WebCHURCH - CheatSheet

last revision 2015/03/14 - feedback is welcome: claus.moebus(at)uni-oldenburg.de -

When working through the WebCHURCH-Tutorial Probabilistic Models of Cognition my impression is that the official documentation is only partial compatible with the tutorial. Furthermore, some WebCHURCH-procedures are not compatible with the SCHEME R6RS-Standard (e.g. 'apply', 'case').

Most expressions are evaluated according applicative-order. When expressions are evaluated according normal-order (= delayed or lazy evaluation) this is mentioned explicitly.

My doc is based on:
1. the WebCHURCH doc
2. the Revised6 Report on the Algorithmic Language Scheme - R6RS
3. Dybvig, The Scheme Programming Language, MIT Press, 2009, 4/e
4. Scott, Programming Language Pragmatics, Morgan Kaufman, 2009, 3/e
5. Lunn et al., The BUGS Book - A Practical Introduction to Bayesian Analysis - , CRC Press, 2013

Math Ops

(+ val …)

• + is the name of the built-in operation for addition.
• val …: A bunch of numeric operands.
• Returns: sum of the numeric operands.

(- val …)

• - is the name of the built-in operation for subtraction.
• val …: A bunch of numeric operands.
• Returns: With two or more arguments, this procedures returns the difference of its arguments, associating to the left.
• Returns: With one argument, however, it returns the additive inverse of its argument.

(* val …)

• * is the name of the built-in operation for multiplication.
• val …: A bunch of numeric operands.
• Returns: product of the numeric operands.

(/ val …)

• / is the name of the built-in operation for division.
• val …: A bunch of numeric operands.
• Returns: With two or more arguments, this procedure returns the quotient of its arguments, associating to the left.
• Returns: With one argument, however, it returns the multiplicative inverse of its argument.

(< val1 val2 …)

• Less than ?
• val1 val2…: A bunch of two ore more numbers.
• Returns: boolean

(<= val1 val2 …)

• Less or equal ?
• val1 val2…: A bunch of two ore more numbers.
• Returns: boolean

(= val1 val2 …)

• equal ?
• val1 val2…: A bunch of two ore more numbers.
• Returns: boolean

(> val1 val2 …)

• greater than ?
• val1 val2…: A bunch of two ore more numbers.
• Returns: boolean

(>= val1 val2 …)

• greater or equal ?
• val1 val2…: A bunch of two ore more numbers.
• Returns: boolean
  

A

(and expr …)

• normal-order evaluation
• and is a sequential and. If there are no expr s, #t is returned. Otherwise, the expr s are evaluated from left to right until an expr returns #f or the last expr is reached. In the former case, the and expression returns a #f value without evaluating the remaining expressions. In the latter case, the last expression is evaluated and its value should be returned. In fact, WebChurch returns #t in this case.(2013/11/20)
• expr …: a sequence of expressions with a boolean value
• Returns: a boolean value

(append lst1 lst2 …)

• Append some lists together.
• lsti …: A list.
• Returns: A concatenated list.

(apply proc obj …)

• Proc: procedure
• obj : object or value
• Returns: the values of applying proc to obj

B

(binomial p n)

• is not implemented (2013/11/23) though it appears in the documentation
  
• A random ERP for binomial distributions
  
• p: probability of success
• n: number of independent trials
• Returns: number
  

C

(case key case-clause …)

• key: expression
• case-clause: (lst expr)
• Returns: the value of expr if the value of key is equal? to a member of lst

D

(define variable expression)

• normal-order evaluation
• The definition form describes a definition used to create variable bindings and may appear anywhere other definitions may appear.
• variable: a symbol which is bound to the value of expression.
• expression: a constant.
• expression: the value of a simple or compound procedure (e.g. a lambda-expression).
  

(define (variable parameter …) body )

• normal-order evaluation
• is equivalent to: (define variable (lambda (parameter …) body )).
• is the definition of a function with name variable and zero or more parameters parameter.
  

(density list {string})

• Displays the graph of a probability density function.
• lst: a list of samples drawn from a continous probability distribution.
• string: optional string which is used as the title of the density diagram.

(display expr)

• Displays the value of expr (including numbers, strings, lists, etc). Note: this is mostly for debugging, not for modeling (not implemented in WebChurch, 2013/11/25)
• expr: a Church expression
• Returns: void

E

(equal? obj1 obj2)

• Check if two things are equivalent. (Recursive on lists, vectors, etc.)
• obj1: Scheme object or value
• obj2: Scheme object or value
• Returns: boolean (#t or #f)

(expt val1 val2)

• Raise a number to a power val1^val2
• val1: A number
• val2: A number
• Returns: the value of val1^val2

F

“false” or “#f”

• boolean constant (must be written without “”)

(fifth lst)

• Returns the fifth element of a list.
• lst: the list
• Returns: the fifth element of the list

(first lst)

• Get the first element of a list or a pair.
• lst: The list or pair.
• Returns: First element of the list or pair.

