Lambda Calculus and Evaluation Strategies

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Lambda Calculus

and

Evaluation Strategies

Ali Saeed Khan

19th December, 2011


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Logic

What is logic?

Formal systematic study of the principles of

Valid inference and

correct reasoning

12/19/2011 EC-215 PLE - Ali Saeed Khan 2


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Formal System

A formal system (also called a logical calculus)

consists of a formal language and a set of

inference rules, used to derive an expression

from one or more other premises that are

supposed or derived.

12/19/2011 3EC-215 PLE - Ali Saeed Khan


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The Lambda Calculus

I t i sa formal system for the study of,

Computability Theory

Computable Recursive Functions

Functions Variable binding and substitution

To model Evaluation Strategies.

typed lambda calculus serves as thefoundation of modern programminglanguages.



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The Lambda Calculus

The -calculus provides simple semantics for

computation, enabling properties of

computation to be studied formally.



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Evaluation Strategy

Set ofrules for evaluating expressions in a

programming language.

Usually these rules are deterministic in nature.

Emphasis is typically placed on functions or

operators: an evaluation strategy defines

when and in what order the arguments to a function

are evaluated, when they are substituted into the function, and

what form that substitution takes.



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Types of Evaluation Strategy

Evaluation strategies divide into two basic

groups, strict and non-strict, based on how

arguments to a function are handled.

Strict Evaluation

Non-Strict Evaluation

Nondeterministic Strategies



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Strict Evaluation

Applicative Order

Call by Value

Call by Reference Call by Sharing

Call by Copy-Restore



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Non-Strict Evaluation

Normal Order

Call by Name

Call by Need/Lazy Evaluation Call by Macro Expansion



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Nondeterministic Strategies

Full Beta-reduction

Call by future

Optimistic Evaluation



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Strict Evaluation

Strict evaluation is where all arguments to a

function are evaluated before the body of the

function is evaluated; and the arguments are

never re-evaluated.

In other words, each argument is evaluated

exactly once.



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Applicative Order(rightmost innermsot)

Applicative order evaluation refers to an

evaluation strategy in which the arguments of

a function are evaluated from left to right in

a post-order traversal.

Unlike call-by-value, applicative order

evaluation reduces terms within a function

body as much as possible before the functionis applied.



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Call by value

Call-by-value or pass-by-value .

Disadvantage(s)??

Performance Degradation in case of large and

complex structure is passed by value.



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Call by Reference

Reference to the parameter is passed instead

of value.

This saves time

Improves memory usage

Synchronization required

Suits concurrency



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Mutable vs. Immutable

The object whose state can be changed afterits creation is said to be Mutable.

The objects whose state cannot be changed or

appears to be unchanged to the external pointof view, is said to be Immutable.

Immutable objects can be useful in multi-

threaded applications. Immutable objects are thread-safethan

mutable objects.



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Copy On Write (COW)

User -> System -> copy an object

System creates a new reference rather than

new object, pointing to same object

User -> modifier object , system -> creates a

new copy and sets reference to the new copy

Advantage?



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Copy On Write (COW)

Under COW -> users -> mutable version of theirobjects,

Although, users do not modify their objects, the

space-saving and speed advantages of immutableobjects are preserved.

string x = "Hello;

string y = x; // x and y use the same buffer

y += ", World!"; // now y uses a different buffer

// x still uses the same old buffer



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Call by Sharing

Also known as, Call by Object-Sharing

Its an object oriented concept

It works like call by reference with a little

difference i.e. assignments to functionarguments within the function are not visibleto the caller.

So if a variable is passed as a variable it is notpossible to simulate an assignment on thatvariable in the callers scope.



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It is also referred to as Call by-Value-Result

It is a special case of call-by-reference, whereinstead of directly working on the reference,

the function works on a copy of thereferenced object, and then assigns("restores") the copy to the referenced objectjust before control is returned to the caller.

Applicable in Multiprocessing context

Fail-Safe



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Example

int a;void unsafe(int x)

{ x= 2; a= 0; }

int main() {

a = 1; unsafe(a); printf(a); } when called by copy-restore? a = 2

When called by reference? a = 0



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Non Strict Evaluation

Here, arguments to a function are not

evaluated unless they are actually used in the

evaluation of the function body.



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Lazy Evaluation

It is an evaluation strategy which delays theevaluation of an expression until the value ofthis is actually required.

Performance Increases because unnecessarycalculations are avoided.

Debugging is difficult why?

As the order of operations becomesindeterminate, Exception Handling andDebugging becomes difficult.



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Normal Order(leftmost outermost)

Normal-orderevaluation is the evaluation

strategy where the outermost reducible

expressions is always reduced, applying

functions before evaluating functionarguments



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Call by-name

In this evaluation, the arguments to a functionare not evaluated before the function is called they are substituted directly into the

function body and then left to be evaluatedwhenever they appear in the function.

If an argument is not used in the functionbody, the argument is never evaluated; if it isused several times, it is re-evaluated eachtime it appears.



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Call by-need

This is a memoized version of call-by-name

where, if the function argument is

evaluated, that value is stored for subsequent

uses.



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Call by Macro-Expansion

Used in case of macros.

Same as call-by-name



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Assignment # 4

Define the triology, Static

Const

Readonly

You have to demonstrate this assignment througha working example. Student with bestexplanatory example will get the maximummarks. No hard copies needed, just demo

Submission Date: 12th January, 2012


Lambda Calculus and Evaluation Strategies

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