author | wenzelm |
Fri, 10 Feb 2006 02:22:16 +0100 | |
changeset 18988 | d6e5fa2ba8b8 |
parent 18728 | 6790126ab5f6 |
child 20217 | 25b068a99d2b |
permissions | -rw-r--r-- |
4 | 1 |
(* Title: Provers/splitter |
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ID: $Id$ |
|
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Author: Tobias Nipkow |
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Copyright 1995 TU Munich |
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Generic case-splitter, suitable for most logics. |
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Deals with equalities of the form ?P(f args) = ... |
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where "f args" must be a first-order term without duplicate variables. |
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*) |
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||
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infix 4 addsplits delsplits; |
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signature SPLITTER_DATA = |
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sig |
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val mk_eq : thm -> thm |
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val meta_eq_to_iff: thm (* "x == y ==> x = y" *) |
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val iffD : thm (* "[| P = Q; Q |] ==> P" *) |
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val disjE : thm (* "[| P | Q; P ==> R; Q ==> R |] ==> R" *) |
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val conjE : thm (* "[| P & Q; [| P; Q |] ==> R |] ==> R" *) |
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val exE : thm (* "[| x. P x; !!x. P x ==> Q |] ==> Q" *) |
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val contrapos : thm (* "[| ~ Q; P ==> Q |] ==> ~ P" *) |
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val contrapos2 : thm (* "[| Q; ~ P ==> ~ Q |] ==> P" *) |
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val notnotD : thm (* "~ ~ P ==> P" *) |
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end |
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||
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signature SPLITTER = |
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sig |
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val split_tac : thm list -> int -> tactic |
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val split_inside_tac: thm list -> int -> tactic |
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val split_asm_tac : thm list -> int -> tactic |
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val addsplits : simpset * thm list -> simpset |
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val delsplits : simpset * thm list -> simpset |
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val Addsplits : thm list -> unit |
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val Delsplits : thm list -> unit |
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val split_add: attribute |
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val split_del: attribute |
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val split_modifiers : (Args.T list -> (Method.modifier * Args.T list)) list |
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val setup: theory -> theory |
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end; |
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functor SplitterFun(Data: SPLITTER_DATA): SPLITTER = |
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struct |
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val Const (const_not, _) $ _ = |
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ObjectLogic.drop_judgment (the_context ()) |
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(#1 (Logic.dest_implies (Thm.prop_of Data.notnotD))); |
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val Const (const_or , _) $ _ $ _ = |
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ObjectLogic.drop_judgment (the_context ()) |
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(#1 (Logic.dest_implies (Thm.prop_of Data.disjE))); |
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val const_Trueprop = ObjectLogic.judgment_name (the_context ()); |
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||
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Rewrote mk_cntxt_splitthm. Added function mk_case_split_inside_tac.
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Little reorganization. Loop tactics have names now.
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fun split_format_err() = error("Wrong format for split rule"); |
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fun split_thm_info thm = case concl_of (Data.mk_eq thm) of |
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Const("==", _) $ (Var _ $ t) $ c => (case strip_comb t of |
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(Const p, _) => (p, case c of (Const (s, _) $ _) => s = const_not | _ => false) |
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| _ => split_format_err ()) |
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addsplits / delsplits no longer ignore type of constant.
