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(* Title: Pure/Isar/element.ML
Author: Makarius
Explicit data structures for some Isar language elements, with derived
logical operations.
*)
signature ELEMENT =
sig
type ('typ, 'term) obtain = binding * ((binding * 'typ option * mixfix) list * 'term list)
type obtains = (string, string) obtain list
type obtains_i = (typ, term) obtain list
datatype ('typ, 'term) stmt =
Shows of (Attrib.binding * ('term * 'term list) list) list |
Obtains of ('typ, 'term) obtain list
type statement = (string, string) stmt
type statement_i = (typ, term) stmt
datatype ('typ, 'term, 'fact) ctxt =
Fixes of (binding * 'typ option * mixfix) list |
Constrains of (string * 'typ) list |
Assumes of (Attrib.binding * ('term * 'term list) list) list |
Defines of (Attrib.binding * ('term * 'term list)) list |
Notes of string * (Attrib.binding * ('fact * Token.src list) list) list |
Lazy_Notes of string * (binding * 'fact lazy)
type context = (string, string, Facts.ref) ctxt
type context_i = (typ, term, thm list) ctxt
val map_ctxt: {binding: binding -> binding, typ: 'typ -> 'a, term: 'term -> 'b,
pattern: 'term -> 'b, fact: 'fact -> 'c, attrib: Token.src -> Token.src} ->
('typ, 'term, 'fact) ctxt -> ('a, 'b, 'c) ctxt
val map_ctxt_attrib: (Token.src -> Token.src) ->
('typ, 'term, 'fact) ctxt -> ('typ, 'term, 'fact) ctxt
val transform_ctxt: morphism -> context_i -> context_i
val pretty_stmt: Proof.context -> statement_i -> Pretty.T list
val pretty_ctxt: Proof.context -> context_i -> Pretty.T list
val pretty_ctxt_no_attribs: Proof.context -> context_i -> Pretty.T list
val pretty_statement: Proof.context -> string -> thm -> Pretty.T
type witness
val prove_witness: Proof.context -> term -> tactic -> witness
val witness_proof: (witness list list -> Proof.context -> Proof.context) ->
term list list -> Proof.context -> Proof.state
val witness_proof_eqs: (witness list list -> thm list -> Proof.context -> Proof.context) ->
term list list -> term list -> Proof.context -> Proof.state
val witness_local_proof: (witness list list -> Proof.state -> Proof.state) ->
string -> term list list -> Proof.context -> Proof.state -> Proof.state
val witness_local_proof_eqs: (witness list list -> thm list -> Proof.state -> Proof.state) ->
string -> term list list -> term list -> Proof.context -> Proof.state -> Proof.state
val transform_witness: morphism -> witness -> witness
val conclude_witness: Proof.context -> witness -> thm
val pretty_witness: Proof.context -> witness -> Pretty.T
val instantiate_normalize_morphism:
((string * sort) * ctyp) list * ((string * typ) * cterm) list -> morphism
val satisfy_morphism: witness list -> morphism
val eq_term_morphism: theory -> term list -> morphism option
val eq_morphism: theory -> thm list -> morphism option
val init: context_i -> Context.generic -> Context.generic
val activate_i: context_i -> Proof.context -> context_i * Proof.context
val activate: (typ, term, Facts.ref) ctxt -> Proof.context -> context_i * Proof.context
end;
structure Element: ELEMENT =
struct
(** language elements **)
(* statement *)
type ('typ, 'term) obtain = binding * ((binding * 'typ option * mixfix) list * 'term list);
type obtains = (string, string) obtain list;
type obtains_i = (typ, term) obtain list;
datatype ('typ, 'term) stmt =