(flip {weight})

• Flip a fair or weighted coin (= Bernouilli trial).
• weight: If given, the coin is biased with this weight.
• Returns: true or false

(flatten nlst)

• flattens a nested list (removes the inner parenthesis of nlst)
• nlst: a nested list
• Returns: a list of the elements of the nested list

(fold proc init lst)

• Fold. (You know you want to….)
• proc: The procedure to apply, which should take two arguments: the next value from lst and the accumulated value.
• init: The value to start with (initial value for the accumulated value argument of proc).
• lst: The list to fold over.
• Returns: the accumulated value
• Example: (fold * 1 '(1 2 3)) => 6
• Example: (fold + 0 '(1 2 3)) => 6

(fourth lst)

• Returns the fourth element of a list.
• lst: the list
• Returns: the fourth element of the list

G

(gaussian mean stdev)

• A random ERP for Gaussian distributions
• : mean of the Gaussian
• stdev: standard deviation of the Gaussian
• Returns: a number sampled from the Normal (Gaussian) Distribution

(geometric weight)

• is not implemented but defined in chapter 01 of the tutorial
• The distribution of the number of failures y = x-1 where x is the number of Bernoulli trials (flips of a fair or weighted coin) required for one success to occur.
• weight: the success probability for each Bernoulli trial
• Returns: x-1 the number of failures before the success occurs

H

(hist list {string})

• displays a histogram.
• lst: a list of samples drawn from a discrete probability distribution
• string: optional string which is used as the title of the histogram.

I

(if test consequent {alternate})

• normal-order evaluation
• test, consequent, and alternate must be expressions.
• Returns: first, test is evaluated. If it yields a true value, then consequent is evaluated and its values are returned. Otherwise alternate is evaluated and its values are returned.
• Returns: If test yields #f and no alternate is specified, then the result of the expression is unspecified.

J

K

L

(lambda formals body)

• normal-order evaluation
• A lambda expression evaluates to a procedure. The environment in effect when the lambda expression is evaluated is remembered as part of the procedure.
• formals must be a formal parameter list.
• body consists of one expression (e.g. a lambda expression).

(length lst)

• Get the length of a list
• lst: The list.
• Returns: The length (an integer).

(let ((var val) …) expr …)

• Let binds variables in the scope of the body of the let.
• assignments: An expression '((var val) …)
• expr …: Body expressions that are evaluated within the environment where variables are assigned.
• Returns: the result of evaluating the last body expr

(list obj …)

• Builds a list of the values of a bunch of obj
  obj …: Things to make into a list
  Returns: A list of the values of the obj …
  

M

(map proc list …)

• Apply a procedure to each element of some lists.
• proc: The procedure to apply.
• list …: The lists to map over.
• Returns: a list of values of procedure applications.

(mem procedure)

• normal-order evaluation
• generates a memoized version of procedure.
• procedure: variable name of a procedure.
• Returns: a memoized version of procedure.
  

(mh-query samples lag defines query-expr condition-expr)

• normal-order evaluation
• Do inference using the Metropolis-Hastings algorithm (as described in Goodman, et al., 2008).
• samples: The number of samples to take.
  
• lag: The number of iterations in between samples.
  
• defines …: A sequence of definitions (usually setting up the generative model).
  
• query-expr: The query expression.
  
• condition-expr = (condition boolean-expr) | boolean-expr.
• boolean-expr: Church-expression with a boolean value.
• Returns: A list of samples from the conditional distribution.
  

N

(null? lst)

• Check if a list is null or empty.
• lst: The list.
• Returns: boolean (#t or #f)
• Returns #t when the list is equal to '().

O

(or expr …)

• normal-order evaluation
• Or is a sequential or. If there are no expr s, #f is returned. Otherwise, the expr s are evaluated from left to right until a expr returns a #t value or the last expr is reached. In the former case, the or expression returns a #t without evaluating the remaining expressions. In the latter case, the last expression is evaluated and its value is returned. In fact, WebChurch returns the value of expr in all cases.(2013/11/20)
• expr …: a sequence of expressions with a boolean value.
• Returns: a boolean value.

P

(pair obj1 obj2)

• Build a pair (obj1 . obj2)
• obj1: The first element (can be selected by “first”)
• obj2: The second element (can be selected by “rest”)
• Returns: A pair

(pair? obj)

• Returns #t if obj is a pair (or list)
• obj: Church object
• Returns: boolean

Q

(quote datum)

• normal-order evaluation
• evaluates to datum
• datum is any valid Church-expression
• Returns: datum

'datum is equivalent to (quote datum)

• normal-order evaluation
• datum is any valid Church-expression.
  

R

(rejection-query defines query-expr condition-expr)

• normal-order evaluation
• implements rejection sampling, which is slow but sound.
• defines …: Definitions to evaluate – set up bindings for the query
• query-expr: The expression you want to know about
• condition-expr = (condition boolean-expr) | boolean-expr.
• Returns: A conditional sample (a value of query-expr, if the value of condition-expr is true)

(repeat N procedure)

• Repeats a procedure a given number of times.
• N: number of times to repeat.
• procedure: the procedure to repeat.
• Returns: a list where each element is the result of a call of proc. If N=0 the list is empty.

(rest lst)

• Get the tail of a list (all but the first element) or the second element of a pair
• lst: a list or a pair
• Returns: tail of list or second element of pair

S

(second lst)

• Returns the second element of a list.
• lst: the list
• Returns: the second element of the list

(seventh lst)

• Returns the seventh element of a list.
• lst: the list
• Returns: the seventh element of the list

(sixth lst)

• Returns the sixth element of a list.
• lst: the list
• Returns: the sixth element of the list

(sum lst)

• Calculates the sum of elements in a list.
• lst: the list
• Returns: The sum of the list

T

(third lst)

• Returns the third element of a list.
• lst: the list
• Returns: the third element of the list

“true” or “#t”

• boolean constant (must be written without “”)

U

(uniform-draw list)

• Samples a random element from list according to a uniform pdf
• list: a list of objects
• Returns: object

V

W

X

Y

Z