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| _ => split_format_err (); |
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fun mk_case_split_tac order = |
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let |
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(************************************************************ |
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Create lift-theorem "trlift" : |
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[| !!x. Q x == R x; P(%x. R x) == C |] ==> P (%x. Q x) == C |
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*************************************************************) |
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val meta_iffD = Data.meta_eq_to_iff RS Data.iffD; |
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val lift = |
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let val ct = read_cterm Pure.thy |
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("(!!x. (Q::('b::{})=>('c::{}))(x) == R(x)) ==> \ |
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\P(%x. Q(x)) == P(%x. R(x))::'a::{}",propT) |
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in OldGoals.prove_goalw_cterm [] ct |
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(fn [prem] => [rewtac prem, rtac reflexive_thm 1]) |
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end; |
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val trlift = lift RS transitive_thm; |
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val _ $ (P $ _) $ _ = concl_of trlift; |
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(************************************************************************ |
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Set up term for instantiation of P in the lift-theorem |
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Ts : types of parameters (i.e. variables bound by meta-quantifiers) |
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t : lefthand side of meta-equality in subgoal |
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the lift theorem is applied to (see select) |
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pos : "path" leading to abstraction, coded as a list |
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T : type of body of P(...) |
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maxi : maximum index of Vars |
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*************************************************************************) |
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fun mk_cntxt Ts t pos T maxi = |
1d8fa2fc4b9c
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let fun var (t,i) = Var(("X",i),type_of1(Ts,t)); |
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fun down [] t i = Bound 0 |
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| down (p::ps) t i = |
1d8fa2fc4b9c
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let val (h,ts) = strip_comb t |
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val v1 = ListPair.map var (Library.take(p,ts), i upto (i+p-1)) |
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val u::us = Library.drop(p,ts) |
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val v2 = ListPair.map var (us, (i+p) upto (i+length(ts)-2)) |
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in list_comb(h,v1@[down ps u (i+length ts)]@v2) end; |
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in Abs("", T, down (rev pos) t maxi) end; |
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(************************************************************************ |
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Set up term for instantiation of P in the split-theorem |
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P(...) == rhs |
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t : lefthand side of meta-equality in subgoal |
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the split theorem is applied to (see select) |
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T : type of body of P(...) |
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tt : the term Const(key,..) $ ... |
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*************************************************************************) |
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fun mk_cntxt_splitthm t tt T = |
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let fun repl lev t = |
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if incr_boundvars lev tt aconv t then Bound lev |
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else case t of |
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(Abs (v, T2, t)) => Abs (v, T2, repl (lev+1) t) |
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| (Bound i) => Bound (if i>=lev then i+1 else i) |
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| (t1 $ t2) => (repl lev t1) $ (repl lev t2) |
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| t => t |
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in Abs("", T, repl 0 t) end; |
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(* add all loose bound variables in t to list is *) |
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fun add_lbnos(is,t) = add_loose_bnos(t,0,is); |
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(* check if the innermost abstraction that needs to be removed |
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has a body of type T; otherwise the expansion thm will fail later on |
136 |
*) |
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fun type_test(T,lbnos,apsns) = |
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let val (_,U,_) = List.nth(apsns, Library.foldl Int.min (hd lbnos, tl lbnos)) |
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in T=U end; |
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(************************************************************************* |
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Create a "split_pack". |
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thm : the relevant split-theorem, i.e. P(...) == rhs , where P(...) |
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is of the form |
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P( Const(key,...) $ t_1 $ ... $ t_n ) (e.g. key = "if") |
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T : type of P(...) |
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148 |
T' : type of term to be scanned |
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n : number of arguments expected by Const(key,...) |
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ts : list of arguments actually found |
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apsns : list of tuples of the form (T,U,pos), one tuple for each |
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abstraction that is encountered on the way to the position where |
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Const(key, ...) $ ... occurs, where |
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T : type of the variable bound by the abstraction |
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U : type of the abstraction's body |
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pos : "path" leading to the body of the abstraction |
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pos : "path" leading to the position where Const(key, ...) $ ... occurs. |
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TB : type of Const(key,...) $ t_1 $ ... $ t_n |
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t : the term Const(key,...) $ t_1 $ ... $ t_n |
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A split pack is a tuple of the form |
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(thm, apsns, pos, TB, tt) |
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Note : apsns is reversed, so that the outermost quantifier's position |
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comes first ! If the terms in ts don't contain variables bound |
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by other than meta-quantifiers, apsns is empty, because no further |
