author | berghofe |
Wed, 29 Jan 2003 17:32:19 +0100 | |
changeset 13794 | 332eb2e69a65 |
parent 13629 | a46362d2b19b |
child 14106 | bbf708a7e27f |
permissions | -rw-r--r-- |
41
97aae241094b
added cons, rcons, last_elem, sort_strings, take_suffix;
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diff
changeset
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1 |
(* Title: Pure/library.ML |
0 | 2 |
ID: $Id$ |
233 | 3 |
Author: Lawrence C Paulson, Cambridge University Computer Laboratory |
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Author: Markus Wenzel, TU Munich |
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License: GPL (GNU GENERAL PUBLIC LICENSE) |
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|
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Basic library: functions, options, pairs, booleans, lists, integers, |
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strings, lists as sets, association lists, generic tables, balanced |
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trees, orders, I/O and diagnostics, timing, misc. |
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*) |
11 |
||
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infix |> |>> |>>> ~~ \ \\ ins ins_string ins_int orf andf prefix upto downto |
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mem mem_int mem_string union union_int union_string inter inter_int |
14 |
inter_string subset subset_int subset_string; |
|
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8ea1a962ad72
files now define a structure to allow SML/NJ to optimize the code
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infix 3 oo ooo oooo; |
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signature LIBRARY = |
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sig |
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(*functions*) |
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21 |
val curry: ('a * 'b -> 'c) -> 'a -> 'b -> 'c |
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22 |
val uncurry: ('a -> 'b -> 'c) -> 'a * 'b -> 'c |
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val I: 'a -> 'a |
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24 |
val K: 'a -> 'b -> 'a |
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25 |
val |> : 'a * ('a -> 'b) -> 'b |
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val |>> : ('a * 'b) * ('a -> 'c) -> 'c * 'b |
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val |>>> : ('a * 'b) * ('a -> 'c * 'd) -> 'c * ('b * 'd) |
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val apl: 'a * ('a * 'b -> 'c) -> 'b -> 'c |
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val apr: ('a * 'b -> 'c) * 'b -> 'a -> 'c |
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30 |
val funpow: int -> ('a -> 'a) -> 'a -> 'a |
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val oo: ('a -> 'b) * ('c -> 'd -> 'a) -> 'c -> 'd -> 'b |
32 |
val ooo: ('a -> 'b) * ('c -> 'd -> 'e -> 'a) -> 'c -> 'd -> 'e -> 'b |
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val oooo: ('a -> 'b) * ('c -> 'd -> 'e -> 'f -> 'a) -> 'c -> 'd -> 'e -> 'f -> 'b |
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(*stamps*) |
36 |
type stamp |
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37 |
val stamp: unit -> stamp |
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38 |
||
39 |
(*options*) |
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datatype 'a option = None | Some of 'a |
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41 |
exception OPTION |
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42 |
val the: 'a option -> 'a |
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val if_none: 'a option -> 'a -> 'a |
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44 |
val is_some: 'a option -> bool |
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45 |
val is_none: 'a option -> bool |
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46 |
val apsome: ('a -> 'b) -> 'a option -> 'b option |
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val try: ('a -> 'b) -> 'a -> 'b option |
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val can: ('a -> 'b) -> 'a -> bool |
49 |
||
50 |
(*pairs*) |
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51 |
val pair: 'a -> 'b -> 'a * 'b |
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val rpair: 'a -> 'b -> 'b * 'a |
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val fst: 'a * 'b -> 'a |
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val snd: 'a * 'b -> 'b |
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val eq_fst: (''a * 'b) * (''a * 'c) -> bool |
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val eq_snd: ('a * ''b) * ('c * ''b) -> bool |
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val swap: 'a * 'b -> 'b * 'a |
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val apfst: ('a -> 'b) -> 'a * 'c -> 'b * 'c |
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val apsnd: ('a -> 'b) -> 'c * 'a -> 'c * 'b |
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val pairself: ('a -> 'b) -> 'a * 'a -> 'b * 'b |
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||
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(*booleans*) |
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val equal: ''a -> ''a -> bool |
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val not_equal: ''a -> ''a -> bool |
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val orf: ('a -> bool) * ('a -> bool) -> 'a -> bool |
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val andf: ('a -> bool) * ('a -> bool) -> 'a -> bool |
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val exists: ('a -> bool) -> 'a list -> bool |
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val forall: ('a -> bool) -> 'a list -> bool |
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val set: bool ref -> bool |
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val reset: bool ref -> bool |
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val toggle: bool ref -> bool |
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val change: 'a ref -> ('a -> 'a) -> unit |
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val setmp: 'a ref -> 'a -> ('b -> 'c) -> 'b -> 'c |
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val conditional: bool -> (unit -> unit) -> unit |
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(*lists*) |
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exception LIST of string |
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val null: 'a list -> bool |
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val hd: 'a list -> 'a |
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val tl: 'a list -> 'a list |
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val cons: 'a -> 'a list -> 'a list |
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val single: 'a -> 'a list |
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val append: 'a list -> 'a list -> 'a list |
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val rev_append: 'a list -> 'a list -> 'a list |
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val apply: ('a -> 'a) list -> 'a -> 'a |
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val foldl: ('a * 'b -> 'a) -> 'a * 'b list -> 'a |
87 |
val foldr: ('a * 'b -> 'b) -> 'a list * 'b -> 'b |
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88 |
val foldr1: ('a * 'a -> 'a) -> 'a list -> 'a |
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added foldl_map: ('a * 'b -> 'a * 'c) -> 'a * 'b list -> 'a * 'c list;
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89 |
val foldl_map: ('a * 'b -> 'a * 'c) -> 'a * 'b list -> 'a * 'c list |
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val foldln: ('a * int -> 'b -> 'b) -> 'a list -> 'b -> 'b |
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val length: 'a list -> int |
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val take: int * 'a list -> 'a list |
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val drop: int * 'a list -> 'a list |
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val splitAt: int * 'a list -> 'a list * 'a list |
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val dropwhile: ('a -> bool) -> 'a list -> 'a list |
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val nth_elem: int * 'a list -> 'a |
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val map_nth_elem: int -> ('a -> 'a) -> 'a list -> 'a list |
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val last_elem: 'a list -> 'a |
99 |
val split_last: 'a list -> 'a list * 'a |
|
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val nth_update: 'a -> int * 'a list -> 'a list |
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val find_index: ('a -> bool) -> 'a list -> int |
102 |
val find_index_eq: ''a -> ''a list -> int |
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val find_first: ('a -> bool) -> 'a list -> 'a option |
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get_first: ('a -> 'b option) -> 'a list -> 'b option;
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val get_first: ('a -> 'b option) -> 'a list -> 'b option |
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val flat: 'a list list -> 'a list |
12136 | 106 |
val unflat: 'a list list -> 'b list -> 'b list list |
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val seq: ('a -> unit) -> 'a list -> unit |
108 |
val separate: 'a -> 'a list -> 'a list |
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109 |
val replicate: int -> 'a -> 'a list |
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val multiply: 'a list * 'a list list -> 'a list list |
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val filter: ('a -> bool) -> 'a list -> 'a list |
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val filter_out: ('a -> bool) -> 'a list -> 'a list |
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val mapfilter: ('a -> 'b option) -> 'a list -> 'b list |
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val map2: ('a * 'b -> 'c) -> 'a list * 'b list -> 'c list |
