doc-src/Logics/HOL.tex
changeset 3487 62a6a08471e4
parent 3315 16d603a560d8
child 3489 afa802078173
equal deleted inserted replaced
3486:10cf84e5d2c2 3487:62a6a08471e4
  1283   \tt\at  & $[\alpha\,list,\alpha\,list]\To \alpha\,list$ & Left 65 & append \\
  1283   \tt\at  & $[\alpha\,list,\alpha\,list]\To \alpha\,list$ & Left 65 & append \\
  1284   \cdx{map}     & $(\alpha\To\beta) \To (\alpha\,list \To \beta\,list)$
  1284   \cdx{map}     & $(\alpha\To\beta) \To (\alpha\,list \To \beta\,list)$
  1285         & & mapping functional\\
  1285         & & mapping functional\\
  1286   \cdx{filter}  & $(\alpha \To bool) \To (\alpha\,list \To \alpha\,list)$
  1286   \cdx{filter}  & $(\alpha \To bool) \To (\alpha\,list \To \alpha\,list)$
  1287         & & filter functional\\
  1287         & & filter functional\\
  1288   \cdx{set_of_list}& $\alpha\,list \To \alpha\,set$ & & elements\\
  1288   \cdx{set}& $\alpha\,list \To \alpha\,set$ & & elements\\
  1289   \sdx{mem}  & $[\alpha,\alpha\,list]\To bool$    &  Left 55   & membership\\
  1289   \sdx{mem}  & $[\alpha,\alpha\,list]\To bool$    &  Left 55   & membership\\
  1290   \cdx{foldl}   & $(\beta\To\alpha\To\beta) \To \beta \To \alpha\,list \To \beta$ &
  1290   \cdx{foldl}   & $(\beta\To\alpha\To\beta) \To \beta \To \alpha\,list \To \beta$ &
  1291   & iteration \\
  1291   & iteration \\
  1292   \cdx{concat}   & $(\alpha\,list)list\To \alpha\,list$ & & concatenation \\
  1292   \cdx{concat}   & $(\alpha\,list)list\To \alpha\,list$ & & concatenation \\
  1293   \cdx{rev}     & $\alpha\,list \To \alpha\,list$ & & reverse \\
  1293   \cdx{rev}     & $\alpha\,list \To \alpha\,list$ & & reverse \\
  1331 map f (x#xs) = f x # map f xs
  1331 map f (x#xs) = f x # map f xs
  1332 
  1332 
  1333 filter P [] = []
  1333 filter P [] = []
  1334 filter P (x#xs) = (if P x then x#filter P xs else filter P xs)
  1334 filter P (x#xs) = (if P x then x#filter P xs else filter P xs)
  1335 
  1335 
  1336 set_of_list [] = \ttlbrace\ttrbrace
  1336 set [] = \ttlbrace\ttrbrace
  1337 set_of_list (x#xs) = insert x (set_of_list xs)
  1337 set (x#xs) = insert x (set xs)
  1338 
  1338 
  1339 x mem [] = False
  1339 x mem [] = False
  1340 x mem (y#ys) = (if y=x then True else x mem ys)
  1340 x mem (y#ys) = (if y=x then True else x mem ys)
  1341 
  1341 
  1342 foldl f a [] = a
  1342 foldl f a [] = a