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lifting is required before applying the split-theorem. |
17881 | 167 |
******************************************************************************) |
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168 |
|
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169 |
fun mk_split_pack(thm, T, T', n, ts, apsns, pos, TB, t) = |
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if n > length ts then [] |
171 |
else let val lev = length apsns |
|
15570 | 172 |
val lbnos = Library.foldl add_lbnos ([],Library.take(n,ts)) |
173 |
val flbnos = List.filter (fn i => i < lev) lbnos |
|
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val tt = incr_boundvars (~lev) t |
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in if null flbnos then |
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176 |
if T = T' then [(thm,[],pos,TB,tt)] else [] |
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177 |
else if type_test(T,flbnos,apsns) then [(thm, rev apsns,pos,TB,tt)] |
2143 | 178 |
else [] |
1064 | 179 |
end; |
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(**************************************************************************** |
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183 |
Recursively scans term for occurences of Const(key,...) $ ... |
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184 |
Returns a list of "split-packs" (one for each occurence of Const(key,...) ) |
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186 |
cmap : association list of split-theorems that should be tried. |
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187 |
The elements have the format (key,(thm,T,n)) , where |
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188 |
key : the theorem's key constant ( Const(key,...) $ ... ) |
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|
189 |
thm : the theorem itself |
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190 |
T : type of P( Const(key,...) $ ... ) |
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191 |
n : number of arguments expected by Const(key,...) |
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192 |
Ts : types of parameters |
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|
193 |
t : the term to be scanned |
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|
194 |
******************************************************************************) |
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|
195 |
|
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|
196 |
(* Simplified first-order matching; |
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|
197 |
assumes that all Vars in the pattern are distinct; |
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198 |
see Pure/pattern.ML for the full version; |
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|
199 |
*) |
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200 |
local |
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|
201 |
exception MATCH |
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202 |
in |
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fun typ_match sg (tyenv, TU) = (Sign.typ_match sg TU tyenv) |
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204 |
handle Type.TYPE_MATCH => raise MATCH; |
16935 | 205 |
fun fomatch sg args = |
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206 |
let |
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207 |
fun mtch tyinsts = fn |
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(Ts,Var(_,T), t) => typ_match sg (tyinsts, (T, fastype_of1(Ts,t))) |
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209 |
| (_,Free (a,T), Free (b,U)) => |
16935 | 210 |
if a=b then typ_match sg (tyinsts,(T,U)) else raise MATCH |
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211 |
| (_,Const (a,T), Const (b,U)) => |
16935 | 212 |
if a=b then typ_match sg (tyinsts,(T,U)) else raise MATCH |
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|
213 |
| (_,Bound i, Bound j) => if i=j then tyinsts else raise MATCH |
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|
214 |
| (Ts,Abs(_,T,t), Abs(_,U,u)) => |
16935 | 215 |
mtch (typ_match sg (tyinsts,(T,U))) (U::Ts,t,u) |
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|
216 |
| (Ts, f$t, g$u) => mtch (mtch tyinsts (Ts,f,g)) (Ts, t, u) |
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217 |
| _ => raise MATCH |
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|
218 |
in (mtch Vartab.empty args; true) handle MATCH => false end; |
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|
219 |
end |
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|
220 |
|
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|
221 |
fun split_posns cmap sg Ts t = |
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222 |
let |
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|
223 |
val T' = fastype_of1 (Ts, t); |
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|
224 |
fun posns Ts pos apsns (Abs (_, T, t)) = |
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|
225 |
let val U = fastype_of1 (T::Ts,t) |
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|
226 |
in posns (T::Ts) (0::pos) ((T, U, pos)::apsns) t end |
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227 |
| posns Ts pos apsns t = |
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|
228 |
let |
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|
229 |
val (h, ts) = strip_comb t |
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|
230 |
fun iter((i, a), t) = (i+1, (posns Ts (i::pos) apsns t) @ a); |
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231 |
val a = case h of |
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|
232 |
Const(c, cT) => |
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|
233 |
let fun find [] = [] |
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|
234 |
| find ((gcT, pat, thm, T, n)::tups) = |
15570 | 235 |
let val t2 = list_comb (h, Library.take (n, ts)) |
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|
236 |
in if Sign.typ_instance sg (cT, gcT) |
16935 | 237 |
andalso fomatch sg (Ts,pat,t2) |
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|
238 |
then mk_split_pack(thm,T,T',n,ts,apsns,pos,type_of1(Ts,t2),t2) |
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|
239 |
else find tups |
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|
240 |
end |
17184 | 241 |
in find (these (AList.lookup (op =) cmap c)) end |
6130
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|
242 |
| _ => [] |
15570 | 243 |
in snd(Library.foldl iter ((0, a), ts)) end |
1030
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|
244 |
in posns Ts [] [] t end; |
0 | 245 |
|
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|
246 |
|
15570 | 247 |
fun nth_subgoal i thm = List.nth(prems_of thm,i-1); |
0 | 248 |
|
1721
445654b6cb95
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|
249 |
fun shorter((_,ps,pos,_,_),(_,qs,qos,_,_)) = |
4519 | 250 |
prod_ord (int_ord o pairself length) (order o pairself length) |
251 |
((ps, pos), (qs, qos)); |
|
252 |
||
1686
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berghofe
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|
253 |
|
c67d543bc395
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berghofe
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|
254 |
|
c67d543bc395
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berghofe
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|
255 |
(************************************************************ |
c67d543bc395
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berghofe
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|
256 |
call split_posns with appropriate parameters |
c67d543bc395
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berghofe
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|
257 |
*************************************************************) |
0 | 258 |
|
1030
1d8fa2fc4b9c
Completely rewrote split_tac. The old one failed in strange circumstances.