Shows of (Attrib.binding * ('term * 'term list) list) list |
Obtains of ('typ, 'term) obtain list;
type statement = (string, string) stmt;
type statement_i = (typ, term) stmt;
(* context *)
datatype ('typ, 'term, 'fact) ctxt =
Fixes of (binding * 'typ option * mixfix) list |
Constrains of (string * 'typ) list |
Assumes of (Attrib.binding * ('term * 'term list) list) list |
Defines of (Attrib.binding * ('term * 'term list)) list |
Notes of string * (Attrib.binding * ('fact * Token.src list) list) list |
Lazy_Notes of string * (binding * 'fact lazy);
type context = (string, string, Facts.ref) ctxt;
type context_i = (typ, term, thm list) ctxt;
fun map_ctxt {binding, typ, term, pattern, fact, attrib} =
fn Fixes fixes => Fixes (fixes |> map (fn (x, T, mx) => (binding x, Option.map typ T, mx)))
| Constrains xs => Constrains (xs |> map (fn (x, T) =>
(Variable.check_name (binding (Binding.name x)), typ T)))
| Assumes asms => Assumes (asms |> map (fn ((a, atts), propps) =>
((binding a, map attrib atts), propps |> map (fn (t, ps) => (term t, map pattern ps)))))
| Defines defs => Defines (defs |> map (fn ((a, atts), (t, ps)) =>
((binding a, map attrib atts), (term t, map pattern ps))))
| Notes (kind, facts) => Notes (kind, facts |> map (fn ((a, atts), bs) =>
((binding a, map attrib atts), bs |> map (fn (ths, btts) => (fact ths, map attrib btts)))))
| Lazy_Notes (kind, (a, ths)) => Lazy_Notes (kind, (binding a, Lazy.map fact ths));
fun map_ctxt_attrib attrib =
map_ctxt {binding = I, typ = I, term = I, pattern = I, fact = I, attrib = attrib};
fun transform_ctxt phi = map_ctxt
{binding = Morphism.binding phi,
typ = Morphism.typ phi,
term = Morphism.term phi,
pattern = Morphism.term phi,
fact = Morphism.fact phi,
attrib = map (Token.transform phi)};
(** pretty printing **)
fun pretty_items _ _ [] = []
| pretty_items keyword sep (x :: ys) =
Pretty.block [Pretty.keyword2 keyword, Pretty.brk 1, x] ::
map (fn y => Pretty.block [Pretty.str " ", Pretty.keyword2 sep, Pretty.brk 1, y]) ys;
(* pretty_stmt *)
fun pretty_stmt ctxt =
let
val prt_typ = Pretty.quote o Syntax.pretty_typ ctxt;
val prt_term = Pretty.quote o Syntax.pretty_term ctxt;
val prt_terms = separate (Pretty.keyword2 "and") o map prt_term;
val prt_binding = Attrib.pretty_binding ctxt;
val prt_name = Proof_Context.pretty_name ctxt;
fun prt_show (a, ts) =
Pretty.block (Pretty.breaks (prt_binding a ":" @ prt_terms (map fst ts)));
fun prt_var (x, SOME T, _) = Pretty.block
[prt_name (Binding.name_of x), Pretty.str " ::", Pretty.brk 1, prt_typ T]
| prt_var (x, NONE, _) = prt_name (Binding.name_of x);
val prt_vars = separate (Pretty.keyword2 "and") o map prt_var;
fun prt_obtain (_, ([], props)) = Pretty.block (Pretty.breaks (prt_terms props))
| prt_obtain (_, (vars, props)) = Pretty.block (Pretty.breaks
(prt_vars vars @ [Pretty.keyword2 "where"] @ prt_terms props));
in
fn Shows shows => pretty_items "shows" "and" (map prt_show shows)
| Obtains obtains => pretty_items "obtains" "|" (map prt_obtain obtains)
end;
(* pretty_ctxt *)
fun gen_pretty_ctxt show_attribs ctxt =
let
val prt_typ = Pretty.quote o Syntax.pretty_typ ctxt;
val prt_term = Pretty.quote o Syntax.pretty_term ctxt;
val prt_thm = Pretty.cartouche o Thm.pretty_thm ctxt;
val prt_name = Proof_Context.pretty_name ctxt;
fun prt_binding (b, atts) =
