Type | Arity |
---|---|
word_ptree | 2 |
Constant | Type |
ADD_LISTs | :α ptree -> (string, α) alist -> α ptree |
ADD_LISTw | :(α, β) word_ptree -> (α word, β) alist -> (α, β) word_ptree |
ADDs | :α ptree -> string # α -> α ptree |
ADDw | :(α, β) word_ptree -> α word # β -> (α, β) word_ptree |
DEPTHw | :(α, β) word_ptree -> num |
EVERY_LEAFw | :(α word -> β -> bool) -> (α, β) word_ptree -> bool |
EXISTS_LEAFw | :(α word -> β -> bool) -> (α, β) word_ptree -> bool |
FINDs | :α ptree -> string -> α |
FINDw | :(β, α) word_ptree -> β word -> α |
INSERT_PTREEs | :string -> ptreeset -> ptreeset |
INSERT_PTREEw | :α word -> α word_ptreeset -> α word_ptreeset |
IN_PTREEs | :string -> ptreeset -> bool |
IN_PTREEw | :α word -> α word_ptreeset -> bool |
KEYSs | :α ptree -> string list |
KEYSw | :(α, β) word_ptree -> α word list |
PEEKs | :α ptree -> string -> α option |
PEEKw | :(α, β) word_ptree -> α word -> β option |
PTREE_OF_STRINGSET | :ptreeset -> (string -> bool) -> ptreeset |
PTREE_OF_WORDSET | :α word_ptreeset -> (α word -> bool) -> α word_ptreeset |
REMOVEs | :α ptree -> string -> α ptree |
REMOVEw | :(α, β) word_ptree -> α word -> (α, β) word_ptree |
SIZEw | :(α, β) word_ptree -> num |
SKIP1 | :string -> string |
SOME_PTREE | :β ptree -> (α, β) word_ptree |
STRINGSET_OF_PTREE | :ptreeset -> string -> bool |
THE_PTREE | :(β, α) word_ptree -> α ptree |
TRANSFORMw | :(α -> β) -> (γ, α) word_ptree -> (γ, β) word_ptree |
TRAVERSEs | :α ptree -> string list |
TRAVERSEw | :(α, β) word_ptree -> α word list |
UNION_PTREEw | :β word_ptreeset -> γ word_ptreeset -> α word_ptreeset |
WORDSET_OF_PTREE | :α word_ptreeset -> α word -> bool |
WordEmpty | :(α, β) word_ptree |
Word_ptree | :(α -> unit) -> β ptree -> (α, β) word_ptree |
num_to_string | :num -> string |
string_to_num | :string -> num |
word_ptree_CASE | :(α, β) word_ptree -> ((α -> unit) -> β ptree -> γ) -> γ |
word_ptree_size | :(α -> num) -> (β -> num) -> (α, β) word_ptree -> num |
|- ∀c s. SKIP1 (STRING c s) = s
|- ∀s. string_to_num s = s2n 256 ORD (STRING #"\^A" s)
|- ∀n. num_to_string n = SKIP1 (n2s 256 CHR n)
|- ∀t w. t ' w = t ' (string_to_num w)
|- ∀t w. FINDs t w = THE (t ' w)
|- ∀t w d. t |+ (w,d) = t |+ (string_to_num w,d)
|- $|++ = FOLDL $|+
|- ∀t w. t \\ w = t \\ string_to_num w
|- ∀t. TRAVERSEs t = MAP num_to_string (TRAVERSE t)
|- ∀t. KEYSs t = QSORT $< (TRAVERSEs t)
|- ∀w t. w IN_PTREEs t ⇔ string_to_num w IN_PTREE t
|- ∀w t. w INSERT_PTREEs t = string_to_num w INSERT_PTREE t
|- ∀t. STRINGSET_OF_PTREE t = LIST_TO_SET (TRAVERSEs t)