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val exists2: ('a * 'b -> bool) -> 'a list * 'b list -> bool |
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val forall2: ('a * 'b -> bool) -> 'a list * 'b list -> bool |
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4956
a7538e43896e
added foldl_map: ('a * 'b -> 'a * 'c) -> 'a * 'b list -> 'a * 'c list;
wenzelm
parents:
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diff
changeset
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117 |
val seq2: ('a * 'b -> unit) -> 'a list * 'b list -> unit |
4621 | 118 |
val ~~ : 'a list * 'b list -> ('a * 'b) list |
119 |
val split_list: ('a * 'b) list -> 'a list * 'b list |
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equal_lists: ('a * 'b -> bool) -> 'a list * 'b list -> bool;
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val equal_lists: ('a * 'b -> bool) -> 'a list * 'b list -> bool |
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val prefix: ''a list * ''a list -> bool |
122 |
val take_prefix: ('a -> bool) -> 'a list -> 'a list * 'a list |
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val take_suffix: ('a -> bool) -> 'a list -> 'a list * 'a list |
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val prefixes1: 'a list -> 'a list list |
125 |
val suffixes1: 'a list -> 'a list list |
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4621 | 126 |
|
127 |
(*integers*) |
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val gcd: int * int -> int |
129 |
val lcm: int * int -> int |
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val inc: int ref -> int |
131 |
val dec: int ref -> int |
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val upto: int * int -> int list |
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val downto: int * int -> int list |
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val downto0: int list * int -> bool |
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val radixpand: int * int -> int list |
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val radixstring: int * string * int -> string |
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val string_of_int: int -> string |
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val string_of_indexname: string * int -> string |
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139 |
||
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(*rational numbers*) |
141 |
type rat |
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142 |
val rep_rat: rat -> int * int |
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val ratadd: rat * rat -> rat |
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val ratmul: rat * rat -> rat |
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val ratinv: rat -> rat |
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val int_ratdiv: int * int -> rat |
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val ratneg: rat -> rat |
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val rat_of_int: int -> rat |
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149 |
||
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(*strings*) |
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val nth_elem_string: int * string -> string |
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val foldl_string: ('a * string -> 'a) -> 'a * string -> 'a |
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val exists_string: (string -> bool) -> string -> bool |
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val enclose: string -> string -> string -> string |
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val unenclose: string -> string |
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val quote: string -> string |
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val space_implode: string -> string list -> string |
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val commas: string list -> string |
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val commas_quote: string list -> string |
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val cat_lines: string list -> string |
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val space_explode: string -> string -> string list |
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val std_output: string -> unit |
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val std_error: string -> unit |
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val writeln_default: string -> unit |
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val prefix_lines: string -> string -> string |
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val split_lines: string -> string list |
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val untabify: string list -> string list |
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val suffix: string -> string -> string |
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val unsuffix: string -> string -> string |
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val replicate_string: int -> string -> string |
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(*lists as sets*) |
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173 |
val mem: ''a * ''a list -> bool |
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val mem_int: int * int list -> bool |
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175 |
val mem_string: string * string list -> bool |
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176 |
val gen_mem: ('a * 'b -> bool) -> 'a * 'b list -> bool |
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val ins: ''a * ''a list -> ''a list |
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178 |
val ins_int: int * int list -> int list |
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179 |
val ins_string: string * string list -> string list |
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180 |
val gen_ins: ('a * 'a -> bool) -> 'a * 'a list -> 'a list |
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val union: ''a list * ''a list -> ''a list |
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182 |
val union_int: int list * int list -> int list |
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183 |
val union_string: string list * string list -> string list |
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184 |
val gen_union: ('a * 'a -> bool) -> 'a list * 'a list -> 'a list |
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val gen_inter: ('a * 'b -> bool) -> 'a list * 'b list -> 'a list |
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val inter: ''a list * ''a list -> ''a list |
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val inter_int: int list * int list -> int list |
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val inter_string: string list * string list -> string list |
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val subset: ''a list * ''a list -> bool |
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val subset_int: int list * int list -> bool |
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val subset_string: string list * string list -> bool |
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val eq_set: ''a list * ''a list -> bool |
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val eq_set_string: string list * string list -> bool |
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val gen_subset: ('a * 'b -> bool) -> 'a list * 'b list -> bool |
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val \ : ''a list * ''a -> ''a list |
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val \\ : ''a list * ''a list -> ''a list |
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val gen_rem: ('a * 'b -> bool) -> 'a list * 'b -> 'a list |
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val gen_rems: ('a * 'b -> bool) -> 'a list * 'b list -> 'a list |
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val gen_distinct: ('a * 'a -> bool) -> 'a list -> 'a list |
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val distinct: ''a list -> ''a list |
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val findrep: ''a list -> ''a list |
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val gen_duplicates: ('a * 'a -> bool) -> 'a list -> 'a list |
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val duplicates: ''a list -> ''a list |
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(*association lists*) |
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206 |
val assoc: (''a * 'b) list * ''a -> 'b option |
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207 |
val assoc_int: (int * 'a) list * int -> 'a option |
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208 |
val assoc_string: (string * 'a) list * string -> 'a option |
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val assoc_string_int: ((string * int) * 'a) list * (string * int) -> 'a option |
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val assocs: (''a * 'b list) list -> ''a -> 'b list |
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val assoc2: (''a * (''b * 'c) list) list * (''a * ''b) -> 'c option |
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val gen_assoc: ('a * 'b -> bool) -> ('b * 'c) list * 'a -> 'c option |
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val overwrite: (''a * 'b) list * (''a * 'b) -> (''a * 'b) list |
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val overwrite_warn: (''a * 'b) list * (''a * 'b) -> string -> (''a * 'b) list |
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val gen_overwrite: ('a * 'a -> bool) -> ('a * 'b) list * ('a * 'b) -> ('a * 'b) list |
216 |
||
12284 | 217 |
(*lists as tables*) |
218 |
val gen_merge_lists: ('a * 'a -> bool) -> 'a list -> 'a list -> 'a list |
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219 |
val gen_merge_lists': ('a * 'a -> bool) -> 'a list -> 'a list -> 'a list |
|
4621 | 220 |
val merge_lists: ''a list -> ''a list -> ''a list |
12284 | 221 |
val merge_lists': ''a list -> ''a list -> ''a list |
4692 | 222 |