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|
259 |
fun select cmap state i = |
6130
30b84ad2131d
Fixed old bug: selection of constant to be split should depend not just on
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|
260 |
let val sg = #sign(rep_thm state) |
30b84ad2131d
Fixed old bug: selection of constant to be split should depend not just on
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|
261 |
val goali = nth_subgoal i state |
1030
1d8fa2fc4b9c
Completely rewrote split_tac. The old one failed in strange circumstances.
nipkow
parents:
943
diff
changeset
|
262 |
val Ts = rev(map #2 (Logic.strip_params goali)) |
1d8fa2fc4b9c
Completely rewrote split_tac. The old one failed in strange circumstances.
nipkow
parents:
943
diff
changeset
|
263 |
val _ $ t $ _ = Logic.strip_assums_concl goali; |
6130
30b84ad2131d
Fixed old bug: selection of constant to be split should depend not just on
nipkow
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diff
changeset
|
264 |
in (Ts,t, sort shorter (split_posns cmap sg Ts t)) end; |
1030
1d8fa2fc4b9c
Completely rewrote split_tac. The old one failed in strange circumstances.
nipkow
parents:
943
diff
changeset
|
265 |
|
1686
c67d543bc395
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berghofe
parents:
1064
diff
changeset
|
266 |
|
c67d543bc395
Added functions mk_cntxt_splitthm and inst_split which instantiate
berghofe
parents:
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|
267 |
(************************************************************* |
c67d543bc395
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berghofe
parents:
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changeset
|
268 |
instantiate lift theorem |
c67d543bc395
Added functions mk_cntxt_splitthm and inst_split which instantiate
berghofe
parents:
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diff
changeset
|
269 |
|
c67d543bc395
Added functions mk_cntxt_splitthm and inst_split which instantiate
berghofe
parents:
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|
270 |
if t is of the form |
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berghofe
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|
271 |
... ( Const(...,...) $ Abs( .... ) ) ... |
c67d543bc395
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berghofe
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|
272 |
then |
c67d543bc395
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berghofe
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|
273 |
P = %a. ... ( Const(...,...) $ a ) ... |
c67d543bc395
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berghofe
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|
274 |
where a has type T --> U |
c67d543bc395
Added functions mk_cntxt_splitthm and inst_split which instantiate
berghofe
parents:
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diff
changeset
|
275 |
|
c67d543bc395
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berghofe
parents:
1064
diff
changeset
|
276 |
Ts : types of parameters |
c67d543bc395
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berghofe
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changeset
|
277 |
t : lefthand side of meta-equality in subgoal |
c67d543bc395
Added functions mk_cntxt_splitthm and inst_split which instantiate
berghofe
parents:
1064
diff
changeset
|
278 |
the split theorem is applied to (see cmap) |
c67d543bc395
Added functions mk_cntxt_splitthm and inst_split which instantiate
berghofe
parents:
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diff
changeset
|
279 |
T,U,pos : see mk_split_pack |
c67d543bc395
Added functions mk_cntxt_splitthm and inst_split which instantiate
berghofe
parents:
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diff
changeset
|
280 |
state : current proof state |
c67d543bc395
Added functions mk_cntxt_splitthm and inst_split which instantiate
berghofe
parents:
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diff
changeset
|
281 |
lift : the lift theorem |
c67d543bc395
Added functions mk_cntxt_splitthm and inst_split which instantiate
berghofe
parents:
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diff
changeset
|
282 |
i : no. of subgoal |
c67d543bc395
Added functions mk_cntxt_splitthm and inst_split which instantiate
berghofe
parents:
1064
diff
changeset
|
283 |
**************************************************************) |
c67d543bc395