|- ∀t s. t |++ s = t |++ IMAGE string_to_num s
|- ∃rep. TYPE_DEFINITION (λa0'. ∀'word_ptree' . (∀a0'. (∃a0 a1. a0' = (λa0 a1. ind_type$CONSTR 0 (a0,a1) (λn. ind_type$BOTTOM)) a0 a1) ⇒ 'word_ptree' a0') ⇒ 'word_ptree' a0') rep
|- ∀a0 a1 f. word_ptree_CASE (Word_ptree a0 a1) f = f a0 a1
|- ∀f f1 a0 a1. word_ptree_size f f1 (Word_ptree a0 a1) = 1 + ptree_size f1 a1
|- ∀a t. THE_PTREE (Word_ptree a t) = t
|- ∀t. SOME_PTREE t = Word_ptree (K ()) t
|- +{}+ = SOME_PTREE -{}-
|- ∀t w. t ' w = THE_PTREE t ' (w2n w)
|- ∀t w. FINDw t w = THE (t ' w)
|- ∀t w d. t |+ (w,d) = SOME_PTREE (THE_PTREE t |+ (w2n w,d))
|- $|++ = FOLDL $|+
|- ∀t w. t \\ w = SOME_PTREE (THE_PTREE t \\ w2n w)
|- ∀t. TRAVERSEw t = MAP n2w (TRAVERSE (THE_PTREE t))
|- ∀t. KEYSw t = QSORT $<+ (TRAVERSEw t)
|- ∀f t. TRANSFORMw f t = SOME_PTREE (TRANSFORM f (THE_PTREE t))
|- ∀P t. EVERY_LEAFw P t ⇔ EVERY_LEAF (λk d. P (n2w k) d) (THE_PTREE t)
|- ∀P t. EXISTS_LEAFw P t ⇔ EXISTS_LEAF (λk d. P (n2w k) d) (THE_PTREE t)
|- ∀t. SIZEw t = SIZE (THE_PTREE t)
|- ∀t. DEPTHw t = DEPTH (THE_PTREE t)
|- ∀w t. w IN_PTREEw t ⇔ w2n w IN_PTREE THE_PTREE t
|- ∀w t. w INSERT_PTREEw t = SOME_PTREE (w2n w INSERT_PTREE THE_PTREE t)
|- ∀t. WORDSET_OF_PTREE t = LIST_TO_SET (TRAVERSEw t)
|- ∀t1 t2. t1 UNION_PTREEw t2 = SOME_PTREE (THE_PTREE t1 UNION_PTREE THE_PTREE t2)
|- ∀t s. t |++ s = SOME_PTREE (THE_PTREE t |++ IMAGE w2n s)
|- DATATYPE (word_ptree Word_ptree)
|- ∀a0 a1 a0' a1'. (Word_ptree a0 a1 = Word_ptree a0' a1') ⇔ (a0 = a0') ∧ (a1 = a1')
|- ∀M M' f. (M = M') ∧ (∀a0 a1. (M' = Word_ptree a0 a1) ⇒ (f a0 a1 = f' a0 a1)) ⇒ (word_ptree_CASE M f = word_ptree_CASE M' f')
|- ∀ww. ∃f p. ww = Word_ptree f p
|- ∀f. ∃fn. ∀a0 a1. fn (Word_ptree a0 a1) = f a0 a1
|- ∀P. (∀f p. P (Word_ptree f p)) ⇒ ∀w. P w
|- ∀w v t. t |+ (w,v) = t |+ (w,())
|- ∀b l1 l2. l2n b (l1 ++ l2) = l2n b l1 + b ** LENGTH l1 * l2n b l2
|- ∀b l. 1 < b ⇒ l2n b l < b ** LENGTH l
|- ∀b l1 l2. 1 < b ∧ EVERY ($> b) l1 ∧ EVERY ($> b) l2 ⇒ ((l2n b (l1 ++ [1]) = l2n b (l2 ++ [1])) ⇔ (l1 = l2))
|- ∀l. EVERY ($> 256) (MAP ORD l)
|- ∀f l1 l2. (∀x y. (f x = f y) ⇔ (x = y)) ⇒ ((MAP f l1 = MAP f l2) ⇔ (l1 = l2))
|- ∀l1 l2. (REVERSE l1 = REVERSE l2) ⇔ (l1 = l2)
|- ∀s t. (string_to_num s = string_to_num t) ⇔ (s = t)
|- ∀n. (n = 1) ∨ 256 ≤ n ∧ (n DIV 256 ** LOG 256 n = 1) ⇔ n ∈ IMAGE string_to_num 𝕌(:string)
|- ∀n. n ∈ IMAGE string_to_num 𝕌(:string) ⇒ (string_to_num (num_to_string n) = n)
|- ∀s. num_to_string (string_to_num s) = s
|- ∀w v t. t |+ (w,v) = t |+ (w,())
|- ∀t. THE_PTREE (SOME_PTREE t) = t