val merge_alists: (''a * 'b) list -> (''a * 'b) list -> (''a * 'b) list |
4621 | 223 |
|
224 |
(*balanced trees*) |
|
225 |
exception Balance |
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226 |
val fold_bal: ('a * 'a -> 'a) -> 'a list -> 'a |
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227 |
val access_bal: ('a -> 'a) * ('a -> 'a) * 'a -> int -> int -> 'a |
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228 |
val accesses_bal: ('a -> 'a) * ('a -> 'a) * 'a -> int -> 'a list |
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229 |
||
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(*orders*) |
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fixed the discrepancy in the ordering of the constructors LESS EQUAL GREATER
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231 |
datatype order = LESS | EQUAL | GREATER |
4621 | 232 |
val rev_order: order -> order |
233 |
val make_ord: ('a * 'a -> bool) -> 'a * 'a -> order |
|
234 |
val int_ord: int * int -> order |
|
235 |
val string_ord: string * string -> order |
|
236 |
val prod_ord: ('a * 'b -> order) -> ('c * 'd -> order) -> ('a * 'c) * ('b * 'd) -> order |
|
237 |
val dict_ord: ('a * 'b -> order) -> 'a list * 'b list -> order |
|
238 |
val list_ord: ('a * 'b -> order) -> 'a list * 'b list -> order |
|
239 |
val sort: ('a * 'a -> order) -> 'a list -> 'a list |
|
240 |
val sort_strings: string list -> string list |
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241 |
val sort_wrt: ('a -> string) -> 'a list -> 'a list |
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11514 | 242 |
val unique_strings: string list -> string list |
4621 | 243 |
|
244 |
(*I/O and diagnostics*) |
|
245 |
val cd: string -> unit |
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246 |
val pwd: unit -> string |
|
5966
60f80b2a2777
removed prs / prs_fn (broken, because it did not include \n in its
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247 |
val writeln_fn: (string -> unit) ref |
9774 | 248 |
val priority_fn: (string -> unit) ref |
12260 | 249 |
val tracing_fn: (string -> unit) ref |
4621 | 250 |
val warning_fn: (string -> unit) ref |
251 |
val error_fn: (string -> unit) ref |
|
252 |
val writeln: string -> unit |
|
9774 | 253 |
val priority: string -> unit |
12260 | 254 |
val tracing: string -> unit |
4621 | 255 |
val warning: string -> unit |
256 |
exception ERROR |
|
257 |
val error_msg: string -> unit |
|
258 |
val error: string -> 'a |
|
259 |
val sys_error: string -> 'a |
|
260 |
val assert: bool -> string -> unit |
|
261 |
val deny: bool -> string -> unit |
|
262 |
val assert_all: ('a -> bool) -> 'a list -> ('a -> string) -> unit |
|
263 |
datatype 'a error = Error of string | OK of 'a |
|
264 |
val get_error: 'a error -> string option |
|
265 |
val get_ok: 'a error -> 'a option |
|
266 |
val handle_error: ('a -> 'b) -> 'a -> 'b error |
|
4923 | 267 |
exception ERROR_MESSAGE of string |
268 |
val transform_error: ('a -> 'b) -> 'a -> 'b |
|
5904 | 269 |
val transform_failure: (exn -> exn) -> ('a -> 'b) -> 'a -> 'b |
4621 | 270 |
|
271 |
(*timing*) |
|
272 |
val cond_timeit: bool -> (unit -> 'a) -> 'a |
|
273 |
val timeit: (unit -> 'a) -> 'a |
|
274 |
val timeap: ('a -> 'b) -> 'a -> 'b |
|
12795 | 275 |
val timeap_msg: string -> ('a -> 'b) -> 'a -> 'b |
8999 | 276 |
val timing: bool ref |
4621 | 277 |
|
278 |
(*misc*) |
|
279 |
val make_keylist: ('a -> 'b) -> 'a list -> ('a * 'b) list |
|
280 |
val keyfilter: ('a * ''b) list -> ''b -> 'a list |
|
281 |
val partition: ('a -> bool) -> 'a list -> 'a list * 'a list |
|
282 |
val partition_eq: ('a * 'a -> bool) -> 'a list -> 'a list list |
|
283 |
val partition_list: (int -> 'a -> bool) -> int -> int -> 'a list -> 'a list list |
|
284 |
val transitive_closure: (string * string list) list -> (string * string list) list |
|
285 |
val gensym: string -> string |
|
286 |
val scanwords: (string -> bool) -> string list -> string list |
|
287 |
datatype 'a mtree = Join of 'a * 'a mtree list |
|
288 |
end; |
|
289 |
||
290 |
structure Library: LIBRARY = |
|
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clasohm
parents:
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diff
changeset
|
291 |
struct |
0 | 292 |
|
4995 | 293 |
|
233 | 294 |
(** functions **) |
0 | 295 |
|
233 | 296 |
(*handy combinators*) |
297 |
fun curry f x y = f (x, y); |
|
298 |
fun uncurry f (x, y) = f x y; |
|
299 |
fun I x = x; |
|
300 |
fun K x y = x; |
|
0 | 301 |
|
380 | 302 |
(*reverse apply*) |
410 | 303 |
fun (x |> f) = f x; |
8418 | 304 |
fun ((x, y) |>> f) = (f x, y); |
305 |
fun ((x, y) |>>> f) = let val (x', z) = f x in (x', (y, z)) end; |
|
380 | 306 |
|
233 | 307 |
(*application of (infix) operator to its left or right argument*) |
308 |
fun apl (x, f) y = f (x, y); |
|
309 |
fun apr (f, y) x = f (x, y); |
|
0 | 310 |
|
233 | 311 |
(*function exponentiation: f(...(f x)...) with n applications of f*) |
312 |
fun funpow n f x = |
|
313 |
let fun rep (0, x) = x |
|
314 |
| rep (n, x) = rep (n - 1, f x) |
|
315 |
in rep (n, x) end; |
|
160 | 316 |
|
5893 | 317 |
(*concatenation: 2 and 3 args*) |
318 |
fun (f oo g) x y = f (g x y); |
|
319 |
fun (f ooo g) x y z = f (g x y z); |
|
6510 | 320 |
fun (f oooo g) x y z w = f (g x y z w); |
321 |
||
160 | 322 |
|
323 |
||
2471 | 324 |
(** stamps **) |
325 |
||
326 |
type stamp = unit ref; |
|
327 |
val stamp: unit -> stamp = ref; |
|
328 |
||
329 |
||
330 |
||
233 | 331 |
(** options **) |
0 | 332 |
|
333 |
datatype 'a option = None | Some of 'a; |
|
334 |
||
4139 | 335 |
exception OPTION; |
0 | 336 |
|
337 |
fun the (Some x) = x |
|
4139 | 338 |
| the None = raise OPTION; |
0 | 339 |
|
4212 | 340 |
(*strict!*) |
255
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
245
diff
changeset
|
341 |
fun if_none None y = y |
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
245
diff
changeset
|
342 |
| if_none (Some x) _ = x; |
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
245
diff
changeset
|
343 |
|
0 | 344 |
fun is_some (Some _) = true |
345 |
| is_some None = false; |
|
346 |
||
347 |
fun is_none (Some _) = false |
|
348 |
| is_none None = true; |
|
349 |
||
233 | 350 |
fun apsome f (Some x) = Some (f x) |
351 |
| apsome _ None = None; |
|
0 | 352 |
|
6959 | 353 |
|
354 |
(* exception handling *) |
|
355 |
||
356 |
exception ERROR; |
|
357 |
||
358 |
fun try f x = Some (f x) |
|
359 |
handle Interrupt => raise Interrupt | ERROR => raise ERROR | _ => None; |
|
360 |
||
361 |
fun can f x = is_some (try f x); |
|
4139 | 362 |
|
363 |
||
364 |
||
233 | 365 |
(** pairs **) |
366 |
||
367 |
fun pair x y = (x, y); |
|
368 |
fun rpair x y = (y, x); |
|
369 |
||
370 |
fun fst (x, y) = x; |
|
371 |
fun snd (x, y) = y; |
|
372 |
||
373 |
fun eq_fst ((x1, _), (x2, _)) = x1 = x2; |
|
374 |
fun eq_snd ((_, y1), (_, y2)) = y1 = y2; |
|
375 |
||
376 |
fun swap (x, y) = (y, x); |
|
377 |
||
4212 | 378 |
(*apply function to components*) |
233 | 379 |
fun apfst f (x, y) = (f x, y); |
380 |
fun apsnd f (x, y) = (x, f y); |
|
4212 | 381 |
fun pairself f (x, y) = (f x, f y); |
233 | 382 |
|
383 |
||
384 |
||
385 |
(** booleans **) |
|
386 |
||
387 |
(* equality *) |
|
388 |
||
389 |
fun equal x y = x = y; |
|
390 |
fun not_equal x y = x <> y; |
|
391 |
||
392 |
||
393 |
(* operators for combining predicates *) |
|
394 |
||
2175
21fde76bc742
Updated syntax; shortened comments; put in monomorphic versions of ins
paulson
parents:
2157
diff
changeset
|
395 |
fun (p orf q) = fn x => p x orelse q x; |
21fde76bc742
Updated syntax; shortened comments; put in monomorphic versions of ins
paulson
parents:
2157
diff
changeset
|
396 |
fun (p andf q) = fn x => p x andalso q x; |
233 | 397 |
|
398 |
||
399 |
(* predicates on lists *) |
|
400 |
||
401 |
(*exists pred [x1, ..., xn] ===> pred x1 orelse ... orelse pred xn*) |
|
402 |
fun exists (pred: 'a -> bool) : 'a list -> bool = |
|
403 |
let fun boolf [] = false |
|
404 |
| boolf (x :: xs) = pred x orelse boolf xs |
|
405 |
in boolf end; |
|
406 |
||
407 |
(*forall pred [x1, ..., xn] ===> pred x1 andalso ... andalso pred xn*) |
|
408 |
fun forall (pred: 'a -> bool) : 'a list -> bool = |
|
409 |
let fun boolf [] = true |
|
410 |
| boolf (x :: xs) = pred x andalso boolf xs |
|
411 |
in boolf end; |
|
0 | 412 |
|
233 | 413 |
|
380 | 414 |
(* flags *) |
415 |
||
416 |
fun set flag = (flag := true; true); |
|
417 |
fun reset flag = (flag := false; false); |
|
418 |
fun toggle flag = (flag := not (! flag); ! flag); |
|
419 |
||
9118 | 420 |
fun change r f = r := f (! r); |
421 |
||
4212 | 422 |
(*temporarily set flag, handling errors*) |
2978 | 423 |
fun setmp flag value f x = |
2958 | 424 |
let |
425 |
val orig_value = ! flag; |
|
426 |
fun return y = (flag := orig_value; y); |
|
427 |
in |
|
428 |
flag := value; |
|
429 |
return (f x handle exn => (return (); raise exn)) |
|
430 |
end; |
|
431 |
||
380 | 432 |
|
11853 | 433 |
(* conditional execution *) |
434 |
||
435 |
fun conditional b f = if b then f () else (); |
|
436 |
||
437 |
||
233 | 438 |
|
439 |
(** lists **) |
|
440 |
||
441 |
exception LIST of string; |
|
442 |
||
443 |
fun null [] = true |
|
444 |
| null (_ :: _) = false; |
|
445 |
||
446 |
fun hd [] = raise LIST "hd" |
|
447 |
| hd (x :: _) = x; |
|
448 |
||
449 |
fun tl [] = raise LIST "tl" |
|
450 |
| tl (_ :: xs) = xs; |
|
451 |
||
452 |
fun cons x xs = x :: xs; |
|
5285 | 453 |
fun single x = [x]; |
233 | 454 |
|
4629 | 455 |
fun append xs ys = xs @ ys; |
456 |
||
13794 | 457 |
(* tail recursive version *) |
458 |
fun rev_append [] ys = ys |
|
459 |
| rev_append (x :: xs) ys = rev_append xs (x :: ys); |
|
460 |
||
5904 | 461 |
fun apply [] x = x |
462 |
| apply (f :: fs) x = apply fs (f x); |
|
463 |
||
233 | 464 |
|
465 |
(* fold *) |
|
466 |
||
467 |
(*the following versions of fold are designed to fit nicely with infixes*) |
|
0 | 468 |
|
233 | 469 |
(* (op @) (e, [x1, ..., xn]) ===> ((e @ x1) @ x2) ... @ xn |
470 |
for operators that associate to the left (TAIL RECURSIVE)*) |
|
471 |
fun foldl (f: 'a * 'b -> 'a) : 'a * 'b list -> 'a = |
|
472 |
let fun itl (e, []) = e |
|
473 |
| itl (e, a::l) = itl (f(e, a), l) |
|
474 |
in itl end; |
|
475 |
||
476 |
(* (op @) ([x1, ..., xn], e) ===> x1 @ (x2 ... @ (xn @ e)) |