Added functions mk_cntxt_splitthm and inst_split which instantiate
berghofe
parents:
1064
diff
changeset
|
284 |
|
7672
c092e67d12f8
- Fixed bug in mk_split_pack which caused application of expansion theorem
berghofe
parents:
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diff
changeset
|
285 |
fun inst_lift Ts t (T, U, pos) state i = |
c092e67d12f8
- Fixed bug in mk_split_pack which caused application of expansion theorem
berghofe
parents:
6130
diff
changeset
|
286 |
let |
c092e67d12f8
- Fixed bug in mk_split_pack which caused application of expansion theorem
berghofe
parents:
6130
diff
changeset
|
287 |
val cert = cterm_of (sign_of_thm state); |
17881 | 288 |
val cntxt = mk_cntxt Ts t pos (T --> U) (#maxidx(rep_thm trlift)); |
7672
c092e67d12f8
- Fixed bug in mk_split_pack which caused application of expansion theorem
berghofe
parents:
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diff
changeset
|
289 |
in cterm_instantiate [(cert P, cert cntxt)] trlift |
c092e67d12f8
- Fixed bug in mk_split_pack which caused application of expansion theorem
berghofe
parents:
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diff
changeset
|
290 |
end; |
0 | 291 |
|
292 |
||
1686
c67d543bc395
Added functions mk_cntxt_splitthm and inst_split which instantiate
berghofe
parents:
1064
diff
changeset
|
293 |
(************************************************************* |
c67d543bc395
Added functions mk_cntxt_splitthm and inst_split which instantiate
berghofe
parents:
1064
diff
changeset
|
294 |
instantiate split theorem |
c67d543bc395
Added functions mk_cntxt_splitthm and inst_split which instantiate
berghofe
parents:
1064
diff
changeset
|
295 |
|
c67d543bc395
Added functions mk_cntxt_splitthm and inst_split which instantiate
berghofe
parents:
1064
diff
changeset
|
296 |
Ts : types of parameters |
c67d543bc395
Added functions mk_cntxt_splitthm and inst_split which instantiate
berghofe
parents:
1064
diff
changeset
|
297 |
t : lefthand side of meta-equality in subgoal |
c67d543bc395
Added functions mk_cntxt_splitthm and inst_split which instantiate
berghofe
parents:
1064
diff
changeset
|
298 |
the split theorem is applied to (see cmap) |
4232 | 299 |
tt : the term Const(key,..) $ ... |
1686
c67d543bc395
Added functions mk_cntxt_splitthm and inst_split which instantiate
berghofe
parents:
1064
diff
changeset
|
300 |
thm : the split theorem |
c67d543bc395
Added functions mk_cntxt_splitthm and inst_split which instantiate
berghofe
parents:
1064
diff
changeset
|
301 |
TB : type of body of P(...) |
c67d543bc395
Added functions mk_cntxt_splitthm and inst_split which instantiate
berghofe
parents:
1064
diff
changeset
|
302 |
state : current proof state |
4232 | 303 |
i : number of subgoal |
1686
c67d543bc395
Added functions mk_cntxt_splitthm and inst_split which instantiate
berghofe
parents:
1064
diff
changeset
|
304 |
**************************************************************) |
c67d543bc395
Added functions mk_cntxt_splitthm and inst_split which instantiate
berghofe
parents:
1064
diff
changeset
|
305 |
|
4232 | 306 |
fun inst_split Ts t tt thm TB state i = |
17881 | 307 |
let |
18145 | 308 |
val thm' = Thm.lift_rule (Thm.cprem_of state i) thm; |
7672
c092e67d12f8
- Fixed bug in mk_split_pack which caused application of expansion theorem
berghofe
parents:
6130
diff
changeset
|
309 |
val (P, _) = strip_comb (fst (Logic.dest_equals |
c092e67d12f8
- Fixed bug in mk_split_pack which caused application of expansion theorem
berghofe
parents:
6130
diff
changeset
|
310 |
(Logic.strip_assums_concl (#prop (rep_thm thm'))))); |
c092e67d12f8
- Fixed bug in mk_split_pack which caused application of expansion theorem
berghofe
parents:
6130
diff
changeset
|
311 |
val cert = cterm_of (sign_of_thm state); |
c092e67d12f8
- Fixed bug in mk_split_pack which caused application of expansion theorem
berghofe
parents:
6130
diff
changeset
|
312 |
val cntxt = mk_cntxt_splitthm t tt TB; |
15570 | 313 |
val abss = Library.foldl (fn (t, T) => Abs ("", T, t)); |
7672
c092e67d12f8
- Fixed bug in mk_split_pack which caused application of expansion theorem
berghofe
parents:
6130
diff
changeset
|
314 |
in cterm_instantiate [(cert P, cert (abss (cntxt, Ts)))] thm' |
4232 | 315 |
end; |
1686
c67d543bc395
Added functions mk_cntxt_splitthm and inst_split which instantiate
berghofe
parents:
1064
diff
changeset
|
316 |
|
7672
c092e67d12f8
