1 (* Title: functions on lists for Programs
2 Author: Walther Neuper 0108
3 (c) due to copyright terms
7 imports "~~/src/Tools/isac/KEStore"
10 ML_file "~~/src/Tools/isac/ProgLang/termC.sml"
11 ML_file "~~/src/Tools/isac/ProgLang/calculate.sml"
12 ML_file "~~/src/Tools/isac/ProgLang/rewrite.sml"
23 subsection {* Notes on Isac's programming language *}
25 Isac's programming language combines tacticals (TRY, etc) and
26 tactics (Rewrite, etc) with list processing.
28 In order to distinguish list expressions of the meta (programming)
29 language from the object language in Lucas-Interpretation, a
30 new 'type xlist' is introduced.
31 TODO: Switch the role of 'xlist' and 'list' (the former only used
34 Isac's programming language preceeded the function package
35 in 2002. For naming "axiomatization" is used for reasons of uniformity
36 with the other replacements for "axioms".
37 Another reminiscence from Isabelle2002 are Isac-specific numerals,
38 introduced in order to have floating point numerals at a time,
39 when Isabelle did not consider that requirement. For the sake of uniformity
40 'nat' from List.thy is replaced by 'real' by 'fun parse',
41 however, 'fun parseNEW' has started to replace this fix (after finishing
42 this fix, there will be a 'rename all parseNEW --> parse).
44 Note: *one* "axiomatization" over all equations caused strange "'a list list"
48 subsection {* Type 'xlist' for Lucas-Interpretation *}
49 (*TODO: ask for shorter deliminters in xlist *)
52 | XCons 'a "'a xlist" (infixr "@#" 65)
55 -- {* list Enumeration *}
56 "_xlist" :: "args => 'a xlist" ("{|| (_) ||}")
59 "{||x, xs||}" == "x@#{||xs||}"
60 "{||x||}" == "x@#{|| ||}"
65 subsection {* Functions for 'xlist' *}
67 (1) revise, if definition of identifiers like LENGTH_NIL are still required.
68 (2) switch the role of 'xlist' and 'list' in the functions below, in particular for
69 'foldr', 'foldr_Nil', 'foldr_Cons' and 'xfoldr', 'xfoldr_Nil', 'xfoldr_Cons'.
70 For transition phase just outcomment InsSort.thy and inssort.sml.
73 primrec xfoldr :: "('a \<Rightarrow> 'b \<Rightarrow> 'b) \<Rightarrow> 'a xlist \<Rightarrow> 'b \<Rightarrow> 'b" where
74 xfoldr_Nil: "xfoldr f {|| ||} = id" |
75 xfoldr_Cons: "xfoldr f (x @# xs) = f x \<circ> xfoldr f xs"
77 primrec LENGTH :: "'a list => real"
79 LENGTH_NIL: "LENGTH [] = 0" |
80 LENGTH_CONS: "LENGTH (x#xs) = 1 + LENGTH xs"
82 consts NTH :: "[real, 'a list] => 'a"
84 NTH_NIL: "NTH 1 (x # xs) = x" and
85 NTH_CONS: (*NO primrec, fun ..*)"1 < n ==> NTH n (x # xs) = NTH (n + -1) xs"
88 hd_thm: "hd (x # xs) = x"
91 tl_Nil: "tl [] = []" and
92 tl_Cons: "tl (x # xs) = xs"
95 LAST: "last (x # xs) = (if xs = [] then x else last xs)"
98 butlast_Nil: "butlast [] = []" and
99 butlast_Cons: "butlast (x # xs) = (if xs = [] then [] else x # butlast xs)"
102 map_Nil:"map f [] = []" and
103 map_Cons: "map f (x # xs) = f x # map f xs"
106 rev_Nil: "rev [] = []" and
107 rev_Cons: "rev (x # xs) = rev xs @ [x]"
110 filter_Nil: "filter P [] = []" and
111 filter_Cons: "filter P (x # xs) = (if P x then x # filter P xs else filter P xs)"
114 concat_Nil: "concat [] = []" and
115 concat_Cons: "concat (x # xs) = x @ concat xs"
118 takeWhile_Nil: "takeWhile P [] = []" and