|
477 |
for operators that associate to the right (not tail recursive)*) |
|
478 |
fun foldr f (l, e) = |
|
479 |
let fun itr [] = e |
|
480 |
| itr (a::l) = f(a, itr l) |
|
481 |
in itr l end; |
|
482 |
||
483 |
(* (op @) [x1, ..., xn] ===> x1 @ (x2 ... @ (x[n-1] @ xn)) |
|
484 |
for n > 0, operators that associate to the right (not tail recursive)*) |
|
485 |
fun foldr1 f l = |
|
4181 | 486 |
let fun itr [x] = x |
233 | 487 |
| itr (x::l) = f(x, itr l) |
488 |
in itr l end; |
|
489 |
||
4956
a7538e43896e
added foldl_map: ('a * 'b -> 'a * 'c) -> 'a * 'b list -> 'a * 'c list;
wenzelm
parents:
4945
diff
changeset
|
490 |
fun foldl_map _ (x, []) = (x, []) |
a7538e43896e
added foldl_map: ('a * 'b -> 'a * 'c) -> 'a * 'b list -> 'a * 'c list;
wenzelm
parents:
4945
diff
changeset
|
491 |
| foldl_map f (x, y :: ys) = |
a7538e43896e
added foldl_map: ('a * 'b -> 'a * 'c) -> 'a * 'b list -> 'a * 'c list;
wenzelm
parents:
4945
diff
changeset
|
492 |
let |
a7538e43896e
added foldl_map: ('a * 'b -> 'a * 'c) -> 'a * 'b list -> 'a * 'c list;
wenzelm
parents:
4945
diff
changeset
|
493 |
val (x', y') = f (x, y); |
a7538e43896e
added foldl_map: ('a * 'b -> 'a * 'c) -> 'a * 'b list -> 'a * 'c list;
wenzelm
parents:
4945
diff
changeset
|
494 |
val (x'', ys') = foldl_map f (x', ys); |
a7538e43896e
added foldl_map: ('a * 'b -> 'a * 'c) -> 'a * 'b list -> 'a * 'c list;
wenzelm
parents:
4945
diff
changeset
|
495 |
in (x'', y' :: ys') end; |
a7538e43896e
added foldl_map: ('a * 'b -> 'a * 'c) -> 'a * 'b list -> 'a * 'c list;
wenzelm
parents:
4945
diff
changeset
|
496 |
|
11002 | 497 |
fun foldln f xs e = fst (foldl (fn ((e,i), x) => (f (x,i) e, i+1)) ((e,1),xs)); |
233 | 498 |
|
499 |
(* basic list functions *) |
|
500 |
||
501 |
(*length of a list, should unquestionably be a standard function*) |
|
502 |
local fun length1 (n, []) = n (*TAIL RECURSIVE*) |
|
503 |
| length1 (n, x :: xs) = length1 (n + 1, xs) |
|
504 |
in fun length l = length1 (0, l) end; |
|
505 |
||
506 |
(*take the first n elements from a list*) |
|
507 |
fun take (n, []) = [] |
|
508 |
| take (n, x :: xs) = |
|
509 |
if n > 0 then x :: take (n - 1, xs) else []; |
|
510 |
||
511 |
(*drop the first n elements from a list*) |
|
512 |
fun drop (n, []) = [] |
|
513 |
| drop (n, x :: xs) = |
|
514 |
if n > 0 then drop (n - 1, xs) else x :: xs; |
|
0 | 515 |
|
13629 | 516 |
fun splitAt(n,[]) = ([],[]) |
517 |
| splitAt(n,xs as x::ys) = |
|
518 |
if n>0 then let val (ps,qs) = splitAt(n-1,ys) in (x::ps,qs) end |
|
519 |
else ([],xs) |
|
520 |
||
4713 | 521 |
fun dropwhile P [] = [] |
522 |
| dropwhile P (ys as x::xs) = if P x then dropwhile P xs else ys; |
|
523 |
||
233 | 524 |
(*return nth element of a list, where 0 designates the first element; |
525 |
raise EXCEPTION if list too short*) |
|
526 |
fun nth_elem NL = |
|
527 |
(case drop NL of |
|
528 |
[] => raise LIST "nth_elem" |
|
529 |
| x :: _ => x); |
|
530 |
||
11773 | 531 |
fun map_nth_elem 0 f (x :: xs) = f x :: xs |
532 |
| map_nth_elem n f (x :: xs) = x :: map_nth_elem (n - 1) f xs |
|
533 |
| map_nth_elem _ _ [] = raise LIST "map_nth_elem"; |
|
534 |
||
233 | 535 |
(*last element of a list*) |
536 |
fun last_elem [] = raise LIST "last_elem" |
|
537 |
| last_elem [x] = x |
|
538 |
| last_elem (_ :: xs) = last_elem xs; |
|
539 |
||
3762 | 540 |
(*rear decomposition*) |
541 |
fun split_last [] = raise LIST "split_last" |
|
542 |
| split_last [x] = ([], x) |
|
543 |
| split_last (x :: xs) = apfst (cons x) (split_last xs); |
|
544 |
||
4893 | 545 |
(*update nth element*) |
13629 | 546 |
fun nth_update x n_xs = |
547 |
(case splitAt n_xs of |
|
548 |
(_,[]) => raise LIST "nth_update" |
|
549 |
| (prfx, _ :: sffx') => prfx @ (x :: sffx')) |
|
4893 | 550 |
|
4212 | 551 |
(*find the position of an element in a list*) |
552 |
fun find_index pred = |
|
553 |
let fun find _ [] = ~1 |
|
554 |
| find n (x :: xs) = if pred x then n else find (n + 1) xs; |
|
555 |
in find 0 end; |
|
3762 | 556 |
|
4224 | 557 |
fun find_index_eq x = find_index (equal x); |
4212 | 558 |
|
559 |
(*find first element satisfying predicate*) |
|
560 |
fun find_first _ [] = None |
|
561 |
| find_first pred (x :: xs) = |
|
562 |
if pred x then Some x else find_first pred xs; |
|
233 | 563 |
|
4916
fe8b0c82691b
get_first: ('a -> 'b option) -> 'a list -> 'b option;
wenzelm
parents:
4893
diff
changeset
|
564 |
(*get first element by lookup function*) |
fe8b0c82691b
get_first: ('a -> 'b option) -> 'a list -> 'b option;
wenzelm
parents:
4893
diff
changeset
|
565 |
fun get_first _ [] = None |
fe8b0c82691b
get_first: ('a -> 'b option) -> 'a list -> 'b option;
wenzelm
parents:
4893
diff
changeset
|
566 |
| get_first f (x :: xs) = |
fe8b0c82691b
get_first: ('a -> 'b option) -> 'a list -> 'b option;
wenzelm
parents:
4893
diff
changeset
|
567 |
(case f x of |
fe8b0c82691b
get_first: ('a -> 'b option) -> 'a list -> 'b option;
wenzelm
parents:
4893
diff
changeset
|
568 |
None => get_first f xs |
fe8b0c82691b
get_first: ('a -> 'b option) -> 'a list -> 'b option;
wenzelm
parents:
4893
diff
changeset
|
569 |
| some => some); |
fe8b0c82691b
get_first: ('a -> 'b option) -> 'a list -> 'b option;
wenzelm
parents:
4893
diff
changeset
|
570 |
|
233 | 571 |
(*flatten a list of lists to a list*) |
572 |
fun flat (ls: 'c list list) : 'c list = foldr (op @) (ls, []); |
|
573 |
||
12136 | 574 |
fun unflat (xs :: xss) ys = |
13629 | 575 |
let val (ps,qs) = splitAt(length xs,ys) |
576 |
in ps :: unflat xss qs end |
|
12136 | 577 |
| unflat [] [] = [] |
578 |
| unflat _ _ = raise LIST "unflat"; |
|
579 |
||
233 | 580 |
(*like Lisp's MAPC -- seq proc [x1, ..., xn] evaluates |
581 |
(proc x1; ...; proc xn) for side effects*) |
|
582 |
fun seq (proc: 'a -> unit) : 'a list -> unit = |
|
583 |
let fun seqf [] = () |
|
584 |
| seqf (x :: xs) = (proc x; seqf xs) |
|
585 |
in seqf end; |
|
586 |
||
587 |
(*separate s [x1, x2, ..., xn] ===> [x1, s, x2, s, ..., s, xn]*) |
|
588 |
fun separate s (x :: (xs as _ :: _)) = x :: s :: separate s xs |
|
589 |
| separate _ xs = xs; |
|
590 |
||
591 |
(*make the list [x, x, ..., x] of length n*) |
|
592 |
fun replicate n (x: 'a) : 'a list = |
|
593 |
let fun rep (0, xs) = xs |
|
594 |
| rep (n, xs) = rep (n - 1, x :: xs) |
|
595 |
in |
|
596 |
if n < 0 then raise LIST "replicate" |
|
597 |
else rep (n, []) |
|
598 |
end; |
|
599 |
||
4248
5e8a31c41d44
added get_error: 'a error -> string option, get_ok: 'a error -> 'a option;
wenzelm
parents:
4224
diff
changeset
|
600 |
(*multiply [a, b, c, ...] * [xs, ys, zs, ...]*) |
5e8a31c41d44
added get_error: 'a error -> string option, get_ok: 'a error -> 'a option;
wenzelm
parents:
4224
diff
changeset
|
601 |
fun multiply ([], _) = [] |
5e8a31c41d44
added get_error: 'a error -> string option, get_ok: 'a error -> 'a option;
wenzelm
parents:
4224
diff
changeset
|
602 |
| multiply (x :: xs, yss) = map (cons x) yss @ multiply (xs, yss); |
5e8a31c41d44
added get_error: 'a error -> string option, get_ok: 'a error -> 'a option;
wenzelm
parents:
4224
diff
changeset
|
603 |
|
233 | 604 |
|
605 |
(* filter *) |
|
606 |
||
607 |
(*copy the list preserving elements that satisfy the predicate*) |
|
608 |
fun filter (pred: 'a->bool) : 'a list -> 'a list = |
|
0 | 609 |
let fun filt [] = [] |
233 | 610 |
| filt (x :: xs) = if pred x then x :: filt xs else filt xs |
611 |
in filt end; |
|
0 | 612 |
|
613 |
fun filter_out f = filter (not o f); |
|
614 |
||
233 | 615 |
fun mapfilter (f: 'a -> 'b option) ([]: 'a list) = [] : 'b list |
616 |
| mapfilter f (x :: xs) = |
|
617 |
(case f x of |
|
618 |
None => mapfilter f xs |
|
619 |
| Some y => y :: mapfilter f xs); |
|
620 |
||
621 |
||
622 |
(* lists of pairs *) |
|
623 |
||
380 | 624 |
fun map2 _ ([], []) = [] |
625 |
| map2 f (x :: xs, y :: ys) = (f (x, y) :: map2 f (xs, ys)) |
|
626 |
| map2 _ _ = raise LIST "map2"; |
|
627 |
||
628 |
fun exists2 _ ([], []) = false |
|
629 |
| exists2 pred (x :: xs, y :: ys) = pred (x, y) orelse exists2 pred (xs, ys) |
|
630 |
| exists2 _ _ = raise LIST "exists2"; |
|
631 |
||
632 |
fun forall2 _ ([], []) = true |
|
633 |
| forall2 pred (x :: xs, y :: ys) = pred (x, y) andalso forall2 pred (xs, ys) |
|
634 |
| forall2 _ _ = raise LIST "forall2"; |
|
635 |
||
4956
a7538e43896e
added foldl_map: ('a * 'b -> 'a * 'c) -> 'a * 'b list -> 'a * 'c list;
wenzelm
parents:
4945
diff
changeset
|
636 |
fun seq2 _ ([], []) = () |
a7538e43896e
added foldl_map: ('a * 'b -> 'a * 'c) -> 'a * 'b list -> 'a * 'c list;
wenzelm
parents:
4945
diff
changeset
|
637 |
| seq2 f (x :: xs, y :: ys) = (f (x, y); seq2 f (xs, ys)) |
a7538e43896e
added foldl_map: ('a * 'b -> 'a * 'c) -> 'a * 'b list -> 'a * 'c list;
wenzelm
parents:
4945
diff
changeset
|
638 |
| seq2 _ _ = raise LIST "seq2"; |
a7538e43896e
added foldl_map: ('a * 'b -> 'a * 'c) -> 'a * 'b list -> 'a * 'c list;
wenzelm
parents:
4945
diff
changeset
|
639 |
|
233 | 640 |
(*combine two lists forming a list of pairs: |
641 |
[x1, ..., xn] ~~ [y1, ..., yn] ===> [(x1, y1), ..., (xn, yn)]*) |
|
642 |
fun [] ~~ [] = [] |
|
643 |
| (x :: xs) ~~ (y :: ys) = (x, y) :: (xs ~~ ys) |
|
644 |
| _ ~~ _ = raise LIST "~~"; |
|
645 |
||
646 |
(*inverse of ~~; the old 'split': |
|
647 |
[(x1, y1), ..., (xn, yn)] ===> ([x1, ..., xn], [y1, ..., yn])*) |
|
648 |
fun split_list (l: ('a * 'b) list) = (map #1 l, map #2 l); |
|
649 |
||
7468
6ce03d2f7d91
equal_lists: ('a * 'b -> bool) -> 'a list * 'b list -> bool;
wenzelm
parents:
7090
diff
changeset
|
650 |
fun equal_lists eq (xs, ys) = length xs = length ys andalso forall2 eq (xs, ys); |
6ce03d2f7d91
equal_lists: ('a * 'b -> bool) -> 'a list * 'b list -> bool;
wenzelm
parents:
7090
diff
changeset
|
651 |
|
233 | 652 |
|
653 |
(* prefixes, suffixes *) |
|
654 |
||
655 |
fun [] prefix _ = true |
|
656 |
| (x :: xs) prefix (y :: ys) = x = y andalso (xs prefix ys) |
|
657 |
| _ prefix _ = false; |
|
658 |
||
659 |
(* [x1, ..., xi, ..., xn] ---> ([x1, ..., x(i-1)], [xi, ..., xn]) |
|
660 |
where xi is the first element that does not satisfy the predicate*) |
|
661 |
fun take_prefix (pred : 'a -> bool) (xs: 'a list) : 'a list * 'a list = |
|
662 |
let fun take (rxs, []) = (rev rxs, []) |
|
255
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
