Write You a Haskell Stephen Diehl

Well-typed programs cannot “go wrong”.
— Robin Milner
Evaluation
While the lambda calculus is exceedingly simple, there is a great deal of variety in ways to evaluate
and implement the reduction of lambda expressions. e different models for evaluation are evaluation
stratgies.
ere is a bifurcation between two points in the design space: strict and non-strict evaluation. An evaluation
strategy is strict if the arguments to a lambda expression are necessarily evaluated before a lambda
is reduced. A language in which the arguments are not necessarily evaluated before a lambda is reduced
is non-strict.
Alternatively expressed, diverging terms are represented up to equivalence by the bottom value, written
as ⊥. A function f is non-strict if:
f⊥ ≠ ⊥
Evaluation Models
ere are many different models, and various hybrids thereof. We will consider three dominant models:
• Call-by-value: arguments are evaluated before a function is entered
• Call-by-name: arguments are passed unevaluated
• Call-by-need: arguments are passed unevaluated but an expression is only evaluated once and
shared upon subsequent references
Given an expression fx the reduction in different evaluation models proceeds differently:
Call-by-value:
1. Evaluate x to v
2. Evaluate f to λy.e
3. Evaluate [y/v]e
Call-by-name:
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