module EqManips.BaseLibrary( defaultSymbolTable ) where

import EqManips.Types
import Data.Map

defaultSymbolTable :: Map String (Formula ListForm)
defaultSymbolTable =  fromList [("concat",{-(lambda (((list )  y) y)((x (list ) ) x)(((:: x xs) y) (:: x (apply concat xs y)))((a b) undefined))-} Formula (Lambda 148011272 [([List 12303291 [],Variable "y"],Variable "y"),([Variable "x",List 12303291 []],Variable "x"),([BinOp 867 OpCons [Variable "x",Variable "xs"],Variable "y"],BinOp 9121 OpCons [Variable "x",App 8361 (Variable "concat") [Variable "xs",Variable "y"]]),([Variable "a",Variable "b"],Variable "undefined")])),("cons",{-(lambda ((a b) (:: b a)))-} Formula (Lambda 1821 [([Variable "a",Variable "b"],BinOp 937 OpCons [Variable "b",Variable "a"])])),("derivaten",{-(lambda ((f var 0) f)((f var 1) (derivate (Force f) (Force var)))((f var n) (derivate (Force (apply derivaten f var (poly n (0, -1) (1, 1) ))) (Force var))))-} Formula (Lambda (-1019272245) [([Variable "f",Variable "var",CInteger 0],Variable "f"),([Variable "f",Variable "var",CInteger 1],Derivate (-1808503526) (Meta 1610613004 Force (Variable "f")) (Meta (-1879047910) Force (Variable "var"))),([Variable "f",Variable "var",Variable "n"],Derivate (-1759068902) (Meta (-1342176258) Force (App 12171 (Variable "derivaten") [Variable "f",Variable "var",Poly 107 (Polynome "n" [(CoeffInt 0,PolyRest (CoeffInt (-1))),(CoeffInt 1,PolyRest (CoeffInt 1))])])) (Meta (-1879047910) Force (Variable "var")))])),("eq",{-(lambda ((a a) True)((a b) False))-} Formula (Lambda (-2147479268) [([Variable "a",Variable "a"],Truth True),([Variable "a",Variable "b"],Truth False)])),("filter",{-(lambda ((pred (list ) ) (list ) )((pred (:: x xs)) (apply concat (apply if (apply pred x) (list  x)  (list ) ) (apply filter pred xs)))((a b) undefined))-} Formula (Lambda (-1382858888) [([Variable "pred",List 12303291 []],List 12303291 []),([Variable "pred",BinOp 867 OpCons [Variable "x",Variable "xs"]],App 721864843 (Variable "concat") [App 90233179 (Variable "if") [App 6848 (Variable "pred") [Variable "x"],List 12303299 [Variable "x"],List 12303291 []],App 9691 (Variable "filter") [Variable "pred",Variable "xs"]]),([Variable "a",Variable "b"],Variable "undefined")])),("foldl",{-(lambda ((f acc (list ) ) acc)((f acc (:: x xs)) (apply foldl f (apply f acc x) xs))((a b c) undefined))-} Formula (Lambda 12512956 [([Variable "f",Variable "acc",List 12303291 []],Variable "acc"),([Variable "f",Variable "acc",BinOp 867 OpCons [Variable "x",Variable "xs"]],App 16691 (Variable "foldl") [Variable "f",App 3880 (Variable "f") [Variable "acc",Variable "x"],Variable "xs"]),([Variable "a",Variable "b",Variable "c"],Variable "undefined")])),("foldr",{-(lambda ((f acc (list ) ) acc)((f acc (:: x xs)) (apply f (apply foldr f acc xs) x))((a b c) undefined))-} Formula (Lambda 12855048 [([Variable "f",Variable "acc",List 12303291 []],Variable "acc"),([Variable "f",Variable "acc",BinOp 867 OpCons [Variable "x",Variable "xs"]],App 102216 (Variable "f") [App 12587 (Variable "foldr") [Variable "f",Variable "acc",Variable "xs"],Variable "x"]),([Variable "a",Variable "b",Variable "c"],Variable "undefined")])),("if",{-(lambda ((True a b) a)((False a b) b)((otherwise a b) undefined))-} Formula (Lambda 1025416 [([Truth True,Variable "a",Variable "b"],Variable "a"),([Truth False,Variable "a",Variable "b"],Variable "b"),([Variable "otherwise",Variable "a",Variable "b"],Variable "undefined")])),("length",{-(lambda ((lst) (apply lengthIntern 0 lst)))-} Formula (Lambda 20416 [([Variable "lst"],App 20091 (Variable "lengthIntern") [CInteger 0,Variable "lst"])])),("lengthIntern",{-(lambda ((acc (list ) ) acc)((acc (:: x xs)) (apply lengthIntern (poly acc (0, 1) (1, 1) ) xs))((a b) undefined))-} Formula (Lambda 12413172 [([Variable "acc",List 12303291 []],Variable "acc"),([Variable "acc",BinOp 867 OpCons [Variable "x",Variable "xs"]],App 18057 (Variable "lengthIntern") [Poly 1073742121 (Polynome "acc" [(CoeffInt 0,PolyRest (CoeffInt 1)),(CoeffInt 1,PolyRest (CoeffInt 1))]),Variable "xs"]),([Variable "a",Variable "b"],Variable "undefined")])),("listFromTo",{-(lambda ((a a) (list  a) )((a b) (:: a (apply listFromTo (poly a (0, 1) (1, 1) ) b))))-} Formula (Lambda 12374757 [([Variable "a",Variable "a"],List 12303322 [Variable "a"]),([Variable "a",Variable "b"],BinOp 16768 OpCons [Variable "a",App 16960 (Variable "listFromTo") [Poly 1073741923 (Polynome "a" [(CoeffInt 0,PolyRest (CoeffInt 1)),(CoeffInt 1,PolyRest (CoeffInt 1))]),Variable "b"]])])),("listFromToBy",{-(lambda ((a by a) (list  a) )((a by maxi) (:: a (apply listFromToBy (poly a (0, (poly by (1, 1) )) (1, 1) ) by maxi))))-} Formula (Lambda 12455077 [([Variable "a",Variable "by",Variable "a"],List 12303322 [Variable "a"]),([Variable "a",Variable "by",Variable "maxi"],BinOp 27967 OpCons [Variable "a",App 28175 (Variable "listFromToBy") [Poly 1073741974 (Polynome "a" [(CoeffInt 0,Polynome "by" [(CoeffInt 1,PolyRest (CoeffInt 1))]),(CoeffInt 1,PolyRest (CoeffInt 1))]),Variable "by",Variable "maxi"]])])),("map",{-(lambda ((f (list ) ) (list ) )((f (:: x xs)) (:: (apply f x) (apply map f xs)))((f otherwise) undefined))-} Formula (Lambda 24658672 [([Variable "f",List 12303291 []],List 12303291 []),([Variable "f",BinOp 867 OpCons [Variable "x",Variable "xs"]],BinOp 8427 OpCons [App 1552 (Variable "f") [Variable "x"],App 4147 (Variable "map") [Variable "f",Variable "xs"]]),([Variable "f",Variable "otherwise"],Variable "undefined")])),("max",{-(lambda ((a b) (apply if (> a b) a b)))-} Formula (Lambda 60786 [([Variable "a",Variable "b"],App 59922 (Variable "if") [BinOp 918 OpGt [Variable "a",Variable "b"],Variable "a",Variable "b"])])),("min",{-(lambda ((a b) (apply if (< a b) a b)))-} Formula (Lambda 61554 [([Variable "a",Variable "b"],App 60690 (Variable "if") [BinOp 906 OpLt [Variable "a",Variable "b"],Variable "a",Variable "b"])])),("modintern",{-(lambda ((True rest num) rest)((False rest num) (apply modintern (< (poly num (0, (poly rest (1, 1) )) (1, -1) ) num) (poly num (0, (poly rest (1, 1) )) (1, -1) ) num)))-} Formula (Lambda 1040531 [([Truth True,Variable "rest",Variable "num"],Variable "rest"),([Truth False,Variable "rest",Variable "num"],App 257624 (Variable "modintern") [BinOp 3952 OpLt [Poly 448 (Polynome "num" [(CoeffInt 0,Polynome "rest" [(CoeffInt 1,PolyRest (CoeffInt 1))]),(CoeffInt 1,PolyRest (CoeffInt (-1)))]),Variable "num"],Poly 448 (Polynome "num" [(CoeffInt 0,Polynome "rest" [(CoeffInt 1,PolyRest (CoeffInt 1))]),(CoeffInt 1,PolyRest (CoeffInt (-1)))]),Variable "num"])])),("modulo",{-(lambda ((n p) (apply modintern (< n p) n p)))-} Formula (Lambda 63750 [([Variable "n",Variable "p"],App 62984 (Variable "modintern") [BinOp 800 OpLt [Variable "n",Variable "p"],Variable "n",Variable "p"])])),("reverse",{-(lambda ((lst) (apply foldl cons (list )  lst)))-} Formula (Lambda 98407080 [([Variable "lst"],App 98406739 (Variable "foldl") [Variable "cons",List 12303291 [],Variable "lst"])])),("taylor",{-(lambda ((f var a n) (Sort (Cleanup (apply taylorin (LambdaBuild (lambda (((Force var)) (Force f)))) var a n)))))-} Formula (Lambda 1879091869 [([Variable "f",Variable "var",Variable "a",Variable "n"],Meta 1879051629 Sort (Meta 34423 Cleanup (App 538384 (Variable "taylorin") [Meta (-1895824344) LambdaBuild (Lambda (-268434904) [([Meta (-1879047910) Force (Variable "var")],Meta 1610613004 Force (Variable "f"))]),Variable "var",Variable "a",Variable "n"])))])),("taylorin",{-(lambda ((f var a 0) (apply f a))((f var a n) (+ (apply taylorin f var a (poly n (0, -1) (1, 1) )) (* (/ (apply (apply derivaten f var (Force n)) a) (! n)) (^ (poly a (0, (poly x (1, 1) )) (1, -1) ) n)))))-} Formula (Lambda 50262095 [([Variable "f",Variable "var",Variable "a",CInteger 0],App 1545 (Variable "f") [Variable "a"]),([Variable "f",Variable "var",Variable "a",Variable "n"],BinOp 12514838 OpAdd [App 43531 (Variable "taylorin") [Variable "f",Variable "var",Variable "a",Poly 107 (Polynome "n" [(CoeffInt 0,PolyRest (CoeffInt (-1))),(CoeffInt 1,PolyRest (CoeffInt 1))])],BinOp 12297802 OpMul [BinOp 1537203 OpDiv [App 192167 (App (-536858900) (Variable "derivaten") [Variable "f",Variable "var",Meta (-536870644) Force (Variable "n")]) [Variable "a"],UnOp 403 OpFactorial (Variable "n")],BinOp 934 OpPow [Poly (-2147483521) (Polynome "a" [(CoeffInt 0,Polynome "x" [(CoeffInt 1,PolyRest (CoeffInt 1))]),(CoeffInt 1,PolyRest (CoeffInt (-1)))]),Variable "n"]]])]))]