src/Provers/Arith/extract_common_term.ML
changeset 20114 a1bb4bc68ff3
parent 20044 92cc2f4c7335
child 30649 57753e0ec1d4
equal deleted inserted replaced
20113:90a8d14f3610 20114:a1bb4bc68ff3
     6 Extract common terms in balanced expressions:
     6 Extract common terms in balanced expressions:
     7 
     7 
     8      i + u + j ~~ i' + u + j'  ==  u + (i + j) ~~ u + (i' + j')
     8      i + u + j ~~ i' + u + j'  ==  u + (i + j) ~~ u + (i' + j')
     9      i + u     ~~ u            ==  u + i       ~~ u + 0
     9      i + u     ~~ u            ==  u + i       ~~ u + 0
    10 
    10 
    11 where ~~ is an appropriate balancing operation (e.g. =, <=, <, -) and 0 is a 
    11 where ~~ is an appropriate balancing operation (e.g. =, <=, <, -) and 0 is a
    12 suitable identity for +.
    12 suitable identity for +.
    13 
    13 
    14 This massaged formula is then simplified in a user-specified way.
    14 This massaged formula is then simplified in a user-specified way.
    15 *)
    15 *)
    16 
    16 
    21   val dest_sum: term -> term list
    21   val dest_sum: term -> term list
    22   val mk_bal: term * term -> term
    22   val mk_bal: term * term -> term
    23   val dest_bal: term -> term * term
    23   val dest_bal: term -> term * term
    24   val find_first: term -> term list -> term list
    24   val find_first: term -> term list -> term list
    25   (*proof tools*)
    25   (*proof tools*)
    26   val prove_conv: tactic list -> Proof.context -> 
    26   val prove_conv: tactic list -> Proof.context -> thm list -> term * term -> thm option
    27                   thm list -> string list -> term * term -> thm option
       
    28   val norm_tac: simpset -> tactic                (*proves the result*)
    27   val norm_tac: simpset -> tactic                (*proves the result*)
    29   val simplify_meta_eq: simpset -> thm -> thm    (*simplifies the result*)
    28   val simplify_meta_eq: simpset -> thm -> thm    (*simplifies the result*)
    30 end;
    29 end;
    31 
    30 
    32 
    31 
    33 functor ExtractCommonTermFun(Data: EXTRACT_COMMON_TERM_DATA):
    32 functor ExtractCommonTermFun(Data: EXTRACT_COMMON_TERM_DATA):
    34   sig
    33   sig
    35   val proc: simpset -> term -> thm option
    34   val proc: simpset -> term -> thm option
    36   end 
    35   end
    37 =
    36 =
    38 struct
    37 struct
    39 
    38 
    40 (*a left-to-right scan of terms1, seeking a term u that is also in terms2*)
    39 (*a left-to-right scan of terms1, seeking a term u that is also in terms2*)
    41 fun find_common (terms1,terms2) =
    40 fun find_common (terms1,terms2) =
    42   let val tab2 = fold (Termtab.update o rpair ()) terms2 Termtab.empty
    41   let val tab2 = fold (Termtab.update o rpair ()) terms2 Termtab.empty
    43       fun seek [] = raise TERM("find_common", []) 
    42       fun seek [] = raise TERM("find_common", [])
    44 	| seek (u::terms) =
    43         | seek (u::terms) =
    45 	      if Termtab.defined tab2 u then u
    44               if Termtab.defined tab2 u then u
    46 	      else seek terms
    45               else seek terms
    47   in seek terms1 end;
    46   in seek terms1 end;
    48 
    47 
    49 (*the simplification procedure*)
    48 (*the simplification procedure*)
    50 fun proc ss t =
    49 fun proc ss t =
    51   let
    50   let
    52       val ctxt = Simplifier.the_context ss;
    51     val ctxt = Simplifier.the_context ss;
    53       val hyps = prems_of_ss ss;
    52     val prems = prems_of_ss ss;
    54       (*first freeze any Vars in the term to prevent flex-flex problems*)
    53     val ([t'], ctxt') = Variable.import_terms true [t] ctxt
    55       val (t', xs) = Term.adhoc_freeze_vars t;
    54     val export = singleton (Variable.export ctxt' ctxt)
    56       val (t1,t2) = Data.dest_bal t' 
    55 
    57       val terms1 = Data.dest_sum t1
    56     val (t1,t2) = Data.dest_bal t'
    58       and terms2 = Data.dest_sum t2
    57     val terms1 = Data.dest_sum t1
    59       val u = find_common (terms1,terms2)
    58     and terms2 = Data.dest_sum t2
    60       val terms1' = Data.find_first u terms1
    59 
    61       and terms2' = Data.find_first u terms2
    60     val u = find_common (terms1,terms2)
    62       and T = Term.fastype_of u
    61     val terms1' = Data.find_first u terms1
    63       val reshape = 
    62     and terms2' = Data.find_first u terms2
    64 	    Data.prove_conv [Data.norm_tac ss] ctxt hyps xs
    63     and T = Term.fastype_of u
    65 	        (t', 
    64 
    66 		 Data.mk_bal (Data.mk_sum T (u::terms1'), 
    65     val reshape =
    67 		              Data.mk_sum T (u::terms2')))
    66       Data.prove_conv [Data.norm_tac ss] ctxt prems
       
    67         (t', Data.mk_bal (Data.mk_sum T (u::terms1'), Data.mk_sum T (u::terms2')))
    68   in
    68   in
    69       Option.map (Data.simplify_meta_eq ss) reshape
    69     Option.map (export o Data.simplify_meta_eq ss) reshape
    70   end
    70   end
       
    71   (* FIXME avoid handling of generic exceptions *)
    71   handle TERM _ => NONE
    72   handle TERM _ => NONE
    72        | TYPE _ => NONE;   (*Typically (if thy doesn't include Numeral)
    73        | TYPE _ => NONE;   (*Typically (if thy doesn't include Numeral)
    73 			     Undeclared type constructor "Numeral.bin"*)
    74                              Undeclared type constructor "Numeral.bin"*)
    74 
    75 
    75 end;
    76 end;