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