (con_def I true (length cons)) 0 cons))); |
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(* -- definitions concerning the constructors, discriminators and selectors - *) |
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val con_defs = mapn (fn n => fn (con,args) => (extern_name con ^"_def", |
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%%:con == con_def (fn t => dc_abs`t) false (length cons) n (con,args))) 0 cons; |
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val dis_defs = let |
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fun ddef (con,_) = (dis_name con ^"_def",%%:(dis_name con) == |
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mk_cRep_CFun(%%:(dname^"_when"),map |
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(fn (con',args) => (foldr /\# |
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(if con'=con then %%:TT_N else %%:FF_N) args)) cons)) |
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in map ddef cons end; |
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val mat_defs = let |
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fun mdef (con,_) = (mat_name con ^"_def",%%:(mat_name con) == |
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mk_cRep_CFun(%%:(dname^"_when"),map |
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(fn (con',args) => (foldr /\# |
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(if con'=con |
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then %%:returnN`(mk_ctuple (map (bound_arg args) args)) |
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else %%:failN) args)) cons)) |
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in map mdef cons end; |
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val sel_defs = let |
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fun sdef con n arg = Option.map (fn sel => (sel^"_def",%%:sel == |
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mk_cRep_CFun(%%:(dname^"_when"),map |
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(fn (con',args) => if con'<>con then UU else |
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foldr /\# (Bound (length args - n)) args) cons))) (sel_of arg); |
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in List.mapPartial I (List.concat(map (fn (con,args) => mapn (sdef con) 1 args) cons)) end; |
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(* ----- axiom and definitions concerning induction ------------------------- *) |
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val reach_ax = ("reach", mk_trp(cproj (%%:fixN`%%(comp_dname^"_copy")) eqs n |
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`%x_name === %:x_name)); |
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val take_def = ("take_def",%%:(dname^"_take") == mk_lam("n",cproj' |
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(%%:iterateN $ Bound 0 $ %%:(comp_dname^"_copy") $ UU) eqs n)); |
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val finite_def = ("finite_def",%%:(dname^"_finite") == mk_lam(x_name, |
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mk_ex("n",(%%:(dname^"_take") $ Bound 0)`Bound 1 === Bound 1))); |
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in (dnam, |
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[abs_iso_ax, rep_iso_ax, reach_ax], |
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[when_def, copy_def] @ |
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con_defs @ dis_defs @ mat_defs @ sel_defs @ |
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[take_def, finite_def]) |
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end; (* let *) |
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fun add_axioms_i x = #1 o PureThy.add_axioms_i (map Thm.no_attributes x); |
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fun add_axioms_infer axms thy = add_axioms_i (infer_types thy axms) thy; |
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in (* local *) |
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fun add_axioms (comp_dnam, eqs : eq list) thy' = let |
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val comp_dname = Sign.full_name (sign_of thy') comp_dnam; |
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val dnames = map (fst o fst) eqs; |
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val x_name = idx_name dnames "x"; |
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fun copy_app dname = %%:(dname^"_copy")`Bound 0; |
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val copy_def = ("copy_def" , %%:(comp_dname^"_copy") == |
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/\"f"(foldr' cpair (map copy_app dnames))); |
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val bisim_def = ("bisim_def",%%:(comp_dname^"_bisim")==mk_lam("R", |
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let |
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fun one_con (con,args) = let |
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val nonrec_args = filter_out is_rec args; |
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val rec_args = List.filter is_rec args; |
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val recs_cnt = length rec_args; |
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val allargs = nonrec_args @ rec_args |
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@ map (upd_vname (fn s=> s^"'")) rec_args; |
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val allvns = map vname allargs; |
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fun vname_arg s arg = if is_rec arg then vname arg^s else vname arg; |
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val vns1 = map (vname_arg "" ) args; |
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val vns2 = map (vname_arg "'") args; |
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val allargs_cnt = length nonrec_args + 2*recs_cnt; |
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val rec_idxs = (recs_cnt-1) downto 0; |
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val nonlazy_idxs = map snd (filter_out (fn (arg,_) => is_lazy arg) |
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(allargs~~((allargs_cnt-1) downto 0))); |
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fun rel_app i ra = proj (Bound(allargs_cnt+2)) eqs (rec_of ra) $ |
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Bound (2*recs_cnt-i) $ Bound (recs_cnt-i); |
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val capps = foldr mk_conj (mk_conj( |
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Bound(allargs_cnt+1)===mk_cRep_CFun(%%:con,map (bound_arg allvns) vns1), |
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Bound(allargs_cnt+0)===mk_cRep_CFun(%%:con,map (bound_arg allvns) vns2))) |
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(mapn rel_app 1 rec_args); |
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in foldr mk_ex (Library.foldr mk_conj |
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(map (defined o Bound) nonlazy_idxs,capps)) allvns end; |
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fun one_comp n (_,cons) =mk_all(x_name(n+1),mk_all(x_name(n+1)^"'",mk_imp( |
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proj (Bound 2) eqs n $ Bound 1 $ Bound 0, |
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foldr' mk_disj (mk_conj(Bound 1 === UU,Bound 0 === UU) |
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::map one_con cons)))); |
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in foldr' mk_conj (mapn one_comp 0 eqs)end )); |
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fun add_one (thy,(dnam,axs,dfs)) = thy |
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|> Theory.add_path dnam |
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|> add_axioms_infer dfs(*add_defs_i*) |
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|> add_axioms_infer axs |
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|> Theory.parent_path; |
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val thy = Library.foldl add_one (thy', mapn (calc_axioms comp_dname eqs) 0 eqs); |
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in thy |> Theory.add_path comp_dnam |
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|> add_axioms_infer (bisim_def::(if length eqs>1 then [copy_def] else [])) |
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|> Theory.parent_path |
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end; |
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end; (* local *) |
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end; (* struct *) |