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Start of attempt to clean-up list theories.
See github issue #98 for more information. Essence of work to date is that core_list has the type definition, and the “basic” functions on that type. Derived theorems and other constants are left until listScript to be defined.
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| open HolKernel Parse boolLib | ||
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| open BasicProvers Datatype | ||
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| val _ = new_theory "core_list" | ||
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| val _ = Hol_datatype `list = NIL | CONS of 'a => list`; | ||
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| (* Concrete syntax *) | ||
| val _ = add_listform {separator = [TOK ";", BreakSpace(1,0)], | ||
| leftdelim = [TOK "["], rightdelim = [TOK "]"], | ||
| cons = "CONS", nilstr = "NIL", | ||
| block_info = (PP.INCONSISTENT, 0)}; | ||
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| val _ = add_rule {term_name = "CONS", fixity = Infixr 490, | ||
| pp_elements = [TOK "::", BreakSpace(0,2)], | ||
| paren_style = OnlyIfNecessary, | ||
| block_style = (AroundSameName, (PP.INCONSISTENT, 2))}; | ||
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| val list_Axiom = TypeBase.axiom_of ``:'a list``; | ||
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| val NULL_DEF = new_recursive_definition | ||
| {name = "NULL_DEF", | ||
| rec_axiom = list_Axiom, | ||
| def = --`(NULL [] = T) /\ | ||
| (NULL (h::t) = F)`--}; | ||
| val _ = export_rewrites ["NULL_DEF"] | ||
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| val HD = new_recursive_definition | ||
| {name = "HD", | ||
| rec_axiom = list_Axiom, | ||
| def = --`HD (h::t) = h`--}; | ||
| val _ = export_rewrites ["HD"] | ||
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| val TL = new_recursive_definition | ||
| {name = "TL", | ||
| rec_axiom = list_Axiom, | ||
| def = --`TL (h::t) = t`--}; | ||
| val _ = export_rewrites ["TL"] | ||
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| val SUM = new_recursive_definition | ||
| {name = "SUM", | ||
| rec_axiom = list_Axiom, | ||
| def = --`(SUM [] = 0) /\ | ||
| (!h t. SUM (h::t) = h + SUM t)`--}; | ||
| val _ = export_rewrites ["SUM"] | ||
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| val APPEND = new_recursive_definition | ||
| {name = "APPEND", | ||
| rec_axiom = list_Axiom, | ||
| def = --`(!l:'a list. APPEND [] l = l) /\ | ||
| (!l1 l2 h. APPEND (h::l1) l2 = h::APPEND l1 l2)`--}; | ||
| val _ = export_rewrites ["APPEND"] | ||
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| val _ = set_fixity "++" (Infixl 480); | ||
| val _ = overload_on ("++", Term`APPEND`); | ||
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| val FLAT = new_recursive_definition | ||
| {name = "FLAT", | ||
| rec_axiom = list_Axiom, | ||
| def = --`(FLAT [] = []) /\ | ||
| (!h t. FLAT (h::t) = APPEND h (FLAT t))`--}; | ||
| val _ = export_rewrites ["FLAT"] | ||
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| val LENGTH = new_recursive_definition | ||
| {name = "LENGTH", | ||
| rec_axiom = list_Axiom, | ||
| def = --`(LENGTH [] = 0) /\ | ||
| (!(h:'a) t. LENGTH (h::t) = SUC (LENGTH t))`--}; | ||
| val _ = export_rewrites ["LENGTH"] | ||
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| val MAP = new_recursive_definition | ||
| {name = "MAP", | ||
| rec_axiom = list_Axiom, | ||
| def = --`(!f:'a->'b. MAP f [] = []) /\ | ||
| (!f h t. MAP f (h::t) = f h::MAP f t)`--}; | ||
| val _ = export_rewrites ["MAP"] | ||
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| val LIST_TO_SET_DEF = new_recursive_definition{ | ||
| name = "LIST_TO_SET_DEF", | ||
| rec_axiom = list_Axiom, | ||
| def = ``(!x:'a. LIST_TO_SET [] x <=> F) /\ | ||
| (!h:'a t x. LIST_TO_SET (h::t) x = (x = h) \/ LIST_TO_SET t x)``} | ||
| val _ = overload_on ("set", ``LIST_TO_SET``) | ||
| val _ = overload_on ("MEM", ``\h:'a l:'a list. h IN LIST_TO_SET l``) | ||
| val _ = export_rewrites ["LIST_TO_SET_DEF"] | ||
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| val FILTER = new_recursive_definition | ||
| {name = "FILTER", | ||
| rec_axiom = list_Axiom, | ||
| def = --`(!P. FILTER P [] = []) /\ | ||
| (!(P:'a->bool) h t. | ||
| FILTER P (h::t) = | ||
| if P h then (h::FILTER P t) else FILTER P t)`--}; | ||
| val _ = export_rewrites ["FILTER"] | ||
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| val FOLDR = new_recursive_definition | ||
| {name = "FOLDR", | ||
| rec_axiom = list_Axiom, | ||
| def = --`(!f e. FOLDR (f:'a->'b->'b) e [] = e) /\ | ||
| (!f e x l. FOLDR f e (x::l) = f x (FOLDR f e l))`--}; | ||
| val _ = export_rewrites ["FOLDR"] | ||
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| val FOLDL = new_recursive_definition | ||
| {name = "FOLDL", | ||
| rec_axiom = list_Axiom, | ||
| def = --`(!f e. FOLDL (f:'b->'a->'b) e [] = e) /\ | ||
| (!f e x l. FOLDL f e (x::l) = FOLDL f (f e x) l)`--}; | ||
| val _ = export_rewrites ["FOLDL"] | ||
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| val EVERY_DEF = new_recursive_definition | ||
| {name = "EVERY_DEF", | ||
| rec_axiom = list_Axiom, | ||
| def = --`(!P:'a->bool. EVERY P [] = T) /\ | ||
| (!P h t. EVERY P (h::t) = P h /\ EVERY P t)`--}; | ||
| val _ = export_rewrites ["EVERY_DEF"] | ||
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| val EXISTS_DEF = new_recursive_definition | ||
| {name = "EXISTS_DEF", | ||
| rec_axiom = list_Axiom, | ||
| def = --`(!P:'a->bool. EXISTS P [] = F) | ||
| /\ (!P h t. EXISTS P (h::t) = P h \/ EXISTS P t)`--}; | ||
| val _ = export_rewrites ["EXISTS_DEF"] | ||
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| val EL = new_recursive_definition | ||
| {name = "EL", | ||
| rec_axiom = prim_recTheory.num_Axiom, | ||
| def = --`(!l. EL 0 l = (HD l:'a)) /\ | ||
| (!l:'a list. !n. EL (SUC n) l = EL n (TL l))`--}; | ||
| val _ = export_rewrites ["EL"] | ||
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| val _ = computeLib.add_persistent_funs [ | ||
| "APPEND", | ||
| "EXISTS_DEF", | ||
| "EVERY_DEF", | ||
| "FILTER", | ||
| "FLAT", | ||
| "FOLDL", | ||
| "FOLDR", | ||
| "HD", | ||
| "LENGTH", | ||
| "MAP", | ||
| "NULL_DEF", | ||
| "TL" | ||
| ] | ||
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| val _ = export_theory() |
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