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"
14 subsection {* Notes on Isac's programming language *}
16 Isac's programming language combines tacticals (TRY, etc) and
17 tactics (Rewrite, etc) with list processing.
19 In order to distinguish list expressions of the meta (programming)
20 language from the object language in Lucas-Interpretation, a
21 new 'type xlist' is introduced.
22 TODO: Switch the role of 'xlist' and 'list' (the former only used
25 Isac's programming language preceeded the function package
26 in 2002. For naming "axiomatization" is used for reasons of uniformity
27 with the other replacements for "axioms".
28 Another reminiscence from Isabelle2002 are Isac-specific numerals,
29 introduced in order to have floating point numerals at a time,
30 when Isabelle did not consider that requirement. For the sake of uniformity
31 'nat' from List.thy is replaced by 'real' by 'fun parse',
32 however, 'fun parseNEW' has started to replace this fix (after finishing
33 this fix, there will be a 'rename all parseNEW --> parse).
35 Note: *one* "axiomatization" over all equations caused strange "'a list list"
39 subsection {* Type 'xlist' for Lucas-Interpretation *}
40 (*TODO: ask for shorter deliminters in xlist *)
43 | XCons 'a "'a xlist" (infixr "@#" 65)
46 -- {* list Enumeration *}
47 "_xlist" :: "args => 'a xlist" ("[||(_)||]")
50 "[||x, xs||]" == "x@#[||xs||]"
51 "[||x||]" == "x@#[|| ||]"
56 subsection {* Functions for 'xlist' *}
58 (1) revise, if definition of identifiers like LENGTH_NIL are still required.
59 (2) switch the role of 'xlist' and 'list' in the functions below, in particular for
60 'foldr', 'foldr_Nil', 'foldr_Cons' and 'xfoldr', 'xfoldr_Nil', 'xfoldr_Cons'.
61 For transition phase just outcomment InsSort.thy and inssort.sml.
64 primrec xfoldr :: "('a \<Rightarrow> 'b \<Rightarrow> 'b) \<Rightarrow> 'a xlist \<Rightarrow> 'b \<Rightarrow> 'b" where
65 xfoldr_Nil: "xfoldr f [|| ||] = id" |
66 xfoldr_Cons: "xfoldr f (x @# xs) = f x \<circ> xfoldr f xs"
68 primrec LENGTH :: "'a list => real"
70 LENGTH_NIL: "LENGTH [] = 0" |
71 LENGTH_CONS: "LENGTH (x#xs) = 1 + LENGTH xs"
73 consts NTH :: "[real, 'a list] => 'a"
75 NTH_NIL: "NTH 1 (x # xs) = x" and
76 NTH_CONS: (*NO primrec, fun ..*)"1 < n ==> NTH n (x # xs) = NTH (n + -1) xs"
79 hd_thm: "hd (x # xs) = x"
82 tl_Nil: "tl [] = []" and
83 tl_Cons: "tl (x # xs) = xs"
86 LAST: "last (x # xs) = (if xs = [] then x else last xs)"
89 butlast_Nil: "butlast [] = []" and
90 butlast_Cons: "butlast (x # xs) = (if xs = [] then [] else x # butlast xs)"
93 map_Nil:"map f [] = []" and
94 map_Cons: "map f (x # xs) = f x # map f xs"
97 rev_Nil: "rev [] = []" and
98 rev_Cons: "rev (x # xs) = rev xs @ [x]"
101 filter_Nil: "filter P [] = []" and
102 filter_Cons: "filter P (x # xs) = (if P x then x # filter P xs else filter P xs)"
105 concat_Nil: "concat [] = []" and
106 concat_Cons: "concat (x # xs) = x @ concat xs"
109 takeWhile_Nil: "takeWhile P [] = []" and
