la.la

Class Library

java.lang.Object

la.la.Library

public class Library
extends java.lang.Object

The standard library of predefined Functions and other Values; also see Environment.

Nested Class Summary

Nested Classes

Modifier and Type	Class and Description
static class	Library.Power EXPERIMENTAL, The class of Cts2Cts Functions, Power(c,p)(x)=c.xp.

Field Summary

Fields

Modifier and Type	Field and Description
static Function.CtsD2CtsD.WithInverse	cartesian2polar This Function, R2→R2, converts Cartesian coordinates ⟨x,y⟩ to polar coordinates ⟨r,θ⟩.
static Function.Native3	curry curry: ((t, u) → v) → (t → u → v).
static Environment	env An Environment binding names (Strings) to standard Functions, for example, "id"→id, "fst"→fst, etc.
static Function.Cts2Cts.WithInverse	exp exp is a Cts2Cts with an Inverse-Function, i.e., log.
static Function	frth Return the fourth element of a Value.Tuple.
static Function	fst Return the first element of a Value.Tuple.
static Function	id The identity Function, id x = x.
static Function.Cts2Cts.WithInverse	inv The function, inv(x)=1/x.
static Function.Cts2Cts.WithInverse	log log is a Cts2Cts with an Inverse-Function, i.e., exp.
static Function.CtsD2CtsD.WithInverse	polar2cartesian This Function, R2→R2, converts polar coordinates ⟨r,θ⟩ to Cartesian ⟨x,y⟩.
static Function	snd Return the second element of a Value.Tuple.
static Function	thrd Return the third element of a Value.Tuple.
static Function.Native2	uncurry uncurry: (t → u → v) → ((t, u) → v).
static Function.Native2	whnf whnf p0 p1 can be used to make a parameter (p0) strict, say: force p0 to weak head normal form (WHNF), but return p1 (also in WHNF).

Constructor Summary

Constructors

Constructor and Description
Library()

Method Summary

Modifier and Type	Method and Description
static Function.Native2	bOp(int op) Return a curried Function based on the binary operator, 'op' (+, *, etc).
static void	main(java.lang.String[] argv) Run a few simple tests on Library.
static Function.Native	uOp(int op) Return a Function based on the unary operator, 'op' (not, -, hd, etc.).

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Field Detail

id

public static final Function id

The identity Function, id x = x.

fst

public static final Function fst

Return the first element of a Value.Tuple.

snd

public static final Function snd

Return the second element of a Value.Tuple.

thrd

public static final Function thrd

Return the third element of a Value.Tuple.

frth

public static final Function frth

Return the fourth element of a Value.Tuple.

curry

public static final Function.Native3 curry

curry: ((t, u) → v) → (t → u → v). curry fu x y = fu(x, y). Also see uncurry.

uncurry

public static final Function.Native2 uncurry

uncurry: (t → u → v) → ((t, u) → v). uncurry fc (x, y) = fc x y. Also see uncurry.

whnf

public static final Function.Native2 whnf

whnf p0 p1 can be used to make a parameter (p0) strict, say: force p0 to weak head normal form (WHNF), but return p1 (also in WHNF).

inv

public static final Function.Cts2Cts.WithInverse inv

The function, inv(x)=1/x. It is its own Inverse-function, i.e., inv(inv(x))=x, provided x≠0. Its integral is log.

exp

public static final Function.Cts2Cts.WithInverse exp

exp is a Cts2Cts with an Inverse-Function, i.e., log.

log

public static final Function.Cts2Cts.WithInverse log

log is a Cts2Cts with an Inverse-Function, i.e., exp. Its derivative is inv.

polar2cartesian

public static final Function.CtsD2CtsD.WithInverse polar2cartesian

This Function, R²→R², converts polar coordinates ⟨r,θ⟩ to Cartesian ⟨x,y⟩. The Jacobian matrix is {{cos(θ), −r.sin(θ)}, {sin(θ), r.cos(θ)}}. The negative log of its determinant, nlJ(r_t), equals −log(r). These are used by apply(.) to "adjust" the AoMs of the result. The inverse Function is cartesian2polar⟨x,y⟩.
Note that

       {{cos(θ), −r.sin(θ)}, 
        {sin(θ),  r.cos(θ)}}
     × {{x/r,   y/r}, 
        {−y/r2, x/r2}}
     = {{x.cosθ/r+y.sinθ/r, y.cosθ/r−x.sinθ/r},
        {x.sinθ/r−y.cosθ/r, y.sinθ/r+x.cosθ/r}}
     = {{1, 0},
        {0, 1}}. 

cartesian2polar

public static final Function.CtsD2CtsD.WithInverse cartesian2polar

This Function, R²→R², converts Cartesian coordinates ⟨x,y⟩ to polar coordinates ⟨r,θ⟩. The Jacobian-matrix is {{x/r, y/r}, {−y/r², x/r²}}. The negative log of its determinant, nlJ(xy), equals +log(r). These are used by apply(.) to "adjust" the AoMs of the result. The inverse Function is polar2cartesian⟨r,θ⟩.

env

public static final Environment env

An Environment binding names (Strings) to standard Functions, for example, "id"→id, "fst"→fst, etc. Also see lookup

Constructor Detail

Library

public Library()

Method Detail

uOp

public static Function.Native uOp(int op)

Return a Function based on the unary operator, 'op' (not, -, hd, etc.). Also see Value.uOp(int) and bOp(int).

bOp

public static Function.Native2 bOp(int op)

Return a curried Function based on the binary operator, 'op' (+, *, etc). Also see Value.bOp(int, la.la.Value) and uOp(int).

main

public static void main(java.lang.String[] argv)

Run a few simple tests on Library.