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(* Title: functions on lists for Programs
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Author: Walther Neuper 0108
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(c) due to copyright terms
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*)
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theory ListC
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imports "~~/src/Tools/isac/KEStore"
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begin
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ML_file "~~/src/Tools/isac/ProgLang/termC.sml"
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ML_file "~~/src/Tools/isac/ProgLang/calculate.sml"
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ML_file "~~/src/Tools/isac/ProgLang/rewrite.sml"
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ML {*
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*} ML {*
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*}
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subsection {* Notes on Isac's programming language *}
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text {*
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Isac's programming language combines tacticals (TRY, etc) and
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tactics (Rewrite, etc) with list processing.
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In order to distinguish list expressions of the meta (programming)
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language from the object language in Lucas-Interpretation, a
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new 'type xlist' is introduced.
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TODO: Switch the role of 'xlist' and 'list' (the former only used
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by InsSort.thy)
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Isac's programming language preceeded the function package
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in 2002. For naming "axiomatization" is used for reasons of uniformity
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with the other replacements for "axioms".
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Another reminiscence from Isabelle2002 are Isac-specific numerals,
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introduced in order to have floating point numerals at a time,
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when Isabelle did not consider that requirement. For the sake of uniformity
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'nat' from List.thy is replaced by 'real' by 'fun parse',
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however, 'fun parseNEW' has started to replace this fix (after finishing
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this fix, there will be a 'rename all parseNEW --> parse).
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Note: *one* "axiomatization" over all equations caused strange "'a list list"
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types.
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*}
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subsection {* Type 'xlist' for Lucas-Interpretation *}
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(*TODO: ask for shorter deliminters in xlist *)
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datatype 'a xlist =
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XNil ("{|| ||}")
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| XCons 'a "'a xlist" (infixr "@#" 65)
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syntax
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-- {* list Enumeration *}
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"_xlist" :: "args => 'a xlist" ("{|| (_) ||}")
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translations
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"{||x, xs||}" == "x@#{||xs||}"
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"{||x||}" == "x@#{|| ||}"
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term "{|| ||}"
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term "{||1,2,3||}"
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subsection {* Functions for 'xlist' *}
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(* TODO:
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(1) revise, if definition of identifiers like LENGTH_NIL are still required.
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(2) switch the role of 'xlist' and 'list' in the functions below, in particular for
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'foldr', 'foldr_Nil', 'foldr_Cons' and 'xfoldr', 'xfoldr_Nil', 'xfoldr_Cons'.
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For transition phase just outcomment InsSort.thy and inssort.sml.
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*)
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primrec xfoldr :: "('a \<Rightarrow> 'b \<Rightarrow> 'b) \<Rightarrow> 'a xlist \<Rightarrow> 'b \<Rightarrow> 'b" where
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xfoldr_Nil: "xfoldr f {|| ||} = id" |
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xfoldr_Cons: "xfoldr f (x @# xs) = f x \<circ> xfoldr f xs"
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primrec LENGTH :: "'a list => real"
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where
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LENGTH_NIL: "LENGTH [] = 0" |
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LENGTH_CONS: "LENGTH (x#xs) = 1 + LENGTH xs"
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consts NTH :: "[real, 'a list] => 'a"
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axiomatization where
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NTH_NIL: "NTH 1 (x # xs) = x" and
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NTH_CONS: (*NO primrec, fun ..*)"1 < n ==> NTH n (x # xs) = NTH (n + -1) xs"
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axiomatization where
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hd_thm: "hd (x # xs) = x"
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axiomatization where
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tl_Nil: "tl [] = []" and
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tl_Cons: "tl (x # xs) = xs"
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axiomatization where
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LAST: "last (x # xs) = (if xs = [] then x else last xs)"
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axiomatization where
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butlast_Nil: "butlast [] = []" and
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butlast_Cons: "butlast (x # xs) = (if xs = [] then [] else x # butlast xs)"
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axiomatization where
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map_Nil:"map f [] = []" and
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map_Cons: "map f (x # xs) = f x # map f xs"
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axiomatization where