Attrib.pretty_binding ctxt (b, if show_attribs then atts else []);
fun prt_fact (ths, atts) =
if not show_attribs orelse null atts then map prt_thm ths
else
Pretty.enclose "(" ")" (Pretty.breaks (map prt_thm ths)) ::
Attrib.pretty_attribs ctxt atts;
fun prt_mixfix NoSyn = []
| prt_mixfix mx = [Pretty.brk 2, Mixfix.pretty_mixfix mx];
fun prt_fix (x, SOME T, mx) = Pretty.block (prt_name (Binding.name_of x) :: Pretty.str " ::" ::
Pretty.brk 1 :: prt_typ T :: prt_mixfix mx)
| prt_fix (x, NONE, mx) = Pretty.block (prt_name (Binding.name_of x) :: prt_mixfix mx);
fun prt_constrain (x, T) = prt_fix (Binding.name x, SOME T, NoSyn);
fun prt_asm (a, ts) =
Pretty.block (Pretty.breaks (prt_binding a ":" @ map (prt_term o fst) ts));
fun prt_def (a, (t, _)) =
Pretty.block (Pretty.breaks (prt_binding a ":" @ [prt_term t]));
fun prt_note (a, ths) =
Pretty.block (Pretty.breaks (flat (prt_binding a " =" :: map prt_fact ths)));
fun notes_kind "" = "notes"
| notes_kind kind = "notes " ^ kind;
in
fn Fixes fixes => pretty_items "fixes" "and" (map prt_fix fixes)
| Constrains xs => pretty_items "constrains" "and" (map prt_constrain xs)
| Assumes asms => pretty_items "assumes" "and" (map prt_asm asms)
| Defines defs => pretty_items "defines" "and" (map prt_def defs)
| Notes (kind, facts) => pretty_items (notes_kind kind) "and" (map prt_note facts)
| Lazy_Notes (kind, (a, ths)) =>
pretty_items (notes_kind kind) "and" [prt_note ((a, []), [(Lazy.force ths, [])])]
end;
val pretty_ctxt = gen_pretty_ctxt true;
val pretty_ctxt_no_attribs = gen_pretty_ctxt false;
(* pretty_statement *)
local
fun standard_elim ctxt th =
(case Object_Logic.elim_concl ctxt th of
SOME C =>
let
val thesis = Var ((Auto_Bind.thesisN, Thm.maxidx_of th + 1), fastype_of C);
val th' = Thm.instantiate ([], [(Term.dest_Var C, Thm.cterm_of ctxt thesis)]) th;
in (th', true) end
| NONE => (th, false));
fun thm_name ctxt kind th prts =
let val head =
if Thm.has_name_hint th then
Pretty.block [Pretty.keyword1 kind, Pretty.brk 1,
Proof_Context.pretty_name ctxt (Long_Name.base_name (Thm.get_name_hint th)), Pretty.str ":"]
else Pretty.keyword1 kind
in Pretty.block (Pretty.fbreaks (head :: prts)) end;
fun obtain prop ctxt =
let
val ((ps, prop'), ctxt') = Variable.focus NONE prop ctxt;
fun fix (x, T) = (Binding.name (Variable.revert_fixed ctxt' x), SOME T, NoSyn);
val xs = map (fix o #2) ps;
val As = Logic.strip_imp_prems prop';
in ((Binding.empty, (xs, As)), ctxt') end;
in
fun pretty_statement ctxt kind raw_th =
let
val (th, is_elim) = standard_elim ctxt (Raw_Simplifier.norm_hhf ctxt raw_th);
val ((_, [th']), ctxt') = Variable.import true [th] (Variable.set_body true ctxt);
val prop = Thm.prop_of th';
val (prems, concl) = Logic.strip_horn prop;
val concl_term = Object_Logic.drop_judgment ctxt concl;
val (assumes, cases) =
chop_suffix (fn prem => is_elim andalso concl aconv Logic.strip_assums_concl prem) prems;
val is_thesis = if null cases then K false else fn v => v aconv concl_term;
val fixes =
rev (fold_aterms (fn v as Free (x, T) =>
if Variable.is_newly_fixed ctxt' ctxt x andalso not (is_thesis v)
then insert (op =) (Variable.revert_fixed ctxt' x, T) else I | _ => I) prop []);
in
pretty_ctxt ctxt' (Fixes (map (fn (x, T) => (Binding.name x, SOME T, NoSyn)) fixes)) @