245
diff
changeset
|
663 |
| take (rxs, x :: xs) = |
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
245
diff
changeset
|
664 |
if pred x then take(x :: rxs, xs) else (rev rxs, x :: xs) |
233 | 665 |
in take([], xs) end; |
666 |
||
667 |
(* [x1, ..., xi, ..., xn] ---> ([x1, ..., xi], [x(i+1), ..., xn]) |
|
668 |
where xi is the last element that does not satisfy the predicate*) |
|
669 |
fun take_suffix _ [] = ([], []) |
|
670 |
| take_suffix pred (x :: xs) = |
|
671 |
(case take_suffix pred xs of |
|
672 |
([], sffx) => if pred x then ([], x :: sffx) else ([x], sffx) |
|
673 |
| (prfx, sffx) => (x :: prfx, sffx)); |
|
674 |
||
12249 | 675 |
fun prefixes1 [] = [] |
676 |
| prefixes1 (x :: xs) = map (cons x) ([] :: prefixes1 xs); |
|
677 |
||
678 |
fun suffixes1 xs = map rev (prefixes1 (rev xs)); |
|
679 |
||
233 | 680 |
|
681 |
||
682 |
(** integers **) |
|
683 |
||
10692 | 684 |
fun gcd(x,y) = |
685 |
let fun gxd x y = |
|
686 |
if y = 0 then x else gxd y (x mod y) |
|
687 |
in if x < y then gxd y x else gxd x y end; |
|
688 |
||
689 |
fun lcm(x,y) = (x * y) div gcd(x,y); |
|
690 |
||
2958 | 691 |
fun inc i = (i := ! i + 1; ! i); |
692 |
fun dec i = (i := ! i - 1; ! i); |
|
233 | 693 |
|
694 |
||
695 |
(* lists of integers *) |
|
696 |
||
697 |
(*make the list [from, from + 1, ..., to]*) |
|
2175
21fde76bc742
Updated syntax; shortened comments; put in monomorphic versions of ins
paulson
parents:
2157
diff
changeset
|
698 |
fun (from upto to) = |
233 | 699 |
if from > to then [] else from :: ((from + 1) upto to); |
700 |
||
701 |
(*make the list [from, from - 1, ..., to]*) |
|
2175
21fde76bc742
Updated syntax; shortened comments; put in monomorphic versions of ins
paulson
parents:
2157
diff
changeset
|
702 |
fun (from downto to) = |
233 | 703 |
if from < to then [] else from :: ((from - 1) downto to); |
704 |
||
705 |
(*predicate: downto0 (is, n) <=> is = [n, n - 1, ..., 0]*) |
|
706 |
fun downto0 (i :: is, n) = i = n andalso downto0 (is, n - 1) |
|
707 |
| downto0 ([], n) = n = ~1; |
|
708 |
||
709 |
||
710 |
(* convert integers to strings *) |
|
711 |
||
712 |
(*expand the number in the given base; |
|
713 |
example: radixpand (2, 8) gives [1, 0, 0, 0]*) |
|
714 |
fun radixpand (base, num) : int list = |
|
715 |
let |
|
716 |
fun radix (n, tail) = |
|
717 |
if n < base then n :: tail |
|
718 |
else radix (n div base, (n mod base) :: tail) |
|
719 |
in radix (num, []) end; |
|
720 |
||
721 |
(*expands a number into a string of characters starting from "zerochar"; |
|
722 |
example: radixstring (2, "0", 8) gives "1000"*) |
|
723 |
fun radixstring (base, zerochar, num) = |
|
724 |
let val offset = ord zerochar; |
|
725 |
fun chrof n = chr (offset + n) |
|
726 |
in implode (map chrof (radixpand (base, num))) end; |
|
727 |
||
728 |
||
3407
afd288caf573
Removal of radixstring from string_of_int; addition of string_of_indexname
paulson
parents:
3393
diff
changeset
|
729 |
val string_of_int = Int.toString; |
233 | 730 |
|
3407
afd288caf573
Removal of radixstring from string_of_int; addition of string_of_indexname
paulson
parents:
3393
diff
changeset
|
731 |
fun string_of_indexname (a,0) = a |
afd288caf573
Removal of radixstring from string_of_int; addition of string_of_indexname
paulson
parents:
3393
diff
changeset
|
732 |
| string_of_indexname (a,i) = a ^ "_" ^ Int.toString i; |
233 | 733 |
|
734 |
||
735 |
(** strings **) |
|
736 |
||
6312 | 737 |
(*functions tuned for strings, avoiding explode*) |
738 |
||
739 |
fun nth_elem_string (i, str) = |
|
6959 | 740 |
(case try String.substring (str, i, 1) of |
741 |
Some s => s |
|
742 |
| None => raise LIST "nth_elem_string"); |
|
6312 | 743 |
|
6282 | 744 |
fun foldl_string f (x0, str) = |
745 |
let |
|
746 |
val n = size str; |
|
747 |
fun fold (x, i) = if i < n then fold (f (x, String.substring (str, i, 1)), i + 1) else x |
|
748 |
in fold (x0, 0) end; |
|
749 |
||
6312 | 750 |
fun exists_string pred str = foldl_string (fn (b, s) => b orelse pred s) (false, str); |
751 |
||
512
55755ed9fab9
Pure/library/enclose, Pure/Syntax/pretty/enclose: renamed from parents
lcp
parents:
410
diff
changeset
|
752 |
(*enclose in brackets*) |
55755ed9fab9
Pure/library/enclose, Pure/Syntax/pretty/enclose: renamed from parents
lcp
parents:
410
diff
changeset
|
753 |
fun enclose lpar rpar str = lpar ^ str ^ rpar; |
6642 | 754 |
fun unenclose str = String.substring (str, 1, size str - 2); |
255
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
245
diff
changeset
|
755 |
|
233 | 756 |
(*simple quoting (does not escape special chars)*) |
512
55755ed9fab9
Pure/library/enclose, Pure/Syntax/pretty/enclose: renamed from parents
lcp
parents:
410
diff
changeset
|
757 |
val quote = enclose "\"" "\""; |
233 | 758 |
|
4212 | 759 |
(*space_implode "..." (explode "hello") = "h...e...l...l...o"*) |
233 | 760 |
fun space_implode a bs = implode (separate a bs); |
761 |
||
255
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
245
diff
changeset
|
762 |
val commas = space_implode ", "; |
380 | 763 |
val commas_quote = commas o map quote; |
255
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
245
diff
changeset
|
764 |
|
233 | 765 |
(*concatenate messages, one per line, into a string*) |
255
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
245
diff
changeset
|
766 |
val cat_lines = space_implode "\n"; |
233 | 767 |
|
4212 | 768 |
(*space_explode "." "h.e..l.lo" = ["h", "e", "", "l", "lo"]*) |
3832
17a20a2af8f5
fixed space_explode, old one retained as BAD_space_explode;
wenzelm
parents:
3762
diff
changeset
|
769 |
fun space_explode _ "" = [] |
17a20a2af8f5
fixed space_explode, old one retained as BAD_space_explode;
wenzelm
parents:
3762
diff
changeset
|
770 |
| space_explode sep str = |
17a20a2af8f5
fixed space_explode, old one retained as BAD_space_explode;
wenzelm
parents:
3762
diff
changeset
|
771 |
let |
17a20a2af8f5
fixed space_explode, old one retained as BAD_space_explode;
wenzelm
parents:
3762
diff
changeset
|
772 |
fun expl chs = |
17a20a2af8f5
fixed space_explode, old one retained as BAD_space_explode;
wenzelm
parents:
3762
diff
changeset
|
773 |
(case take_prefix (not_equal sep) chs of |
17a20a2af8f5
fixed space_explode, old one retained as BAD_space_explode;
wenzelm
parents:
3762
diff
changeset
|
774 |
(cs, []) => [implode cs] |
17a20a2af8f5
fixed space_explode, old one retained as BAD_space_explode;
wenzelm
parents:
3762
diff
changeset
|
775 |
| (cs, _ :: cs') => implode cs :: expl cs'); |
17a20a2af8f5
fixed space_explode, old one retained as BAD_space_explode;
wenzelm
parents:
3762
diff
changeset
|
776 |
in expl (explode str) end; |
17a20a2af8f5
fixed space_explode, old one retained as BAD_space_explode;
wenzelm
parents:
3762
diff
changeset
|
777 |
|
17a20a2af8f5
fixed space_explode, old one retained as BAD_space_explode;
wenzelm
parents:
3762
diff
changeset
|
778 |
val split_lines = space_explode "\n"; |
17a20a2af8f5
fixed space_explode, old one retained as BAD_space_explode;
wenzelm
parents:
3762
diff
changeset
|
779 |
|
7712 | 780 |
(*untabify*) |
781 |
fun untabify chs = |
|
782 |
let |
|
783 |
val tab_width = 8; |
|
784 |
||
785 |
fun untab (_, "\n") = (0, ["\n"]) |
|
9118 | 786 |
| untab (pos, "\t") = |
787 |
let val d = tab_width - (pos mod tab_width) in (pos + d, replicate d " ") end |
|
7712 | 788 |
| untab (pos, c) = (pos + 1, [c]); |
789 |
in |
|
790 |
if not (exists (equal "\t") chs) then chs |
|
791 |
else flat (#2 (foldl_map untab (0, chs))) |
|
792 |
end; |
|
793 |
||
5285 | 794 |
(*append suffix*) |
795 |
fun suffix sfx s = s ^ sfx; |
|
796 |
||
797 |
(*remove suffix*) |
|
798 |
fun unsuffix sfx s = |
|
799 |
let |
|
800 |
val cs = explode s; |
|
801 |
val prfx_len = size s - size sfx; |
|
802 |
in |
|
803 |
if prfx_len >= 0 andalso implode (drop (prfx_len, cs)) = sfx then |
|
804 |
implode (take (prfx_len, cs)) |
|
805 |
else raise LIST "unsuffix" |
|
806 |
end; |
|
807 |
||
10951 | 808 |
fun replicate_string 0 _ = "" |
809 |
| replicate_string 1 a = a |
|
810 |
| replicate_string k a = |
|
811 |
if k mod 2 = 0 then replicate_string (k div 2) (a ^ a) |
|
812 |
else replicate_string (k div 2) (a ^ a) ^ a; |
|
813 |
||
3832
17a20a2af8f5
fixed space_explode, old one retained as BAD_space_explode;
wenzelm
parents:
3762
diff
changeset
|
814 |
|
233 | 815 |
|
816 |
(** lists as sets **) |
|
817 |
||
818 |
(*membership in a list*) |
|
819 |
fun x mem [] = false |
|
820 |
| x mem (y :: ys) = x = y orelse x mem ys; |
|
0 | 821 |
|
2175
21fde76bc742
Updated syntax; shortened comments; put in monomorphic versions of ins
paulson
parents:
2157
diff
changeset
|
822 |
(*membership in a list, optimized version for ints*) |
1576
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset
|
823 |
fun (x:int) mem_int [] = false |
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset
|
824 |
| x mem_int (y :: ys) = x = y orelse x mem_int ys; |
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset
|
825 |
|
2175
21fde76bc742
Updated syntax; shortened comments; put in monomorphic versions of ins
paulson
parents:
2157
diff
changeset
|
826 |
(*membership in a list, optimized version for strings*) |
1576
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset
|
827 |
fun (x:string) mem_string [] = false |
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset
|
828 |
| x mem_string (y :: ys) = x = y orelse x mem_string ys; |
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset
|
829 |
|
0 | 830 |
(*generalized membership test*) |
233 | 831 |
fun gen_mem eq (x, []) = false |
832 |
| gen_mem eq (x, y :: ys) = eq (x, y) orelse gen_mem eq (x, ys); |
|
833 |
||
834 |
||
835 |
(*insertion into list if not already there*) |
|
2175
21fde76bc742
Updated syntax; shortened comments; put in monomorphic versions of ins
paulson
parents:
2157
diff
changeset
|
836 |
fun (x ins xs) = if x mem xs then xs else x :: xs; |
0 | 837 |
|
2175
21fde76bc742
Updated syntax; shortened comments; put in monomorphic versions of ins
paulson
parents:
2157
diff
changeset
|
838 |
(*insertion into list, optimized version for ints*) |
21fde76bc742
Updated syntax; shortened comments; put in monomorphic versions of ins
paulson
parents:
2157
diff
changeset
|
839 |