- Fixed bug in mk_split_pack which caused application of expansion theorem
berghofe
parents:
6130
diff
changeset
|
317 |
|
1686
c67d543bc395
Added functions mk_cntxt_splitthm and inst_split which instantiate
berghofe
parents:
1064
diff
changeset
|
318 |
(***************************************************************************** |
c67d543bc395
Added functions mk_cntxt_splitthm and inst_split which instantiate
berghofe
parents:
1064
diff
changeset
|
319 |
The split-tactic |
17881 | 320 |
|
1686
c67d543bc395
Added functions mk_cntxt_splitthm and inst_split which instantiate
berghofe
parents:
1064
diff
changeset
|
321 |
splits : list of split-theorems to be tried |
c67d543bc395
Added functions mk_cntxt_splitthm and inst_split which instantiate
berghofe
parents:
1064
diff
changeset
|
322 |
i : number of subgoal the tactic should be applied to |
c67d543bc395
Added functions mk_cntxt_splitthm and inst_split which instantiate
berghofe
parents:
1064
diff
changeset
|
323 |
*****************************************************************************) |
c67d543bc395
Added functions mk_cntxt_splitthm and inst_split which instantiate
berghofe
parents:
1064
diff
changeset
|
324 |
|
0 | 325 |
fun split_tac [] i = no_tac |
326 |
| split_tac splits i = |
|
5553 | 327 |
let val splits = map Data.mk_eq splits; |
9267
dbf30a2d1b56
Now two split thms for same constant at different types is allowed.
nipkow
parents:
8815
diff
changeset
|
328 |
fun add_thm(cmap,thm) = |
3918 | 329 |
(case concl_of thm of _$(t as _$lhs)$_ => |
6130
30b84ad2131d
Fixed old bug: selection of constant to be split should depend not just on
nipkow
parents:
5553
diff
changeset
|
330 |
(case strip_comb lhs of (Const(a,aT),args) => |
13157
4a4599f78f18
allowed more general split rules to cope with div/mod 2
nipkow
parents:
10821
diff
changeset
|
331 |
let val info = (aT,lhs,thm,fastype_of t,length args) |
17184 | 332 |
in case AList.lookup (op =) cmap a of |
17325 | 333 |
SOME infos => AList.update (op =) (a, info::infos) cmap |
15531 | 334 |
| NONE => (a,[info])::cmap |
9267
dbf30a2d1b56
Now two split thms for same constant at different types is allowed.
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parents:
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diff
changeset
|
335 |
end |
4668
131989b78417
Little reorganization. Loop tactics have names now.
nipkow
parents:
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diff
changeset
|
336 |
| _ => split_format_err()) |
131989b78417
Little reorganization. Loop tactics have names now.
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parents:
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diff
changeset
|
337 |
| _ => split_format_err()) |
15570 | 338 |
val cmap = Library.foldl add_thm ([],splits); |
7672
c092e67d12f8
- Fixed bug in mk_split_pack which caused application of expansion theorem
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parents:
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diff
changeset
|
339 |
fun lift_tac Ts t p st = rtac (inst_lift Ts t p st i) i st |
c092e67d12f8
- Fixed bug in mk_split_pack which caused application of expansion theorem
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parents:
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diff
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|
340 |
fun lift_split_tac state = |
c092e67d12f8
- Fixed bug in mk_split_pack which caused application of expansion theorem
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parents:
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diff
changeset
|
341 |
let val (Ts, t, splits) = select cmap state i |
1030
1d8fa2fc4b9c
Completely rewrote split_tac. The old one failed in strange circumstances.
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parents:
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diff
changeset
|
342 |
in case splits of |
7672
c092e67d12f8
- Fixed bug in mk_split_pack which caused application of expansion theorem
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parents:
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diff
changeset
|
343 |
[] => no_tac state |
c092e67d12f8
- Fixed bug in mk_split_pack which caused application of expansion theorem
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diff
changeset
|
344 |
| (thm, apsns, pos, TB, tt)::_ => |
1030
1d8fa2fc4b9c
Completely rewrote split_tac. The old one failed in strange circumstances.