119 takeWhile_Cons: "takeWhile P (x # xs) = (if P x then x # takeWhile P xs else [])"
122 dropWhile_Nil: "dropWhile P [] = []" and
123 dropWhile_Cons: "dropWhile P (x # xs) = (if P x then dropWhile P xs else x#xs)"
126 zip_Nil: "zip xs [] = []" and
127 zip_Cons: "zip xs (y # ys) = (case xs of [] => [] | z # zs => (z,y) # zip zs ys)"
130 distinct_Nil: "distinct [] = True" and
131 distinct_Cons: "distinct (x # xs) = (x ~: set xs & distinct xs)"
134 remdups_Nil: "remdups [] = []" and
135 remdups_Cons: "remdups (x#xs) = (if x : set xs then remdups xs else x # remdups xs)"
137 (** Lexicographic orderings on lists ...!!!**)
139 ML{* (*the former ListC.ML*)
140 (** rule set for evaluating listexpr in scripts **)
142 Rls{id = "list_rls", preconds = [], rew_ord = ("dummy_ord", dummy_ord),
143 erls = Erls, srls = Erls, calc = [], errpatts = [],
144 rules = [Thm ("refl", TermC.num_str @{thm refl}), (*'a<>b -> FALSE' by fun eval_equal*)
145 Thm ("o_apply", TermC.num_str @{thm o_apply}),
147 Thm ("NTH_CONS",TermC.num_str @{thm NTH_CONS}),(*erls for cond. in Atools.ML*)
148 Thm ("NTH_NIL",TermC.num_str @{thm NTH_NIL}),
149 Thm ("append_Cons",TermC.num_str @{thm append_Cons}),
150 Thm ("append_Nil",TermC.num_str @{thm append_Nil}),
151 (* Thm ("butlast_Cons",num_str @{thm butlast_Cons}),
152 Thm ("butlast_Nil",num_str @{thm butlast_Nil}),*)
153 Thm ("concat_Cons",TermC.num_str @{thm concat_Cons}),
154 Thm ("concat_Nil",TermC.num_str @{thm concat_Nil}),
155 (* Thm ("del_base",num_str @{thm del_base}),
156 Thm ("del_rec",num_str @{thm del_rec}), *)
158 Thm ("distinct_Cons",TermC.num_str @{thm distinct_Cons}),
159 Thm ("distinct_Nil",TermC.num_str @{thm distinct_Nil}),
160 Thm ("dropWhile_Cons",TermC.num_str @{thm dropWhile_Cons}),
161 Thm ("dropWhile_Nil",TermC.num_str @{thm dropWhile_Nil}),
162 Thm ("filter_Cons",TermC.num_str @{thm filter_Cons}),
163 Thm ("filter_Nil",TermC.num_str @{thm filter_Nil}),
164 Thm ("foldr_Cons",TermC.num_str @{thm foldr_Cons}),
165 Thm ("foldr_Nil",TermC.num_str @{thm foldr_Nil}),
166 Thm ("hd_thm",TermC.num_str @{thm hd_thm}),
167 Thm ("LAST",TermC.num_str @{thm LAST}),
168 Thm ("LENGTH_CONS",TermC.num_str @{thm LENGTH_CONS}),
169 Thm ("LENGTH_NIL",TermC.num_str @{thm LENGTH_NIL}),
170 (* Thm ("list_diff_def",num_str @{thm list_diff_def}),*)
171 Thm ("map_Cons",TermC.num_str @{thm map_Cons}),
172 Thm ("map_Nil",TermC.num_str @{thm map_Cons}),
173 (* Thm ("mem_Cons",TermC.num_str @{thm mem_Cons}),
174 Thm ("mem_Nil",TermC.num_str @{thm mem_Nil}), *)
175 (* Thm ("null_Cons",TermC.num_str @{thm null_Cons}),
176 Thm ("null_Nil",TermC.num_str @{thm null_Nil}),*)
177 Thm ("remdups_Cons",TermC.num_str @{thm remdups_Cons}),
178 Thm ("remdups_Nil",TermC.num_str @{thm remdups_Nil}),
179 Thm ("rev_Cons",TermC.num_str @{thm rev_Cons}),
180 Thm ("rev_Nil",TermC.num_str @{thm rev_Nil}),
181 Thm ("take_Nil",TermC.num_str @{thm take_Nil}),
182 Thm ("take_Cons",TermC.num_str @{thm take_Cons}),
183 Thm ("tl_Cons",TermC.num_str @{thm tl_Cons}),
184 Thm ("tl_Nil",TermC.num_str @{thm tl_Nil}),
185 Thm ("zip_Cons",TermC.num_str @{thm zip_Cons}),
186 Thm ("zip_Nil",TermC.num_str @{thm zip_Nil})],
189 setup {* KEStore_Elems.add_rlss [("list_rls", (Context.theory_name @{theory}, list_rls))] *}