Lambda Calculus Practice Problems¶
Evaluate each of these expressions, that is, \(\beta\)-reduce each of the following expressions until you cannot \(\beta\)-reduce any more.
- \((λp.λq.pqp)(λx.λy.y)(λx.λy.x)\)
- \((λp.λq.ppq)(λx.λy.y)(λx.λy.x)\)
- \((λp.p(λx.λy.y)(λx.λy.x))(λx.λy.y)\)
- \((λp.λa.λb.pab)(λx.λy.y)(λf.(λx.fx))(λf.(λx.f(fx)))\)
- \((λc.c(λx.λy.y))(λx.λy.λf.fxy)(λf.λx.f(fx))(λf.λx.f(f(fx)))\)