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parents:
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diff
changeset
|
345 |
(case apsns of |
7672
c092e67d12f8
- Fixed bug in mk_split_pack which caused application of expansion theorem
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parents:
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diff
changeset
|
346 |
[] => compose_tac (false, inst_split Ts t tt thm TB state i, 0) i state |
c092e67d12f8
- Fixed bug in mk_split_pack which caused application of expansion theorem
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parents:
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diff
changeset
|
347 |
| p::_ => EVERY [lift_tac Ts t p, |
c092e67d12f8
- Fixed bug in mk_split_pack which caused application of expansion theorem
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parents:
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diff
changeset
|
348 |
rtac reflexive_thm (i+1), |
c092e67d12f8
- Fixed bug in mk_split_pack which caused application of expansion theorem
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diff
changeset
|
349 |
lift_split_tac] state) |
1030
1d8fa2fc4b9c
Completely rewrote split_tac. The old one failed in strange circumstances.
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parents:
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diff
changeset
|
350 |
end |
17881 | 351 |
in COND (has_fewer_prems i) no_tac |
5304 | 352 |
(rtac meta_iffD i THEN lift_split_tac) |
0 | 353 |
end; |
354 |
||
355 |
in split_tac end; |
|
1721
445654b6cb95
Rewrote mk_cntxt_splitthm. Added function mk_case_split_inside_tac.
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parents:
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diff
changeset
|
356 |
|
5304 | 357 |
|
358 |
val split_tac = mk_case_split_tac int_ord; |
|
4189 | 359 |
|
5304 | 360 |
val split_inside_tac = mk_case_split_tac (rev_order o int_ord); |
361 |
||
4189 | 362 |
|
363 |
(***************************************************************************** |
|
364 |
The split-tactic for premises |
|
17881 | 365 |
|
4189 | 366 |
splits : list of split-theorems to be tried |
5304 | 367 |
****************************************************************************) |
4202 | 368 |
fun split_asm_tac [] = K no_tac |
17881 | 369 |
| split_asm_tac splits = |
5304 | 370 |
|
13855
644692eca537
addsplits / delsplits no longer ignore type of constant.
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diff
changeset
|
371 |
let val cname_list = map (fst o fst o split_thm_info) splits; |
4189 | 372 |
fun is_case (a,_) = a mem cname_list; |
17881 | 373 |
fun tac (t,i) = |
374 |
let val n = find_index (exists_Const is_case) |
|
375 |
(Logic.strip_assums_hyp t); |
|
18545 | 376 |
fun first_prem_is_disj (Const ("==>", _) $ (Const (c, _) |
377 |
$ (Const (s, _) $ _ $ _ )) $ _ ) = c = const_Trueprop andalso s = const_or |
|
17881 | 378 |
| first_prem_is_disj (Const("all",_)$Abs(_,_,t)) = |
379 |
first_prem_is_disj t |
|
380 |
| first_prem_is_disj _ = false; |
|
5437 | 381 |
(* does not work properly if the split variable is bound by a quantfier *) |
17881 | 382 |
fun flat_prems_tac i = SUBGOAL (fn (t,i) => |
383 |
(if first_prem_is_disj t |
|
384 |
then EVERY[etac Data.disjE i,rotate_tac ~1 i, |
|
385 |
rotate_tac ~1 (i+1), |
|
386 |
flat_prems_tac (i+1)] |
|
387 |
else all_tac) |
|
388 |
THEN REPEAT (eresolve_tac [Data.conjE,Data.exE] i) |
|
389 |
THEN REPEAT (dresolve_tac [Data.notnotD] i)) i; |
|
390 |
in if n<0 then no_tac else DETERM (EVERY' |
|
391 |
[rotate_tac n, etac Data.contrapos2, |
|
392 |
split_tac splits, |
|
393 |
rotate_tac ~1, etac Data.contrapos, rotate_tac ~1, |
|
394 |
flat_prems_tac] i) |
|
395 |
end; |
|
4189 | 396 |
in SUBGOAL tac |
397 |
end; |
|
398 |
||
10652 | 399 |