pretty_ctxt ctxt' (Assumes (map (fn t => (Binding.empty_atts, [(t, [])])) assumes)) @
(if null cases then pretty_stmt ctxt' (Shows [(Binding.empty_atts, [(concl, [])])])
else
let val (clauses, ctxt'') = fold_map obtain cases ctxt'
in pretty_stmt ctxt'' (Obtains clauses) end)
end |> thm_name ctxt kind raw_th;
end;
(** logical operations **)
(* witnesses -- hypotheses as protected facts *)
datatype witness = Witness of term * thm;
val mark_witness = Logic.protect;
fun witness_prop (Witness (t, _)) = t;
fun witness_hyps (Witness (_, th)) = Thm.hyps_of th;
fun map_witness f (Witness witn) = Witness (f witn);
fun transform_witness phi = map_witness (fn (t, th) => (Morphism.term phi t, Morphism.thm phi th));
fun prove_witness ctxt t tac =
Witness (t,
Goal.prove ctxt [] [] (mark_witness t)
(fn _ => resolve_tac ctxt [Drule.protectI] 1 THEN tac)
|> Thm.close_derivation \<^here>);
local
val refine_witness =
Proof.refine_singleton (Method.Basic (fn ctxt => CONTEXT_TACTIC o
K (ALLGOALS (CONJUNCTS (ALLGOALS (CONJUNCTS (TRYALL (resolve_tac ctxt [Drule.protectI]))))))));
fun gen_witness_proof proof after_qed wit_propss eq_props =
let
val propss =
(map o map) (fn prop => (mark_witness prop, [])) wit_propss @
[map (rpair []) eq_props];
fun after_qed' thmss =
let val (wits, eqs) = split_last ((map o map) (Thm.close_derivation \<^here>) thmss);
in after_qed ((map2 o map2) (curry Witness) wit_propss wits) eqs end;
in proof after_qed' propss #> refine_witness end;
fun proof_local cmd goal_ctxt after_qed propp =
let
fun after_qed' (result_ctxt, results) state' =
after_qed (burrow (Proof_Context.export result_ctxt (Proof.context_of state')) results) state';
in
Proof.map_context (K goal_ctxt) #>
Proof.internal_goal (K (K ())) (Proof_Context.get_mode goal_ctxt) true cmd
NONE after_qed' [] [] (map (pair Binding.empty_atts) propp) #> snd
end;
in
fun witness_proof after_qed wit_propss =
gen_witness_proof (Proof.theorem NONE) (fn wits => fn _ => after_qed wits)
wit_propss [];
val witness_proof_eqs = gen_witness_proof (Proof.theorem NONE);
fun witness_local_proof after_qed cmd wit_propss goal_ctxt =
gen_witness_proof (proof_local cmd goal_ctxt)
(fn wits => fn _ => after_qed wits) wit_propss [];
fun witness_local_proof_eqs after_qed cmd wit_propss eq_props goal_ctxt =
gen_witness_proof (proof_local cmd goal_ctxt) after_qed wit_propss eq_props;
end;
fun conclude_witness ctxt (Witness (_, th)) =
Goal.conclude th
|> Raw_Simplifier.norm_hhf_protect ctxt
|> Thm.close_derivation \<^here>;
fun pretty_witness ctxt witn =
let val prt_term = Pretty.quote o Syntax.pretty_term ctxt in
Pretty.block (prt_term (witness_prop witn) ::
(if Config.get ctxt show_hyps then [Pretty.brk 2, Pretty.list "[" "]"
(map prt_term (witness_hyps witn))] else []))
end;
(* instantiate frees, with beta normalization *)
fun instantiate_normalize_morphism insts =
Morphism.instantiate_frees_morphism insts $>
Morphism.term_morphism "beta_norm" Envir.beta_norm $>
Morphism.thm_morphism "beta_conversion" (Conv.fconv_rule (Thm.beta_conversion true));
(* satisfy hypotheses *)
local
val norm_term = Envir.beta_eta_contract;
val norm_conv = Drule.beta_eta_conversion;
val norm_cterm = Thm.rhs_of o norm_conv;
fun find_witness witns hyp =
(case find_first (fn Witness (t, _) => hyp aconv t) witns of
NONE =>
let val hyp' = norm_term hyp