110 takeWhile_Cons: "takeWhile P (x # xs) = (if P x then x # takeWhile P xs else [])"
113 dropWhile_Nil: "dropWhile P [] = []" and
114 dropWhile_Cons: "dropWhile P (x # xs) = (if P x then dropWhile P xs else x#xs)"
117 zip_Nil: "zip xs [] = []" and
118 zip_Cons: "zip xs (y # ys) = (case xs of [] => [] | z # zs => (z,y) # zip zs ys)"
121 distinct_Nil: "distinct [] = True" and
122 distinct_Cons: "distinct (x # xs) = (x ~: set xs & distinct xs)"
125 remdups_Nil: "remdups [] = []" and
126 remdups_Cons: "remdups (x#xs) = (if x : set xs then remdups xs else x # remdups xs)"
128 (** Lexicographic orderings on lists ...!!!**)
130 ML{* (*the former ListC.ML*)
131 (** rule set for evaluating listexpr in scripts **)
133 Rls{id = "list_rls", preconds = [], rew_ord = ("dummy_ord", dummy_ord),
134 erls = Erls, srls = Erls, calc = [], errpatts = [],
135 rules = [Thm ("refl", num_str @{thm refl}), (*'a<>b -> FALSE' by fun eval_equal*)
136 Thm ("o_apply", num_str @{thm o_apply}),
138 Thm ("NTH_CONS",num_str @{thm NTH_CONS}),(*erls for cond. in Atools.ML*)
139 Thm ("NTH_NIL",num_str @{thm NTH_NIL}),
140 Thm ("append_Cons",num_str @{thm append_Cons}),
141 Thm ("append_Nil",num_str @{thm append_Nil}),
142 (* Thm ("butlast_Cons",num_str @{thm butlast_Cons}),
143 Thm ("butlast_Nil",num_str @{thm butlast_Nil}),*)
144 Thm ("concat_Cons",num_str @{thm concat_Cons}),
145 Thm ("concat_Nil",num_str @{thm concat_Nil}),
146 (* Thm ("del_base",num_str @{thm del_base}),
147 Thm ("del_rec",num_str @{thm del_rec}), *)
149 Thm ("distinct_Cons",num_str @{thm distinct_Cons}),
150 Thm ("distinct_Nil",num_str @{thm distinct_Nil}),
151 Thm ("dropWhile_Cons",num_str @{thm dropWhile_Cons}),
152 Thm ("dropWhile_Nil",num_str @{thm dropWhile_Nil}),
153 Thm ("filter_Cons",num_str @{thm filter_Cons}),
154 Thm ("filter_Nil",num_str @{thm filter_Nil}),
155 Thm ("foldr_Cons",num_str @{thm foldr_Cons}),
156 Thm ("foldr_Nil",num_str @{thm foldr_Nil}),
157 Thm ("hd_thm",num_str @{thm hd_thm}),
158 Thm ("LAST",num_str @{thm LAST}),
159 Thm ("LENGTH_CONS",num_str @{thm LENGTH_CONS}),
160 Thm ("LENGTH_NIL",num_str @{thm LENGTH_NIL}),
161 (* Thm ("list_diff_def",num_str @{thm list_diff_def}),*)
162 Thm ("map_Cons",num_str @{thm map_Cons}),
163 Thm ("map_Nil",num_str @{thm map_Cons}),
164 (* Thm ("mem_Cons",num_str @{thm mem_Cons}),
165 Thm ("mem_Nil",num_str @{thm mem_Nil}), *)
166 (* Thm ("null_Cons",num_str @{thm null_Cons}),
167 Thm ("null_Nil",num_str @{thm null_Nil}),*)
168 Thm ("remdups_Cons",num_str @{thm remdups_Cons}),
169 Thm ("remdups_Nil",num_str @{thm remdups_Nil}),
170 Thm ("rev_Cons",num_str @{thm rev_Cons}),
171 Thm ("rev_Nil",num_str @{thm rev_Nil}),
172 Thm ("take_Nil",num_str @{thm take_Nil}),
173 Thm ("take_Cons",num_str @{thm take_Cons}),
174 Thm ("tl_Cons",num_str @{thm tl_Cons}),
175 Thm ("tl_Nil",num_str @{thm tl_Nil}),
176 Thm ("zip_Cons",num_str @{thm zip_Cons}),
177 Thm ("zip_Nil",num_str @{thm zip_Nil})],
180 setup {* KEStore_Elems.add_rlss [("list_rls", (Context.theory_name @{theory}, list_rls))] *}