fun gen_split_tac [] = K no_tac |
400 |
| gen_split_tac (split::splits) = |
|
401 |
let val (_,asm) = split_thm_info split |
|
402 |
in (if asm then split_asm_tac else split_tac) [split] ORELSE' |
|
403 |
gen_split_tac splits |
|
404 |
end; |
|
8468 | 405 |
|
18688 | 406 |
|
8468 | 407 |
(** declare split rules **) |
408 |
||
409 |
(* addsplits / delsplits *) |
|
410 |
||
13859
adf68d9e5dec
split_name no longer uses Sign.string_of_typ to encode types, since
berghofe
parents:
13855
diff
changeset
|
411 |
fun string_of_typ (Type (s, Ts)) = (if null Ts then "" |
adf68d9e5dec
split_name no longer uses Sign.string_of_typ to encode types, since
berghofe
parents:
13855
diff
changeset
|
412 |
else enclose "(" ")" (commas (map string_of_typ Ts))) ^ s |
adf68d9e5dec
split_name no longer uses Sign.string_of_typ to encode types, since
berghofe
parents:
13855
diff
changeset
|
413 |
| string_of_typ _ = "_"; |
adf68d9e5dec
split_name no longer uses Sign.string_of_typ to encode types, since
berghofe
parents:
13855
diff
changeset
|
414 |
|
17881 | 415 |
fun split_name (name, T) asm = "split " ^ |
13859
adf68d9e5dec
split_name no longer uses Sign.string_of_typ to encode types, since
berghofe
parents:
13855
diff
changeset
|
416 |
(if asm then "asm " else "") ^ name ^ " :: " ^ string_of_typ T; |
4189 | 417 |
|
5304 | 418 |
fun ss addsplits splits = |
419 |
let fun addsplit (ss,split) = |
|
420 |
let val (name,asm) = split_thm_info split |
|
13859
adf68d9e5dec
split_name no longer uses Sign.string_of_typ to encode types, since
berghofe
parents:
13855
diff
changeset
|
421 |
in Simplifier.addloop (ss, (split_name name asm, |
17881 | 422 |
(if asm then split_asm_tac else split_tac) [split])) end |
15570 | 423 |
in Library.foldl addsplit (ss,splits) end; |
1721
445654b6cb95
Rewrote mk_cntxt_splitthm. Added function mk_case_split_inside_tac.
berghofe
parents:
1686
diff
changeset
|
424 |
|
5304 | 425 |
fun ss delsplits splits = |
426 |
let fun delsplit(ss,split) = |
|
427 |
let val (name,asm) = split_thm_info split |
|
13859
adf68d9e5dec
split_name no longer uses Sign.string_of_typ to encode types, since
berghofe
parents:
13855
diff
changeset
|
428 |
in Simplifier.delloop (ss, split_name name asm) |
15570 | 429 |
end in Library.foldl delsplit (ss,splits) end; |
1721
445654b6cb95
Rewrote mk_cntxt_splitthm. Added function mk_case_split_inside_tac.
berghofe
parents:
1686
diff
changeset
|
430 |
|
17881 | 431 |
fun Addsplits splits = (change_simpset (fn ss => ss addsplits splits)); |
432 |
fun Delsplits splits = (change_simpset (fn ss => ss delsplits splits)); |
|
8468 | 433 |
|
434 |
||
435 |
(* attributes *) |
|
436 |
||
437 |
val splitN = "split"; |
|
438 |
||
18688 | 439 |
val split_add = Simplifier.attrib (op addsplits); |
440 |
val split_del = Simplifier.attrib (op delsplits); |
|
8634 | 441 |
|
442 |
||
9703 | 443 |
(* methods *) |
8468 | 444 |
|
445 |
val split_modifiers = |
|
18728 | 446 |
[Args.$$$ splitN -- Args.colon >> K ((I, split_add): Method.modifier), |
447 |
Args.$$$ splitN -- Args.add -- Args.colon >> K (I, split_add), |
|
448 |
Args.$$$ splitN -- Args.del -- Args.colon >> K (I, split_del)]; |
|
8468 | 449 |
|
18688 | 450 |
fun split_meth src = |
18988 | 451 |
Method.syntax Attrib.thms src |
18688 | 452 |
#> (fn (_, ths) => Method.SIMPLE_METHOD' HEADGOAL (CHANGED_PROP o gen_split_tac ths)); |
9703 | 453 |
|
8468 | 454 |
|
18688 | 455 |
(* theory setup *) |
8468 | 456 |
|
9703 | 457 |
val setup = |
18708 | 458 |
(Attrib.add_attributes |
18728 | 459 |
[(splitN, Attrib.add_del_args split_add split_del, "declaration of case split rule")] #> |
18708 | 460 |
Method.add_methods [(splitN, split_meth, "apply case split rule")]); |
4189 | 461 |
|
1721
445654b6cb95
Rewrote mk_cntxt_splitthm. Added function mk_case_split_inside_tac.
berghofe
parents:
1686
diff
changeset
|
462 |
end; |