X-Git-Url: http://lambda.jimpryor.net/git/gitweb.cgi?p=lambda.git;a=blobdiff_plain;f=week4.mdwn;h=8714eae88f924c42f7ba6560530d3094be741f07;hp=8fe37ad2be182d92c8cc1298794ced2cc6a99b9d;hb=3be23d511f494d473da5aabb67375e25073f7e2c;hpb=c3998b2b5a85bd4b5a47c1b2518739fe9948807f diff --git a/week4.mdwn b/week4.mdwn index 8fe37ad2..8714eae8 100644 --- a/week4.mdwn +++ b/week4.mdwn @@ -217,7 +217,7 @@ and so on. #Typed lambda terms# -Given a set of types `T`, we define the set of typed lambda terms &Lamda;_T, +Given a set of types `T`, we define the set of typed lambda terms Λ_T, which is the smallest set such that * each type `t` has an infinite set of distinct variables, {x^t}_1, @@ -227,12 +227,12 @@ which is the smallest set such that σ, then the application `(M N)` has type τ. * If a variable `a` has type σ, and term `M` has type τ, - then the abstract `λ a M` has type `σ --> τ`. + then the abstract λ a M has type σ --> τ. The definitions of types and of typed terms should be highly familiar -to semanticists, except that instead of writing `σ --> τ`, -linguists (following Montague, who followed Church) write `<σ, -τ>`. We will use the arrow notation, since it is more iconic. +to semanticists, except that instead of writing σ --> τ, +linguists (following Montague, who followed Church) write <σ, +τ>. We will use the arrow notation, since it is more iconic. Some examples (assume that `x` has type `o`):