(* Title: Pure/Isar/element.ML
ID: $Id$
Author: Makarius
Explicit data structures for some Isar language elements.
*)
signature ELEMENT =
sig
datatype ('typ, 'term) stmt =
Shows of ((string * Attrib.src list) * ('term * ('term list * 'term list)) list) list |
Obtains of (string * ((string * 'typ option) list * 'term list)) list
type statement (*= (string, string) stmt*)
type statement_i (*= (typ, term) stmt*)
datatype ('typ, 'term, 'fact) ctxt =
Fixes of (string * 'typ option * mixfix) list |
Constrains of (string * 'typ) list |
Assumes of ((string * Attrib.src list) * ('term * ('term list * 'term list)) list) list |
Defines of ((string * Attrib.src list) * ('term * 'term list)) list |
Notes of ((string * Attrib.src list) * ('fact * Attrib.src list) list) list
type context (*= (string, string, thmref) ctxt*)
type context_i (*= (typ, term, thm list) ctxt*)
val map_ctxt: {name: string -> string,
var: string * mixfix -> string * mixfix,
typ: 'typ -> 'a, term: 'term -> 'b, fact: 'fact -> 'c,
attrib: Attrib.src -> Attrib.src} -> ('typ, 'term, 'fact) ctxt -> ('a, 'b, 'c) ctxt
val map_ctxt_values: (typ -> typ) -> (term -> term) -> (thm -> thm) -> context_i -> context_i
val rename: (string * (string * mixfix option)) list -> string -> string
val rename_var: (string * (string * mixfix option)) list -> string * mixfix -> string * mixfix
val rename_term: (string * (string * mixfix option)) list -> term -> term
val rename_thm: (string * (string * mixfix option)) list -> thm -> thm
val rename_ctxt: (string * (string * mixfix option)) list -> context_i -> context_i
val instT_type: typ Symtab.table -> typ -> typ
val instT_term: typ Symtab.table -> term -> term
val instT_thm: theory -> typ Symtab.table -> thm -> thm
val instT_ctxt: theory -> typ Symtab.table -> context_i -> context_i
val inst_term: typ Symtab.table * term Symtab.table -> term -> term
val inst_thm: theory -> typ Symtab.table * term Symtab.table -> thm -> thm
val inst_ctxt: theory -> typ Symtab.table * term Symtab.table -> context_i -> context_i
val pretty_stmt: ProofContext.context -> statement_i -> Pretty.T list
val pretty_ctxt: ProofContext.context -> context_i -> Pretty.T list
val pretty_statement: ProofContext.context -> string -> thm -> Pretty.T
end;
structure Element: ELEMENT =
struct
(** conclusions **)
datatype ('typ, 'term) stmt =
Shows of ((string * Attrib.src list) * ('term * ('term list * 'term list)) list) list |
Obtains of (string * ((string * 'typ option) list * 'term list)) list;
type statement = (string, string) stmt;
type statement_i = (typ, term) stmt;
(** context elements **)
(* datatype ctxt *)
datatype ('typ, 'term, 'fact) ctxt =
Fixes of (string * 'typ option * mixfix) list |
Constrains of (string * 'typ) list |
Assumes of ((string * Attrib.src list) * ('term * ('term list * 'term list)) list) list |
Defines of ((string * Attrib.src list) * ('term * 'term list)) list |
Notes of ((string * Attrib.src list) * ('fact * Attrib.src list) list) list;
type context = (string, string, thmref) ctxt;
type context_i = (typ, term, thm list) ctxt;
fun map_ctxt {name, var, typ, term, fact, attrib} =
fn Fixes fixes => Fixes (fixes |> map (fn (x, T, mx) =>
let val (x', mx') = var (x, mx) in (x', Option.map typ T, mx') end))
| Constrains xs => Constrains (xs |> map (fn (x, T) => (#1 (var (x, NoSyn)), typ T)))
| Assumes asms => Assumes (asms |> map (fn ((a, atts), propps) =>
((name a, map attrib atts), propps |> map (fn (t, (ps, qs)) =>
(term t, (map term ps, map term qs))))))
| Defines defs => Defines (defs |> map (fn ((a, atts), (t, ps)) =>
((name a, map attrib atts), (term t, map term ps))))
| Notes facts => Notes (facts |> map (fn ((a, atts), bs) =>
((name a, map attrib atts), bs |> map (fn (ths, btts) => (fact ths, map attrib btts)))));
fun map_ctxt_values typ term thm = map_ctxt
{name = I, var = I, typ = typ, term = term, fact = map thm,
attrib = Args.map_values I typ term thm};
(** logical operations **)
(* derived rules *)