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rev_Nil: "rev [] = []" and
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rev_Cons: "rev (x # xs) = rev xs @ [x]"
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axiomatization where
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filter_Nil: "filter P [] = []" and
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filter_Cons: "filter P (x # xs) = (if P x then x # filter P xs else filter P xs)"
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axiomatization where
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concat_Nil: "concat [] = []" and
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concat_Cons: "concat (x # xs) = x @ concat xs"
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axiomatization where
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takeWhile_Nil: "takeWhile P [] = []" and
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takeWhile_Cons: "takeWhile P (x # xs) = (if P x then x # takeWhile P xs else [])"
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axiomatization where
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dropWhile_Nil: "dropWhile P [] = []" and
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dropWhile_Cons: "dropWhile P (x # xs) = (if P x then dropWhile P xs else x#xs)"
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axiomatization where
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zip_Nil: "zip xs [] = []" and
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zip_Cons: "zip xs (y # ys) = (case xs of [] => [] | z # zs => (z,y) # zip zs ys)"
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axiomatization where
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distinct_Nil: "distinct [] = True" and
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distinct_Cons: "distinct (x # xs) = (x ~: set xs & distinct xs)"
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axiomatization where
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remdups_Nil: "remdups [] = []" and
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remdups_Cons: "remdups (x#xs) = (if x : set xs then remdups xs else x # remdups xs)"
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(** Lexicographic orderings on lists ...!!!**)
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ML{* (*the former ListC.ML*)
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(** rule set for evaluating listexpr in scripts **)
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val list_rls =
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Rls{id = "list_rls", preconds = [], rew_ord = ("dummy_ord", dummy_ord),
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erls = Erls, srls = Erls, calc = [], errpatts = [],
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rules = [Thm ("refl", num_str @{thm refl}), (*'a<>b -> FALSE' by fun eval_equal*)
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Thm ("o_apply", num_str @{thm o_apply}),
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Thm ("NTH_CONS",num_str @{thm NTH_CONS}),(*erls for cond. in Atools.ML*)
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Thm ("NTH_NIL",num_str @{thm NTH_NIL}),
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Thm ("append_Cons",num_str @{thm append_Cons}),
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Thm ("append_Nil",num_str @{thm append_Nil}),
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(* Thm ("butlast_Cons",num_str @{thm butlast_Cons}),
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Thm ("butlast_Nil",num_str @{thm butlast_Nil}),*)
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Thm ("concat_Cons",num_str @{thm concat_Cons}),
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Thm ("concat_Nil",num_str @{thm concat_Nil}),
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(* Thm ("del_base",num_str @{thm del_base}),
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Thm ("del_rec",num_str @{thm del_rec}), *)
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Thm ("distinct_Cons",num_str @{thm distinct_Cons}),
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Thm ("distinct_Nil",num_str @{thm distinct_Nil}),
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Thm ("dropWhile_Cons",num_str @{thm dropWhile_Cons}),
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Thm ("dropWhile_Nil",num_str @{thm dropWhile_Nil}),
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Thm ("filter_Cons",num_str @{thm filter_Cons}),
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Thm ("filter_Nil",num_str @{thm filter_Nil}),
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Thm ("foldr_Cons",num_str @{thm foldr_Cons}),
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Thm ("foldr_Nil",num_str @{thm foldr_Nil}),
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Thm ("hd_thm",num_str @{thm hd_thm}),
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Thm ("LAST",num_str @{thm LAST}),
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Thm ("LENGTH_CONS",num_str @{thm LENGTH_CONS}),
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Thm ("LENGTH_NIL",num_str @{thm LENGTH_NIL}),
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(* Thm ("list_diff_def",num_str @{thm list_diff_def}),*)
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Thm ("map_Cons",num_str @{thm map_Cons}),
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Thm ("map_Nil",num_str @{thm map_Cons}),
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(* Thm ("mem_Cons",num_str @{thm mem_Cons}),
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Thm ("mem_Nil",num_str @{thm mem_Nil}), *)
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(* Thm ("null_Cons",num_str @{thm null_Cons}),
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Thm ("null_Nil",num_str @{thm null_Nil}),*)
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Thm ("remdups_Cons",num_str @{thm remdups_Cons}),
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Thm ("remdups_Nil",num_str @{thm remdups_Nil}),
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Thm ("rev_Cons",num_str @{thm rev_Cons}),
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Thm ("rev_Nil",num_str @{thm rev_Nil}),
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Thm ("take_Nil",num_str @{thm take_Nil}),
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Thm ("take_Cons",num_str @{thm take_Cons}),
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Thm ("tl_Cons",num_str @{thm tl_Cons}),
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Thm ("tl_Nil",num_str @{thm tl_Nil}),
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Thm ("zip_Cons",num_str @{thm zip_Cons}),
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Thm ("zip_Nil",num_str @{thm zip_Nil})],
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scr = EmptyScr}:rls;
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*}
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setup {* KEStore_Elems.add_rlss [("list_rls", (Context.theory_name @{theory}, list_rls))] *}
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end
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