fun (x ins_int xs) = if x mem_int xs then xs else x :: xs; |
1576
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset
|
840 |
|
2175
21fde76bc742
Updated syntax; shortened comments; put in monomorphic versions of ins
paulson
parents:
2157
diff
changeset
|
841 |
(*insertion into list, optimized version for strings*) |
21fde76bc742
Updated syntax; shortened comments; put in monomorphic versions of ins
paulson
parents:
2157
diff
changeset
|
842 |
fun (x ins_string xs) = if x mem_string xs then xs else x :: xs; |
1576
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset
|
843 |
|
0 | 844 |
(*generalized insertion*) |
233 | 845 |
fun gen_ins eq (x, xs) = if gen_mem eq (x, xs) then xs else x :: xs; |
846 |
||
847 |
||
848 |
(*union of sets represented as lists: no repetitions*) |
|
849 |
fun xs union [] = xs |
|
850 |
| [] union ys = ys |
|
851 |
| (x :: xs) union ys = xs union (x ins ys); |
|
0 | 852 |
|
2175
21fde76bc742
Updated syntax; shortened comments; put in monomorphic versions of ins
paulson
parents:
2157
diff
changeset
|
853 |
(*union of sets, optimized version for ints*) |
1576
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset
|
854 |
fun (xs:int list) union_int [] = xs |
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset
|
855 |
| [] union_int ys = ys |
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset
|
856 |
| (x :: xs) union_int ys = xs union_int (x ins_int ys); |
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset
|
857 |
|
2175
21fde76bc742
Updated syntax; shortened comments; put in monomorphic versions of ins
paulson
parents:
2157
diff
changeset
|
858 |
(*union of sets, optimized version for strings*) |
1576
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset
|
859 |
fun (xs:string list) union_string [] = xs |
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset
|
860 |
| [] union_string ys = ys |
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset
|
861 |
| (x :: xs) union_string ys = xs union_string (x ins_string ys); |
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset
|
862 |
|
0 | 863 |
(*generalized union*) |
233 | 864 |
fun gen_union eq (xs, []) = xs |
865 |
| gen_union eq ([], ys) = ys |
|
866 |
| gen_union eq (x :: xs, ys) = gen_union eq (xs, gen_ins eq (x, ys)); |
|
867 |
||
868 |
||
869 |
(*intersection*) |
|
870 |
fun [] inter ys = [] |
|
871 |
| (x :: xs) inter ys = |
|
872 |
if x mem ys then x :: (xs inter ys) else xs inter ys; |
|
873 |
||
2175
21fde76bc742
Updated syntax; shortened comments; put in monomorphic versions of ins
paulson
parents:
2157
diff
changeset
|
874 |
(*intersection, optimized version for ints*) |
1576
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset
|
875 |
fun ([]:int list) inter_int ys = [] |
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset
|
876 |
| (x :: xs) inter_int ys = |
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset
|
877 |
if x mem_int ys then x :: (xs inter_int ys) else xs inter_int ys; |
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset
|
878 |
|
2175
21fde76bc742
Updated syntax; shortened comments; put in monomorphic versions of ins
paulson
parents:
2157
diff
changeset
|
879 |
(*intersection, optimized version for strings *) |
1576
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset
|
880 |
fun ([]:string list) inter_string ys = [] |
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset
|
881 |
| (x :: xs) inter_string ys = |
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset
|
882 |
if x mem_string ys then x :: (xs inter_string ys) else xs inter_string ys; |
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset
|
883 |
|
7090 | 884 |
(*generalized intersection*) |
885 |
fun gen_inter eq ([], ys) = [] |
|
12284 | 886 |
| gen_inter eq (x::xs, ys) = |
7090 | 887 |
if gen_mem eq (x,ys) then x :: gen_inter eq (xs, ys) |
12284 | 888 |
else gen_inter eq (xs, ys); |
7090 | 889 |
|
233 | 890 |
|
891 |
(*subset*) |
|
892 |
fun [] subset ys = true |
|
893 |
| (x :: xs) subset ys = x mem ys andalso xs subset ys; |
|
894 |
||
2175
21fde76bc742
Updated syntax; shortened comments; put in monomorphic versions of ins
paulson
parents:
2157
diff
changeset
|
895 |
(*subset, optimized version for ints*) |
1576
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset
|
896 |
fun ([]:int list) subset_int ys = true |
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset
|
897 |
| (x :: xs) subset_int ys = x mem_int ys andalso xs subset_int ys; |
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset
|
898 |
|
2175
21fde76bc742
Updated syntax; shortened comments; put in monomorphic versions of ins
paulson
parents:
2157
diff
changeset
|
899 |
(*subset, optimized version for strings*) |
1576
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset
|
900 |
fun ([]:string list) subset_string ys = true |
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset
|
901 |
| (x :: xs) subset_string ys = x mem_string ys andalso xs subset_string ys; |
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset
|
902 |
|
4363 | 903 |
(*set equality*) |
904 |
fun eq_set (xs, ys) = |
|
905 |
xs = ys orelse (xs subset ys andalso ys subset xs); |
|
906 |
||
2182
29e56f003599
Removal of polymorphic equality via mem, subset, eq_set, etc
paulson
parents:
2175
diff
changeset
|
907 |
(*set equality for strings*) |
1576
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset
|
908 |
fun eq_set_string ((xs:string list), ys) = |
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset
|
909 |
xs = ys orelse (xs subset_string ys andalso ys subset_string xs); |
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset
|
910 |
|
2182
29e56f003599
Removal of polymorphic equality via mem, subset, eq_set, etc
paulson
parents:
2175
diff
changeset
|
911 |
fun gen_subset eq (xs, ys) = forall (fn x => gen_mem eq (x, ys)) xs; |
29e56f003599
Removal of polymorphic equality via mem, subset, eq_set, etc
paulson
parents:
2175
diff
changeset
|
912 |
|
265 | 913 |
|
233 | 914 |
(*removing an element from a list WITHOUT duplicates*) |
915 |
fun (y :: ys) \ x = if x = y then ys else y :: (ys \ x) |
|
916 |
| [] \ x = []; |
|
917 |
||
2243
3ebeaaacfbd1
Eta-expanded some declarations that are illegal under value polymorphism
paulson
parents:
2196
diff
changeset
|
918 |
fun ys \\ xs = foldl (op \) (ys,xs); |
0 | 919 |
|
233 | 920 |
(*removing an element from a list -- possibly WITH duplicates*) |
921 |
fun gen_rem eq (xs, y) = filter_out (fn x => eq (x, y)) xs; |
|
12295 | 922 |
fun gen_rems eq (xs, ys) = filter_out (fn x => gen_mem eq (x, ys)) xs; |
233 | 923 |
|
924 |
||
925 |
(*makes a list of the distinct members of the input; preserves order, takes |
|
926 |
first of equal elements*) |
|
927 |
fun gen_distinct eq lst = |
|
928 |
let |
|
929 |
val memb = gen_mem eq; |
|
0 | 930 |
|
233 | 931 |
fun dist (rev_seen, []) = rev rev_seen |
932 |
| dist (rev_seen, x :: xs) = |
|
933 |
if memb (x, rev_seen) then dist (rev_seen, xs) |
|
934 |
else dist (x :: rev_seen, xs); |
|
935 |
in |
|
936 |
dist ([], lst) |
|
937 |
end; |
|
938 |
||
2243
3ebeaaacfbd1
Eta-expanded some declarations that are illegal under value polymorphism
paulson
parents:
2196
diff
changeset
|
939 |
fun distinct l = gen_distinct (op =) l; |
233 | 940 |
|
941 |
||
942 |
(*returns the tail beginning with the first repeated element, or []*) |
|
943 |
fun findrep [] = [] |
|
944 |
| findrep (x :: xs) = if x mem xs then x :: xs else findrep xs; |
|
945 |
||
946 |
||
255
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
245
diff
changeset
|
947 |
(*returns a list containing all repeated elements exactly once; preserves |
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
245
diff
changeset
|
948 |
order, takes first of equal elements*) |
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
245
diff
changeset
|
949 |
fun gen_duplicates eq lst = |
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
245
diff
changeset
|
950 |
let |
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
245
diff
changeset
|
951 |
val memb = gen_mem eq; |
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
245
diff
changeset
|
952 |
|
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
245
diff
changeset
|
953 |
fun dups (rev_dups, []) = rev rev_dups |
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
245
diff
changeset
|
954 |
| dups (rev_dups, x :: xs) = |
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
245
diff
changeset
|
955 |
if memb (x, rev_dups) orelse not (memb (x, xs)) then |
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
245
diff
changeset
|
956 |
dups (rev_dups, xs) |
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
245
diff
changeset
|
957 |
else dups (x :: rev_dups, xs); |
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
245
diff
changeset
|
958 |
in |
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
245
diff
changeset
|
959 |
dups ([], lst) |
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
245
diff
changeset
|
960 |
end; |
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
245
diff
changeset
|
961 |
|
2243
3ebeaaacfbd1
Eta-expanded some declarations that are illegal under value polymorphism
paulson
parents:
2196
diff
changeset
|
962 |
fun duplicates l = gen_duplicates (op =) l; |
255
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
245
diff
changeset
|
963 |
|
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
245
diff
changeset
|
964 |
|
233 | 965 |
|
966 |
(** association lists **) |
|
0 | 967 |
|
233 | 968 |
(*association list lookup*) |
969 |
fun assoc ([], key) = None |
|
970 |
| assoc ((keyi, xi) :: pairs, key) = |
|
971 |
if key = keyi then Some xi else assoc (pairs, key); |
|
972 |
||
2175
21fde76bc742
Updated syntax; shortened comments; put in monomorphic versions of ins
paulson
parents:
2157
diff
changeset
|
973 |
(*association list lookup, optimized version for ints*) |
1576
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset
|
974 |
fun assoc_int ([], (key:int)) = None |
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset
|
975 |
| assoc_int ((keyi, xi) :: pairs, key) = |
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset
|
976 |
if key = keyi then Some xi else assoc_int (pairs, key); |