fun instantiate_tfrees thy subst =
let
val certT = Thm.ctyp_of thy;
fun inst vs (a, T) = AList.lookup (op =) vs a
|> Option.map (fn v => (certT (TVar v), certT T));
in
Drule.tvars_intr_list (map fst subst) #->
(fn vs => Thm.instantiate (List.mapPartial (inst vs) subst, []))
end;
fun instantiate_frees thy subst =
let val cert = Thm.cterm_of thy in
Drule.forall_intr_list (map (cert o Free o fst) subst) #>
Drule.forall_elim_list (map (cert o snd) subst)
end;
fun hyps_rule rule th =
let
val cterm_rule = Thm.reflexive #> rule #> Thm.cprop_of #> Drule.dest_equals #> #1;
val {hyps, ...} = Thm.crep_thm th;
in
Drule.implies_elim_list
(rule (Drule.implies_intr_list hyps th))
(map (Thm.assume o cterm_rule) hyps)
end;
(* renaming *)
fun rename ren x =
(case AList.lookup (op =) ren (x: string) of
NONE => x
| SOME (x', _) => x');
fun rename_var ren (x, mx) =
(case (AList.lookup (op =) ren (x: string), mx) of
(NONE, _) => (x, mx)
| (SOME (x', NONE), Structure) => (x', mx)
| (SOME (x', SOME _), Structure) =>
error ("Attempt to change syntax of structure parameter " ^ quote x)
| (SOME (x', NONE), _) => (x', NoSyn)
| (SOME (x', SOME mx'), _) => (x', mx'));
fun rename_term ren (Free (x, T)) = Free (rename ren x, T)
| rename_term ren (t $ u) = rename_term ren t $ rename_term ren u
| rename_term ren (Abs (x, T, t)) = Abs (x, T, rename_term ren t)
| rename_term _ a = a;
fun rename_thm ren th =
let
val subst = Drule.frees_of th
|> List.mapPartial (fn (x, T) =>
let val x' = rename ren x
in if x = x' then NONE else SOME ((x, T), (Free (x', T))) end);
in
if null subst then th
else th |> hyps_rule (instantiate_frees (Thm.theory_of_thm th) subst)
end;
fun rename_ctxt ren =
map_ctxt_values I (rename_term ren) (rename_thm ren)
#> map_ctxt {name = I, typ = I, term = I, fact = I, attrib = I, var = rename_var ren};
(* type instantiation *)
fun instT_type env =
if Symtab.is_empty env then I
else Term.map_type_tfree (fn (x, S) => the_default (TFree (x, S)) (Symtab.lookup env x));
fun instT_term env =
if Symtab.is_empty env then I
else Term.map_term_types (instT_type env);
fun instT_subst env th =
Drule.tfrees_of th
|> List.mapPartial (fn (a, S) =>
let
val T = TFree (a, S);
val T' = the_default T (Symtab.lookup env a);
in if T = T' then NONE else SOME (a, T') end);
fun instT_thm thy env th =
if Symtab.is_empty env then th
else
let val subst = instT_subst env th
in if null subst then th else th |> hyps_rule (instantiate_tfrees thy subst) end;
fun instT_ctxt thy env =
map_ctxt_values (instT_type env) (instT_term env) (instT_thm thy env);
(* type and term instantiation *)
fun inst_term (envT, env) =
if Symtab.is_empty env then instT_term envT
else
let
val instT = instT_type envT;
fun inst (Const (x, T)) = Const (x, instT T)
| inst (Free (x, T)) =
(case Symtab.lookup env x of
NONE => Free (x, instT T)
| SOME t => t)
| inst (Var (xi, T)) = Var (xi, instT T)
| inst (b as Bound _) = b
| inst (Abs (x, T, t)) = Abs (x, instT T, inst t)
| inst (t $ u) = inst t $ inst u;
in Envir.beta_norm o inst end;
fun inst_thm thy (envT, env) th =
if Symtab.is_empty env then instT_thm thy envT th
else
let
val substT = instT_subst envT th;
val subst = Drule.frees_of th
|> List.mapPartial (fn (x, T) =>
let
val T' = instT_type envT T;
val t = Free (x, T');
val t' = the_default t (Symtab.lookup env x);
in if t aconv t' then NONE else SOME ((x, T'), t') end);
in
if null substT andalso null subst then th
else th |> hyps_rule
(instantiate_tfrees thy substT #>
instantiate_frees thy subst #>
Drule.fconv_rule (Thm.beta_conversion true))
end;
fun inst_ctxt thy envs =
map_ctxt_values (instT_type (#1 envs)) (inst_term envs) (inst_thm thy envs);
(** pretty printing **)
fun pretty_items _ _ [] = []
| pretty_items keyword sep (x :: ys) =
Pretty.block [Pretty.keyword keyword, Pretty.brk 1, x] ::
map (fn y => Pretty.block [Pretty.str " ", Pretty.keyword sep, Pretty.brk 1, y]) ys;
fun pretty_name_atts ctxt (name, atts) sep =
if name = "" andalso null atts then []