in find_first (fn Witness (t, _) => hyp' aconv norm_term t) witns end
| some => some);
fun compose_witness (Witness (_, th)) r =
let
val th' = Goal.conclude th;
val A = Thm.cprem_of r 1;
in
Thm.implies_elim
(Conv.gconv_rule norm_conv 1 r)
(Conv.fconv_rule norm_conv
(Thm.instantiate (Thm.match (apply2 norm_cterm (Thm.cprop_of th', A))) th'))
end;
in
fun satisfy_thm witns thm =
(Thm.chyps_of thm, thm) |-> fold (fn hyp =>
(case find_witness witns (Thm.term_of hyp) of
NONE => I
| SOME w => Thm.implies_intr hyp #> compose_witness w));
val satisfy_morphism = Morphism.thm_morphism "Element.satisfy" o satisfy_thm;
end;
(* rewriting with equalities *)
(* for activating declarations only *)
fun eq_term_morphism _ [] = NONE
| eq_term_morphism thy props =
let
fun decomp_simp prop =
let
val ctxt = Proof_Context.init_global thy;
val _ = Logic.count_prems prop = 0 orelse
error ("Bad conditional rewrite rule " ^ Syntax.string_of_term ctxt prop);
val lhsrhs = Logic.dest_equals prop
handle TERM _ => error ("Rewrite rule not a meta-equality " ^ Syntax.string_of_term ctxt prop);
in lhsrhs end;
val phi =
Morphism.morphism "Element.eq_term_morphism"
{binding = [],
typ = [],
term = [Pattern.rewrite_term thy (map decomp_simp props) []],
fact = [fn _ => error "Illegal application of Element.eq_term_morphism"]};
in SOME phi end;
fun eq_morphism _ [] = NONE
| eq_morphism thy thms =
let
(* FIXME proper context!? *)
fun rewrite th = rewrite_rule (Proof_Context.init_global (Thm.theory_of_thm th)) thms th;
val phi =
Morphism.morphism "Element.eq_morphism"
{binding = [],
typ = [],
term = [Raw_Simplifier.rewrite_term thy thms []],
fact = [map rewrite]};
in SOME phi end;
(** activate in context **)
(* init *)
fun init (Fixes fixes) = Context.map_proof (Proof_Context.add_fixes fixes #> #2)
| init (Constrains _) = I
| init (Assumes asms) = Context.map_proof (fn ctxt =>
let
val asms' = Attrib.map_specs (map (Attrib.attribute ctxt)) asms;
val (_, ctxt') = ctxt
|> fold Proof_Context.augment (maps (map #1 o #2) asms')
|> Proof_Context.add_assms Assumption.assume_export asms';
in ctxt' end)
| init (Defines defs) = Context.map_proof (fn ctxt =>
let
val defs' = Attrib.map_specs (map (Attrib.attribute ctxt)) defs;
val asms = defs' |> map (fn (b, (t, ps)) =>
let val (_, t') = Local_Defs.cert_def ctxt (K []) t (* FIXME adapt ps? *)
in (t', (b, [(t', ps)])) end);
val (_, ctxt') = ctxt
|> fold Proof_Context.augment (map #1 asms)
|> Proof_Context.add_assms Local_Defs.def_export (map #2 asms);
in ctxt' end)
| init (Notes (kind, facts)) = Attrib.generic_notes kind facts #> #2
| init (Lazy_Notes (kind, ths)) = Attrib.lazy_notes kind ths;
(* activate *)
fun activate_i elem ctxt =
let
val elem' =
(case (map_ctxt_attrib o map) Token.init_assignable elem of
Defines defs =>
Defines (defs |> map (fn ((a, atts), (t, ps)) =>
((Thm.def_binding_optional
(Binding.name (#1 (#1 (Local_Defs.cert_def ctxt (K []) t)))) a, atts),
(t, ps))))
| e => e);
val ctxt' = Context.proof_map (init elem') ctxt;
in ((map_ctxt_attrib o map) Token.closure elem', ctxt') end;
fun activate raw_elem ctxt =
let val elem = raw_elem |> map_ctxt
{binding = I,
typ = I,
term = I,
pattern = I,
fact = Proof_Context.get_fact ctxt,
attrib = Attrib.check_src ctxt}
in activate_i elem ctxt end;
end;
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