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset
|
977 |
|
2175
21fde76bc742
Updated syntax; shortened comments; put in monomorphic versions of ins
paulson
parents:
2157
diff
changeset
|
978 |
(*association list lookup, optimized version for strings*) |
1576
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset
|
979 |
fun assoc_string ([], (key:string)) = None |
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset
|
980 |
| assoc_string ((keyi, xi) :: pairs, key) = |
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset
|
981 |
if key = keyi then Some xi else assoc_string (pairs, key); |
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset
|
982 |
|
2175
21fde76bc742
Updated syntax; shortened comments; put in monomorphic versions of ins
paulson
parents:
2157
diff
changeset
|
983 |
(*association list lookup, optimized version for string*ints*) |
1576
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset
|
984 |
fun assoc_string_int ([], (key:string*int)) = None |
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset
|
985 |
| assoc_string_int ((keyi, xi) :: pairs, key) = |
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset
|
986 |
if key = keyi then Some xi else assoc_string_int (pairs, key); |
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset
|
987 |
|
233 | 988 |
fun assocs ps x = |
989 |
(case assoc (ps, x) of |
|
990 |
None => [] |
|
991 |
| Some ys => ys); |
|
992 |
||
255
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
245
diff
changeset
|
993 |
(*two-fold association list lookup*) |
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
245
diff
changeset
|
994 |
fun assoc2 (aal, (key1, key2)) = |
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
245
diff
changeset
|
995 |
(case assoc (aal, key1) of |
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
245
diff
changeset
|
996 |
Some al => assoc (al, key2) |
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
245
diff
changeset
|
997 |
| None => None); |
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
245
diff
changeset
|
998 |
|
233 | 999 |
(*generalized association list lookup*) |
1000 |
fun gen_assoc eq ([], key) = None |
|
1001 |
| gen_assoc eq ((keyi, xi) :: pairs, key) = |
|
1002 |
if eq (key, keyi) then Some xi else gen_assoc eq (pairs, key); |
|
1003 |
||
1004 |
(*association list update*) |
|
1005 |
fun overwrite (al, p as (key, _)) = |
|
1006 |
let fun over ((q as (keyi, _)) :: pairs) = |
|
1007 |
if keyi = key then p :: pairs else q :: (over pairs) |
|
1008 |
| over [] = [p] |
|
1009 |
in over al end; |
|
1010 |
||
2522 | 1011 |
fun gen_overwrite eq (al, p as (key, _)) = |
1012 |
let fun over ((q as (keyi, _)) :: pairs) = |
|
1013 |
if eq (keyi, key) then p :: pairs else q :: (over pairs) |
|
1014 |
| over [] = [p] |
|
1015 |
in over al end; |
|
1016 |
||
233 | 1017 |
|
12284 | 1018 |
(* lists as tables *) |
233 | 1019 |
|
12284 | 1020 |
fun gen_merge_lists _ xs [] = xs |
1021 |
| gen_merge_lists _ [] ys = ys |
|
1022 |
| gen_merge_lists eq xs ys = xs @ gen_rems eq (ys, xs); |
|
0 | 1023 |
|
12284 | 1024 |
fun gen_merge_lists' _ xs [] = xs |
1025 |
| gen_merge_lists' _ [] ys = ys |
|
12295 | 1026 |
| gen_merge_lists' eq xs ys = gen_rems eq (ys, xs) @ xs; |
0 | 1027 |
|
12284 | 1028 |
fun merge_lists xs ys = gen_merge_lists (op =) xs ys; |
1029 |
fun merge_lists' xs ys = gen_merge_lists' (op =) xs ys; |
|
1030 |
fun merge_alists al = gen_merge_lists eq_fst al; |
|
380 | 1031 |
|
0 | 1032 |
|
1033 |
||
233 | 1034 |
(** balanced trees **) |
1035 |
||
1036 |
exception Balance; (*indicates non-positive argument to balancing fun*) |
|
1037 |
||
1038 |
(*balanced folding; avoids deep nesting*) |
|
1039 |
fun fold_bal f [x] = x |
|
1040 |
| fold_bal f [] = raise Balance |
|
1041 |
| fold_bal f xs = |
|
13629 | 1042 |
let val (ps,qs) = splitAt(length xs div 2, xs) |
1043 |
in f (fold_bal f ps, fold_bal f qs) end; |
|
233 | 1044 |
|
1045 |
(*construct something of the form f(...g(...(x)...)) for balanced access*) |
|
1046 |
fun access_bal (f, g, x) n i = |
|
1047 |
let fun acc n i = (*1<=i<=n*) |
|
1048 |
if n=1 then x else |
|
1049 |
let val n2 = n div 2 |
|
1050 |
in if i<=n2 then f (acc n2 i) |
|
1051 |
else g (acc (n-n2) (i-n2)) |
|
1052 |
end |
|
1053 |
in if 1<=i andalso i<=n then acc n i else raise Balance end; |
|
1054 |
||
1055 |
(*construct ALL such accesses; could try harder to share recursive calls!*) |
|
1056 |
fun accesses_bal (f, g, x) n = |
|
1057 |
let fun acc n = |
|
1058 |
if n=1 then [x] else |
|
1059 |
let val n2 = n div 2 |
|
1060 |
val acc2 = acc n2 |
|
1061 |
in if n-n2=n2 then map f acc2 @ map g acc2 |
|
1062 |
else map f acc2 @ map g (acc (n-n2)) end |
|
1063 |
in if 1<=n then acc n else raise Balance end; |
|
1064 |
||
1065 |
||
1066 |
||
2506 | 1067 |
(** orders **) |
1068 |
||
1069 |
datatype order = LESS | EQUAL | GREATER; |
|
1070 |
||
4445 | 1071 |
fun rev_order LESS = GREATER |
1072 |
| rev_order EQUAL = EQUAL |
|
1073 |
| rev_order GREATER = LESS; |
|
1074 |
||
4479 | 1075 |
(*assume rel is a linear strict order*) |
4445 | 1076 |
fun make_ord rel (x, y) = |
1077 |
if rel (x, y) then LESS |
|
1078 |
else if rel (y, x) then GREATER |
|
1079 |
else EQUAL; |
|
1080 |
||
4343 | 1081 |
fun int_ord (i, j: int) = |
2506 | 1082 |
if i < j then LESS |
1083 |
else if i = j then EQUAL |
|
1084 |
else GREATER; |
|
1085 |
||
4343 | 1086 |
fun string_ord (a, b: string) = |
2506 | 1087 |
if a < b then LESS |
1088 |
else if a = b then EQUAL |
|
1089 |
else GREATER; |
|
1090 |
||
4343 | 1091 |
(*lexicographic product*) |
1092 |
fun prod_ord a_ord b_ord ((x, y), (x', y')) = |
|
1093 |
(case a_ord (x, x') of EQUAL => b_ord (y, y') | ord => ord); |
|
1094 |
||
1095 |
(*dictionary order -- in general NOT well-founded!*) |
|
1096 |
fun dict_ord _ ([], []) = EQUAL |
|
1097 |
| dict_ord _ ([], _ :: _) = LESS |
|
1098 |
| dict_ord _ (_ :: _, []) = GREATER |
|
1099 |
| dict_ord elem_ord (x :: xs, y :: ys) = |
|
1100 |
(case elem_ord (x, y) of EQUAL => dict_ord elem_ord (xs, ys) | ord => ord); |
|
1101 |
||
1102 |
(*lexicographic product of lists*) |
|
1103 |
fun list_ord elem_ord (xs, ys) = |
|
1104 |
prod_ord int_ord (dict_ord elem_ord) ((length xs, xs), (length ys, ys)); |
|
1105 |
||
2506 | 1106 |
|
4621 | 1107 |
(* sorting *) |
1108 |
||
1109 |
(*quicksort (stable, i.e. does not reorder equal elements)*) |
|
1110 |
fun sort ord = |
|
1111 |
let |
|
1112 |
fun qsort xs = |
|
1113 |
let val len = length xs in |
|
1114 |
if len <= 1 then xs |
|
1115 |
else |
|
1116 |
let val (lts, eqs, gts) = part (nth_elem (len div 2, xs)) xs in |
|
1117 |
qsort lts @ eqs @ qsort gts |
|
1118 |
end |
|
1119 |
end |
|
1120 |
and part _ [] = ([], [], []) |
|
1121 |
| part pivot (x :: xs) = add (ord (x, pivot)) x (part pivot xs) |
|
1122 |
and add LESS x (lts, eqs, gts) = (x :: lts, eqs, gts) |
|
1123 |
| add EQUAL x (lts, eqs, gts) = (lts, x :: eqs, gts) |
|
1124 |
| add GREATER x (lts, eqs, gts) = (lts, eqs, x :: gts); |
|
1125 |
in qsort end; |
|
1126 |
||
1127 |
(*sort strings*) |
|
1128 |
val sort_strings = sort string_ord; |
|
1129 |
fun sort_wrt sel xs = sort (string_ord o pairself sel) xs; |
|
1130 |
||
11514 | 1131 |
fun unique_strings ([]: string list) = [] |
1132 |
| unique_strings [x] = [x] |
|
1133 |
| unique_strings (x :: y :: ys) = |
|
1134 |
if x = y then unique_strings (y :: ys) |
|
1135 |
else x :: unique_strings (y :: ys); |
|
4621 | 1136 |
|
2506 | 1137 |
|
3525 | 1138 |
(** input / output and diagnostics **) |
233 | 1139 |
|
2243
3ebeaaacfbd1
Eta-expanded some declarations that are illegal under value polymorphism
paulson
parents:
2196
diff
changeset
|
1140 |
val cd = OS.FileSys.chDir; |
2317 | 1141 |
val pwd = OS.FileSys.getDir; |
2243
3ebeaaacfbd1
Eta-expanded some declarations that are illegal under value polymorphism
paulson
parents:
2196
diff
changeset
|
1142 |
|
11853 | 1143 |
fun std_output s = (TextIO.output (TextIO.stdOut, s); TextIO.flushOut TextIO.stdOut); |
1144 |
fun std_error s = (TextIO.output (TextIO.stdErr, s); TextIO.flushOut TextIO.stdErr); |
|
3525 | 1145 |
|
12419 | 1146 |
fun prefix_lines "" txt = txt |
1147 |
| prefix_lines prfx txt = txt |> split_lines |> map (fn s => prfx ^ s) |> cat_lines; |
|
3525 | 1148 |
|
12419 | 1149 |
val writeln_default = std_output o suffix "\n"; |
1150 |
||
1151 |
(*hooks for various output channels*) |
|
1152 |
val writeln_fn = ref writeln_default; |
|
9774 | 1153 |
val priority_fn = ref (fn s => ! writeln_fn s); |
12260 | 1154 |
val tracing_fn = ref (fn s => ! writeln_fn s); |
5949 | 1155 |
val warning_fn = ref (std_output o suffix "\n" o prefix_lines "### "); |
1156 |
val error_fn = ref (std_output o suffix "\n" o prefix_lines "*** "); |
|
1580
e3fd931e6095
Added some functions which allow redirection of Isabelle's output
berghofe
parents:
1576
diff
changeset
|
1157 |
|
5966
60f80b2a2777
removed prs / prs_fn (broken, because it did not include \n in its
wenzelm
parents:
5949
diff
changeset
|
1158 |
fun writeln s = ! writeln_fn s; |
9774 | 1159 |
fun priority s = ! priority_fn s; |
12260 | 1160 |
fun tracing s = ! tracing_fn s; |
5942 | 1161 |
fun warning s = ! warning_fn s; |
233 | 1162 |
|
1163 |
(*print error message and abort to top level*) |
|
6959 | 1164 |
|
5949 | 1165 |
fun error_msg s = ! error_fn s; |
3553 | 1166 |
fun error s = (error_msg s; raise ERROR); |
4849 | 1167 |
fun sys_error msg = error ("## SYSTEM ERROR ##\n" ^ msg); |
233 | 1168 |
|
1169 |
fun assert p msg = if p then () else error msg; |
|
1170 |
fun deny p msg = if p then error msg else (); |
|
1171 |
||
544
c53386a5bcf1
Pure/library/assert_all: new, moved from ZF/ind_syntax.ML
lcp
parents:
512
diff
changeset
|
1172 |
(*Assert pred for every member of l, generating a message if pred fails*) |
4212 | 1173 |
fun assert_all pred l msg_fn = |
544
c53386a5bcf1
Pure/library/assert_all: new, moved from ZF/ind_syntax.ML
lcp
parents:
512
diff
changeset
|
1174 |
let fun asl [] = () |
4212 | 1175 |
| asl (x::xs) = if pred x then asl xs else error (msg_fn x) |
1176 |
in asl l end; |
|
233 | 1177 |
|
3624 | 1178 |
|
4212 | 1179 |
(* handle errors capturing messages *) |
3699 | 1180 |
|
1181 |
datatype 'a error = |
|
1182 |
Error of string | |
|