else [Pretty.block (Pretty.breaks (Pretty.str (ProofContext.extern_thm ctxt name) ::
Args.pretty_attribs ctxt atts @ [Pretty.str sep]))];
(* pretty_stmt *)
fun pretty_stmt ctxt =
let
val prt_typ = Pretty.quote o ProofContext.pretty_typ ctxt;
val prt_term = Pretty.quote o ProofContext.pretty_term ctxt;
val prt_terms = separate (Pretty.keyword "and") o map prt_term;
val prt_name_atts = pretty_name_atts ctxt;
fun prt_show (a, ts) =
Pretty.block (Pretty.breaks (prt_name_atts a ":" @ prt_terms (map fst ts)));
fun prt_var (x, SOME T) = Pretty.block [Pretty.str (x ^ " ::"), Pretty.brk 1, prt_typ T]
| prt_var (x, NONE) = Pretty.str x;
fun prt_obtain (_, ([], ts)) = Pretty.block (Pretty.breaks (prt_terms ts))
| prt_obtain (_, (xs, ts)) = Pretty.block (Pretty.breaks
(map prt_var xs @ [Pretty.keyword "where"] @ prt_terms ts));
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 pretty_ctxt ctxt =
let
val prt_typ = Pretty.quote o ProofContext.pretty_typ ctxt;
val prt_term = Pretty.quote o ProofContext.pretty_term ctxt;
val prt_thm = Pretty.backquote o ProofContext.pretty_thm ctxt;
val prt_name_atts = pretty_name_atts ctxt;
fun prt_mixfix NoSyn = []
| prt_mixfix mx = [Pretty.brk 2, Syntax.pretty_mixfix mx];
fun prt_fix (x, SOME T, mx) = Pretty.block (Pretty.str (x ^ " ::") :: Pretty.brk 1 ::
prt_typ T :: Pretty.brk 1 :: prt_mixfix mx)
| prt_fix (x, NONE, mx) = Pretty.block (Pretty.str x :: Pretty.brk 1 :: prt_mixfix mx);
fun prt_constrain (x, T) = prt_fix (x, SOME T, NoSyn);
fun prt_asm (a, ts) =
Pretty.block (Pretty.breaks (prt_name_atts a ":" @ map (prt_term o fst) ts));
fun prt_def (a, (t, _)) =
Pretty.block (Pretty.breaks (prt_name_atts a ":" @ [prt_term t]));
fun prt_fact (ths, []) = map prt_thm ths
| prt_fact (ths, atts) = Pretty.enclose "(" ")"
(Pretty.breaks (map prt_thm ths)) :: Args.pretty_attribs ctxt atts;
fun prt_note (a, ths) =
Pretty.block (Pretty.breaks (List.concat (prt_name_atts a "=" :: map prt_fact ths)));
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 facts => pretty_items "notes" "and" (map prt_note facts)
end;
(* pretty_statement *)
local
fun thm_name kind th prts =
let val head =
(case #1 (Thm.get_name_tags th) of
"" => Pretty.command kind
| a => Pretty.block [Pretty.command kind, Pretty.brk 1, Pretty.str (Sign.base_name a ^ ":")])
in Pretty.block (Pretty.fbreaks (head :: prts)) end;
fun obtain prop ctxt =
let
val xs = ProofContext.rename_frees ctxt [] (Logic.strip_params prop);
val args = rev (map Free xs);
val As = Logic.strip_assums_hyp prop |> map (fn t => Term.subst_bounds (args, t));
val ctxt' = ctxt |> fold ProofContext.declare_term args;
in (("", (map (apsnd SOME) xs, As)), ctxt') end;
in
fun pretty_statement ctxt kind raw_th =
let
val thy = ProofContext.theory_of ctxt;
val th = Goal.norm_hhf raw_th;
val maxidx = #maxidx (Thm.rep_thm th);
fun standard_thesis t =
let
val C = ObjectLogic.drop_judgment thy (Thm.concl_of th);
val C' = Var ((AutoBind.thesisN, maxidx + 1), Term.fastype_of C);
in Term.subst_atomic [(C, C')] t end;
val raw_prop =
Thm.prop_of th
|> singleton (ProofContext.monomorphic ctxt)
|> K (ObjectLogic.is_elim th) ? standard_thesis
|> Term.zero_var_indexes;
val vars = Term.add_vars raw_prop [];
val frees = ProofContext.rename_frees ctxt [raw_prop] (map (apfst fst) vars);
val fixes = rev (filter_out (fn (x, _) => x = AutoBind.thesisN) frees);
val prop = Term.instantiate ([], vars ~~ map Free frees) raw_prop;
val (prems, concl) = Logic.strip_horn prop;
val thesis = ObjectLogic.fixed_judgment thy AutoBind.thesisN;
val (asms, cases) = take_suffix (fn prem => thesis aconv Logic.strip_assums_concl prem) prems;
in
pretty_ctxt ctxt (Fixes (map (fn (x, T) => (x, SOME T, NoSyn)) fixes)) @
pretty_ctxt ctxt (Assumes (map (fn t => (("", []), [(t, ([], []))])) asms)) @
pretty_stmt ctxt
(if null cases then Shows [(("", []), [(concl, ([], []))])]
else Obtains (#1 (fold_map obtain cases (ctxt |> ProofContext.declare_term prop))))
end |> thm_name kind raw_th;
end;
end;