1183 |
OK of 'a; |
|
1184 |
||
4248
5e8a31c41d44
added get_error: 'a error -> string option, get_ok: 'a error -> 'a option;
wenzelm
parents:
4224
diff
changeset
|
1185 |
fun get_error (Error msg) = Some msg |
5e8a31c41d44
added get_error: 'a error -> string option, get_ok: 'a error -> 'a option;
wenzelm
parents:
4224
diff
changeset
|
1186 |
| get_error _ = None; |
5e8a31c41d44
added get_error: 'a error -> string option, get_ok: 'a error -> 'a option;
wenzelm
parents:
4224
diff
changeset
|
1187 |
|
5e8a31c41d44
added get_error: 'a error -> string option, get_ok: 'a error -> 'a option;
wenzelm
parents:
4224
diff
changeset
|
1188 |
fun get_ok (OK x) = Some x |
5e8a31c41d44
added get_error: 'a error -> string option, get_ok: 'a error -> 'a option;
wenzelm
parents:
4224
diff
changeset
|
1189 |
| get_ok _ = None; |
5e8a31c41d44
added get_error: 'a error -> string option, get_ok: 'a error -> 'a option;
wenzelm
parents:
4224
diff
changeset
|
1190 |
|
5037
224887671646
handle_error: capture error msgs, even if no exception raised;
wenzelm
parents:
4995
diff
changeset
|
1191 |
datatype 'a result = |
224887671646
handle_error: capture error msgs, even if no exception raised;
wenzelm
parents:
4995
diff
changeset
|
1192 |
Result of 'a | |
224887671646
handle_error: capture error msgs, even if no exception raised;
wenzelm
parents:
4995
diff
changeset
|
1193 |
Exn of exn; |
224887671646
handle_error: capture error msgs, even if no exception raised;
wenzelm
parents:
4995
diff
changeset
|
1194 |
|
3699 | 1195 |
fun handle_error f x = |
1196 |
let |
|
4945 | 1197 |
val buffer = ref ([]: string list); |
1198 |
fun capture s = buffer := ! buffer @ [s]; |
|
5037
224887671646
handle_error: capture error msgs, even if no exception raised;
wenzelm
parents:
4995
diff
changeset
|
1199 |
fun err_msg () = if not (null (! buffer)) then error_msg (cat_lines (! buffer)) else (); |
3699 | 1200 |
in |
5037
224887671646
handle_error: capture error msgs, even if no exception raised;
wenzelm
parents:
4995
diff
changeset
|
1201 |
(case Result (setmp error_fn capture f x) handle exn => Exn exn of |
224887671646
handle_error: capture error msgs, even if no exception raised;
wenzelm
parents:
4995
diff
changeset
|
1202 |
Result y => (err_msg (); OK y) |
224887671646
handle_error: capture error msgs, even if no exception raised;
wenzelm
parents:
4995
diff
changeset
|
1203 |
| Exn ERROR => Error (cat_lines (! buffer)) |
224887671646
handle_error: capture error msgs, even if no exception raised;
wenzelm
parents:
4995
diff
changeset
|
1204 |
| Exn exn => (err_msg (); raise exn)) |
3624 | 1205 |
end; |
1206 |
||
1207 |
||
5037
224887671646
handle_error: capture error msgs, even if no exception raised;
wenzelm
parents:
4995
diff
changeset
|
1208 |
(* transform ERROR into ERROR_MESSAGE *) |
4923 | 1209 |
|
1210 |
exception ERROR_MESSAGE of string; |
|
1211 |
||
1212 |
fun transform_error f x = |
|
1213 |
(case handle_error f x of |
|
1214 |
OK y => y |
|
1215 |
| Error msg => raise ERROR_MESSAGE msg); |
|
1216 |
||
1217 |
||
5904 | 1218 |
(* transform any exception, including ERROR *) |
1219 |
||
1220 |
fun transform_failure exn f x = |
|
13488 | 1221 |
transform_error f x handle Interrupt => raise Interrupt | e => raise exn e; |
5904 | 1222 |
|
1223 |
||
233 | 1224 |
|
1225 |
(** timing **) |
|
1226 |
||
4326 | 1227 |
(*a conditional timing function: applies f to () and, if the flag is true, |
8999 | 1228 |
prints its runtime on warning channel*) |
4326 | 1229 |
fun cond_timeit flag f = |
1230 |
if flag then |
|
1231 |
let val start = startTiming() |
|
1232 |
val result = f () |
|
8999 | 1233 |
in warning (endTiming start); result end |
4326 | 1234 |
else f (); |
1235 |
||
233 | 1236 |
(*unconditional timing function*) |
2243
3ebeaaacfbd1
Eta-expanded some declarations that are illegal under value polymorphism
paulson
parents:
2196
diff
changeset
|
1237 |
fun timeit x = cond_timeit true x; |
233 | 1238 |
|
1239 |
(*timed application function*) |
|
1240 |
fun timeap f x = timeit (fn () => f x); |
|
12795 | 1241 |
fun timeap_msg s f x = (warning s; timeap f x); |
233 | 1242 |
|
8999 | 1243 |
(*global timing mode*) |
1244 |
val timing = ref false; |
|
1245 |
||
3606 | 1246 |
|
233 | 1247 |
|
10692 | 1248 |
(** rational numbers **) |
1249 |
||
1250 |
datatype rat = Rat of bool * int * int |
|
1251 |
||
1252 |
fun rep_rat(Rat(a,p,q)) = (if a then p else ~p,q) |
|
1253 |
||
1254 |
fun ratnorm(a,p,q) = if p=0 then Rat(a,0,1) else |
|
1255 |
let val absp = abs p |
|
1256 |
val m = gcd(absp,q) |
|
1257 |
in Rat(a = (0 <= p), absp div m, q div m) end; |
|
1258 |
||
1259 |
fun ratadd(Rat(a,p,q),Rat(b,r,s)) = |
|
1260 |
let val den = lcm(q,s) |
|
1261 |
val p = p*(den div q) and r = r*(den div s) |
|
1262 |
val num = (if a then p else ~p) + (if b then r else ~r) |
|
1263 |
in ratnorm(true,num,den) end; |
|
1264 |
||
1265 |
fun ratmul(Rat(a,p,q),Rat(b,r,s)) = ratnorm(a=b,p*r,q*s) |
|
1266 |
||
1267 |
fun ratinv(Rat(a,p,q)) = if p=0 then error("ratinv") else Rat(a,q,p) |
|
1268 |
||
1269 |
fun int_ratdiv(p,q) = |
|
1270 |
if q=0 then error("int_ratdiv") else ratnorm(0<=q, p, abs q) |
|
1271 |
||
1272 |
fun ratneg(Rat(b,p,q)) = Rat(not b,p,q); |
|
1273 |
||
1274 |
fun rat_of_int i = if i < 0 then Rat(false,abs i,1) else Rat(true,i,1); |
|
1275 |
||
1276 |
||
4621 | 1277 |
(** misc **) |
233 | 1278 |
|
9830 | 1279 |
fun overwrite_warn (args as (alist, (a, _))) msg = |
1280 |
(if is_none (assoc (alist, a)) then () else warning msg; |
|
1281 |
overwrite args); |
|
9721 | 1282 |
|
233 | 1283 |
(*use the keyfun to make a list of (x, key) pairs*) |
0 | 1284 |
fun make_keylist (keyfun: 'a->'b) : 'a list -> ('a * 'b) list = |
233 | 1285 |
let fun keypair x = (x, keyfun x) |
1286 |
in map keypair end; |
|
0 | 1287 |
|
233 | 1288 |
(*given a list of (x, key) pairs and a searchkey |
0 | 1289 |
return the list of xs from each pair whose key equals searchkey*) |
1290 |
fun keyfilter [] searchkey = [] |
|
233 | 1291 |
| keyfilter ((x, key) :: pairs) searchkey = |
1292 |
if key = searchkey then x :: keyfilter pairs searchkey |
|
1293 |
else keyfilter pairs searchkey; |
|
0 | 1294 |
|
1295 |
||
1296 |
(*Partition list into elements that satisfy predicate and those that don't. |
|
233 | 1297 |
Preserves order of elements in both lists.*) |
0 | 1298 |
fun partition (pred: 'a->bool) (ys: 'a list) : ('a list * 'a list) = |
1299 |
let fun part ([], answer) = answer |
|
233 | 1300 |
| part (x::xs, (ys, ns)) = if pred(x) |
1301 |
then part (xs, (x::ys, ns)) |
|
1302 |
else part (xs, (ys, x::ns)) |
|
1303 |
in part (rev ys, ([], [])) end; |
|
0 | 1304 |
|
1305 |
||
1306 |
fun partition_eq (eq:'a * 'a -> bool) = |
|
1307 |
let fun part [] = [] |
|
233 | 1308 |
| part (x::ys) = let val (xs, xs') = partition (apl(x, eq)) ys |
1309 |
in (x::xs)::(part xs') end |
|
0 | 1310 |
in part end; |
1311 |
||
1312 |
||
233 | 1313 |
(*Partition a list into buckets [ bi, b(i+1), ..., bj ] |
0 | 1314 |
putting x in bk if p(k)(x) holds. Preserve order of elements if possible.*) |
1315 |
fun partition_list p i j = |
|
233 | 1316 |
let fun part k xs = |
1317 |
if k>j then |
|
0 | 1318 |
(case xs of [] => [] |
1319 |
| _ => raise LIST "partition_list") |
|
1320 |
else |
|
233 | 1321 |
let val (ns, rest) = partition (p k) xs; |
1322 |
in ns :: part(k+1)rest end |
|
0 | 1323 |
in part i end; |
1324 |
||
1325 |
||
233 | 1326 |
(* transitive closure (not Warshall's algorithm) *) |
0 | 1327 |
|
233 | 1328 |
fun transitive_closure [] = [] |
1329 |
| transitive_closure ((x, ys)::ps) = |
|
1330 |
let val qs = transitive_closure ps |
|
2182
29e56f003599
Removal of polymorphic equality via mem, subset, eq_set, etc
paulson
parents:
2175
diff
changeset
|
1331 |
val zs = foldl (fn (zs, y) => assocs qs y union_string zs) (ys, ys) |
5904 | 1332 |
fun step(u, us) = (u, if x mem_string us then zs union_string us |
2243
3ebeaaacfbd1
Eta-expanded some declarations that are illegal under value polymorphism
paulson
parents:
2196
diff
changeset
|
1333 |
else us) |
233 | 1334 |
in (x, zs) :: map step qs end; |
0 | 1335 |
|
1336 |
||
233 | 1337 |
(* generating identifiers *) |
0 | 1338 |
|
4063 | 1339 |
(** Freshly generated identifiers; supplied prefix MUST start with a letter **) |
0 | 1340 |
local |
4063 | 1341 |
(*Maps 0-63 to A-Z, a-z, 0-9 or _ or ' for generating random identifiers*) |
1342 |
fun char i = if i<26 then chr (ord "A" + i) |
|
5904 | 1343 |
else if i<52 then chr (ord "a" + i - 26) |
1344 |
else if i<62 then chr (ord"0" + i - 52) |
|
1345 |
else if i=62 then "_" |
|
1346 |
else (*i=63*) "'"; |
|
4063 | 1347 |
|
1348 |
val charVec = Vector.tabulate (64, char); |
|
1349 |
||
5904 | 1350 |
fun newid n = |
1351 |
let |
|
4284 | 1352 |
in implode (map (fn i => Vector.sub(charVec,i)) (radixpand (64,n))) end; |
2003 | 1353 |
|
4284 | 1354 |
val seedr = ref 0; |
0 | 1355 |
|
4063 | 1356 |
in |
4284 | 1357 |
|
12346 | 1358 |
fun gensym pre = pre ^ (#1(newid (!seedr), inc seedr)); |
2003 | 1359 |
|
4063 | 1360 |
end; |
1361 |
||
1362 |
||
233 | 1363 |
(* lexical scanning *) |
0 | 1364 |
|
233 | 1365 |
(*scan a list of characters into "words" composed of "letters" (recognized by |
1366 |
is_let) and separated by any number of non-"letters"*) |
|
1367 |
fun scanwords is_let cs = |
|
0 | 1368 |
let fun scan1 [] = [] |
233 | 1369 |
| scan1 cs = |
1370 |
let val (lets, rest) = take_prefix is_let cs |
|
1371 |
in implode lets :: scanwords is_let rest end; |
|
1372 |
in scan1 (#2 (take_prefix (not o is_let) cs)) end; |
|
24
f3d4ff75d9f2
added functions that operate on filenames: split_filename (originally located
clasohm
parents:
0
diff
changeset
|
1373 |
|
4212 | 1374 |
|
1375 |
||
1376 |
(* Variable-branching trees: for proof terms etc. *) |
|
1377 |
datatype 'a mtree = Join of 'a * 'a mtree list; |
|
1378 |
||
1379 |
||
1364
8ea1a962ad72
files now define a structure to allow SML/NJ to optimize the code
clasohm
parents:
1290
diff
changeset
|
1380 |
end; |
8ea1a962ad72
files now define a structure to allow SML/NJ to optimize the code
clasohm
parents:
1290
diff
changeset
|
1381 |
|
8ea1a962ad72
files now define a structure to allow SML/NJ to optimize the code
clasohm
parents:
1290
diff
changeset
|
1382 |
open Library; |